Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacemen...Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.展开更多
A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the n...A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).展开更多
The Sun has solar rotation;nevertheless, many evidences have suggested that different latitude of the Sun rotates in different speed, which is now known as differential rotation. This work calculates the solar rotatio...The Sun has solar rotation;nevertheless, many evidences have suggested that different latitude of the Sun rotates in different speed, which is now known as differential rotation. This work calculates the solar rotation speeds near the equator and 30? in the northern hemisphere using Fixed-Point Arithmetic method. The calculated results show a greater speed at the equator than the speed at 30?, indicating that the speed decreases as the latitude becomes higher. .展开更多
Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three trans...Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three translational components,but less on rotational ones.As the precision of rotational sensing techniques has increased,many scholars have paid more attention to the seismic rotational motions.Because the rotational observations are not very popular before and now,approximately converting the translational components into rotational components is utilized in rotation analysis.Based on numerical six-component seismic data with the finite difference method,we compare three different conversion methods,the travelling-wave,frequency-domain and the difference method,to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.展开更多
The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engin...The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.展开更多
To ensure the safe performance of deep-sea mining vehicles(DSMVs),it is necessary to study the mechanical characteristics of the interaction between the seabed soil and the track plate.The rotation and digging motions...To ensure the safe performance of deep-sea mining vehicles(DSMVs),it is necessary to study the mechanical characteristics of the interaction between the seabed soil and the track plate.The rotation and digging motions of the track plate are important links in the contact between the driving mechanism of the DSMV and seabed soil.In this study,a numerical simulation is conducted using the coupled Eulerian–Lagrangian(CEL)large deformation numerical method to investigate the interaction between the track plate of the DSMV and the seabed soil under two working conditions:rotating condition and digging condition.First,a soil numerical model is established based on the elastoplastic mechanical characterization using the basic physical and mechanical properties of the seabed soil obtained by in situ sampling.Subsequently,the soil disturbance mechanism and the dynamic mechanical response of the track plate under rotating and digging conditions are obtained through the analysis of the sensitivity of the motion parameters,the grouser structure,the layered soil features and the soil heterogeneity.The results indicate that the above parameters remarkably influence the interaction between the DSMV and the seabed soil.Therefore,it is important to consider the rotating and digging motion of the DSMV in practical engineering to develop a detailed optimization design of the track plate.展开更多
In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental preci...In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.展开更多
A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pa...A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is computed by the proposed method. The result is compared to that obtained by finite element method so as to validate the correction of the method.展开更多
Using the relativistic Lagrangian expression,we develop a method to derive the equation of motion of the torsion balance in a non-inertial reference frame,which is used to analyze the gravitational experiment in measu...Using the relativistic Lagrangian expression,we develop a method to derive the equation of motion of the torsion balance in a non-inertial reference frame,which is used to analyze the gravitational experiment in measuring Newton's constant G with the angular acceleration method.Our calculation shows that the Earth's rotation couples with the vibration,which should be considered in the high-accuracy experiments of determining the gravitational constant G.展开更多
The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces o...The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions.A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method.The fundamental equations’system is solved by utilizing an implicit finite-difference method.This current method is a second-order accurate in time and space;it is also unconditionally stable.To illustrate the present model’s efficiency,we consider a suitable material and acquire the numerical solution of temperature,displacement components,and the components of stresses with time t and through the radial of an infinite cylinder.The results indicate that the effect of coupled thermoelasticity,magnetic field,and rotation on the temperature,stresses,and displacement is quite pronounced.In order to illustrate and verify the analytical developments,the numerical solution of partial differential equations,stress components,displacement components and temperature is carried out and computer simulated results are presented graphically.This study is helpful in the development of piezoelectric devices.展开更多
In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradi...In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.展开更多
It is widely used for the rotational parallel mechanism in the field of spatial orientation. While owing to the existence of coupling, the forward kinematic solution and the control of the general rotational parallel ...It is widely used for the rotational parallel mechanism in the field of spatial orientation. While owing to the existence of coupling, the forward kinematic solution and the control of the general rotational parallel mechanism are especially difficult. If decoupling can be realized, the kinematic analysis of the mechanism will be very simple. Presently, the research of the parallel mechanism is focused on the inverse solution and structure optimization, and there is a lack of rotation decoupled parallel mechanisms (DPMs). So this paper proposes a family of 2 degree of freedom (DOF) rotational DPMs based on the four-bar linkage mechanism, and performs a characteristic analysis. This family of DPMs is composed of a moving platform, a fixed base and three limbs. Taking U_RRU SPU DPM as an example, the motion feature of this DPM is analyzed with the constraint screw method, and its mobility is calculated by using the Modified Kutzbach-Grtibler criterion. The inverse and forward displacement problems of the proposed parallel mechanism are solved. The decoupled feature of the proposed parallel mechanism is validated by the deduction of the expression of the Jaeobian matrix. Three kinds of singularity conditions of this DPM are discussed, and the atlases of the output parameter concerning different geometric parameters are plotted with the theory of the physical model of the solution space. The proposition and characteristic analysis of the novel rotational DPMs in this paper should be useful for further research and application of the parallel mechanisms.展开更多
This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of...This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.展开更多
The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, fl...The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.展开更多
We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence...We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection.This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations,but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange’s equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method(FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions.展开更多
The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing...The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.展开更多
The generalized differential quadrature method (GDQM) is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditi...The generalized differential quadrature method (GDQM) is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton's concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.展开更多
The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deforma...The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.展开更多
Quasiclassical trajectory (QCT) calculations are first carried out to study the stereodynamics of the S (3p) + H2 → SH + H reaction based on the ab initio 13Atr potential energy surface (PES) (Lii etal. 2012...Quasiclassical trajectory (QCT) calculations are first carried out to study the stereodynamics of the S (3p) + H2 → SH + H reaction based on the ab initio 13Atr potential energy surface (PES) (Lii etal. 2012 J. Chem. Phys. 136 094308). The QCT-calculated reaction probabilities and cross sections for the S + H2 (v = 0, j = 0) reaction are in good agreement with the previous quantum mechanics (QM) results. The vector properties including the alignment, orientation, and polarization- dependent differential cross sections (PDDCSs) of the product SH are presented at a collision energy of 1.8 eV. The effects of the vibrational and rotational excitations of reagent on the stereodynamics are also investigated and discussed in the present work. The calculated QCT results indicate that the vibrational and rotational excitations of reagent play an important role in determining the stereodynamic properties of the title reaction.展开更多
The particle path tracking method is proposed and used in two-dimensional(2D) and three-dimensional(3D) numerical simulations of continuously rotating detonation engines(CRDEs). This method is used to analyze th...The particle path tracking method is proposed and used in two-dimensional(2D) and three-dimensional(3D) numerical simulations of continuously rotating detonation engines(CRDEs). This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.展开更多
基金supported by the China Postdoctoral Science Foundation Funded Project (20080430038) the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (05004999200602)
文摘Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.
基金financially supported by the Fundamental Research Funds for the Central Universities(Grant Nos.2018B56414 and2019B12014)the National Natural Science Foundation of China(Grant No.51609077)
文摘A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).
文摘The Sun has solar rotation;nevertheless, many evidences have suggested that different latitude of the Sun rotates in different speed, which is now known as differential rotation. This work calculates the solar rotation speeds near the equator and 30? in the northern hemisphere using Fixed-Point Arithmetic method. The calculated results show a greater speed at the equator than the speed at 30?, indicating that the speed decreases as the latitude becomes higher. .
基金This research is supported by the National Natural Science Foundation of China(grant No.U1839208).
文摘Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three translational components,but less on rotational ones.As the precision of rotational sensing techniques has increased,many scholars have paid more attention to the seismic rotational motions.Because the rotational observations are not very popular before and now,approximately converting the translational components into rotational components is utilized in rotation analysis.Based on numerical six-component seismic data with the finite difference method,we compare three different conversion methods,the travelling-wave,frequency-domain and the difference method,to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.
基金support of the National Natural Science Foundation of China(12072011).
文摘The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.
基金supported by the Natural Science Foundation of Hainan Province(Grant No.520LH015)the Fundamental Research Funds for the Central Universities and the Major Projects of Strategic Emerging Industries in Shanghai(Grant No.BH3230001).
文摘To ensure the safe performance of deep-sea mining vehicles(DSMVs),it is necessary to study the mechanical characteristics of the interaction between the seabed soil and the track plate.The rotation and digging motions of the track plate are important links in the contact between the driving mechanism of the DSMV and seabed soil.In this study,a numerical simulation is conducted using the coupled Eulerian–Lagrangian(CEL)large deformation numerical method to investigate the interaction between the track plate of the DSMV and the seabed soil under two working conditions:rotating condition and digging condition.First,a soil numerical model is established based on the elastoplastic mechanical characterization using the basic physical and mechanical properties of the seabed soil obtained by in situ sampling.Subsequently,the soil disturbance mechanism and the dynamic mechanical response of the track plate under rotating and digging conditions are obtained through the analysis of the sensitivity of the motion parameters,the grouser structure,the layered soil features and the soil heterogeneity.The results indicate that the above parameters remarkably influence the interaction between the DSMV and the seabed soil.Therefore,it is important to consider the rotating and digging motion of the DSMV in practical engineering to develop a detailed optimization design of the track plate.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160 and 11805074)the Postdoctoral Science Foundation of China(Grant Nos.2017M620308 and 2018T110750).
文摘In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.
文摘A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is computed by the proposed method. The result is compared to that obtained by finite element method so as to validate the correction of the method.
基金Supported by the National Natural Science Foundation of China(11175160)the Fundamental Research Funds for the Central Universities(2010079045)the Natural Science Fund of Hubei Province(2010CDB04102).
文摘Using the relativistic Lagrangian expression,we develop a method to derive the equation of motion of the torsion balance in a non-inertial reference frame,which is used to analyze the gravitational experiment in measuring Newton's constant G with the angular acceleration method.Our calculation shows that the Earth's rotation couples with the vibration,which should be considered in the high-accuracy experiments of determining the gravitational constant G.
基金Taif University Researchers Supporting Project Number(TURSP-2020/164),Taif University,Taif,Saudi Arabia.
文摘The present article deals with the investigation thermal stress of a magnetothermoelastic cylinder subjected to rotation,open or closed circuit,thermal and mechanical boundary conditions.The outer and inner surfaces of the cylinder are subjected to both mechanical and thermal boundary conditions.A The transient coupled thermoelasticity in an infinite cylinder with its base abruptly exposed to a heat flux of a decaying exponential function of time is devised solve by the finite-difference method.The fundamental equations’system is solved by utilizing an implicit finite-difference method.This current method is a second-order accurate in time and space;it is also unconditionally stable.To illustrate the present model’s efficiency,we consider a suitable material and acquire the numerical solution of temperature,displacement components,and the components of stresses with time t and through the radial of an infinite cylinder.The results indicate that the effect of coupled thermoelasticity,magnetic field,and rotation on the temperature,stresses,and displacement is quite pronounced.In order to illustrate and verify the analytical developments,the numerical solution of partial differential equations,stress components,displacement components and temperature is carried out and computer simulated results are presented graphically.This study is helpful in the development of piezoelectric devices.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91636216,11974382,and 11474316)the Chinese Academy of Sciences Strategic Priority Research Program(Grant No.XDB21020200)+1 种基金by the YIPA Programthe support of NSERC,SHARCnet,ACEnet of Canada。
文摘In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.
基金supported by National Natural Science Foundation of China (Grant No. 50875227)
文摘It is widely used for the rotational parallel mechanism in the field of spatial orientation. While owing to the existence of coupling, the forward kinematic solution and the control of the general rotational parallel mechanism are especially difficult. If decoupling can be realized, the kinematic analysis of the mechanism will be very simple. Presently, the research of the parallel mechanism is focused on the inverse solution and structure optimization, and there is a lack of rotation decoupled parallel mechanisms (DPMs). So this paper proposes a family of 2 degree of freedom (DOF) rotational DPMs based on the four-bar linkage mechanism, and performs a characteristic analysis. This family of DPMs is composed of a moving platform, a fixed base and three limbs. Taking U_RRU SPU DPM as an example, the motion feature of this DPM is analyzed with the constraint screw method, and its mobility is calculated by using the Modified Kutzbach-Grtibler criterion. The inverse and forward displacement problems of the proposed parallel mechanism are solved. The decoupled feature of the proposed parallel mechanism is validated by the deduction of the expression of the Jaeobian matrix. Three kinds of singularity conditions of this DPM are discussed, and the atlases of the output parameter concerning different geometric parameters are plotted with the theory of the physical model of the solution space. The proposition and characteristic analysis of the novel rotational DPMs in this paper should be useful for further research and application of the parallel mechanisms.
基金funded by the Deanship of Scientific Research,Princess Nourah bint Abdulrahman University,through the Program of Research Project Funding After Publication,grant No(44-PRFA-P-107).
文摘This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.
基金Project supported by the National Natural Science Foundation of China(Nos.11672007,11402028,11322214,and 11290152)the Beijing Natural Science Foundation(No.3172003)the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education,Northeastern University(No.VCAME201601)
文摘The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.
基金the support from the National Natural Science Foundation of China (Grants 11272155, 11132007, and 11502113)the Fundamental Research Funds for Central Universities (Grant 30917011103)the China Scholarship Council for one year study at the University of Cincinnati
文摘We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection.This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations,but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange’s equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method(FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions.
文摘The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.
文摘The generalized differential quadrature method (GDQM) is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton's concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.
基金supported by the Joint Fund of the National Natural Science Foundation of Chinathe China Academy of Engineering Physics(No.11176035)+1 种基金the National Natural Science Foundation of China(No.11072276)the National Basic Research Program of China(No.2011CB612211)
文摘The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.
基金supported by the National Natural Science Foundation of China(Grant Nos.11074103,10974078,and 11174117)the Discipline Construction Fund of Ludong University,China
文摘Quasiclassical trajectory (QCT) calculations are first carried out to study the stereodynamics of the S (3p) + H2 → SH + H reaction based on the ab initio 13Atr potential energy surface (PES) (Lii etal. 2012 J. Chem. Phys. 136 094308). The QCT-calculated reaction probabilities and cross sections for the S + H2 (v = 0, j = 0) reaction are in good agreement with the previous quantum mechanics (QM) results. The vector properties including the alignment, orientation, and polarization- dependent differential cross sections (PDDCSs) of the product SH are presented at a collision energy of 1.8 eV. The effects of the vibrational and rotational excitations of reagent on the stereodynamics are also investigated and discussed in the present work. The calculated QCT results indicate that the vibrational and rotational excitations of reagent play an important role in determining the stereodynamic properties of the title reaction.
文摘The particle path tracking method is proposed and used in two-dimensional(2D) and three-dimensional(3D) numerical simulations of continuously rotating detonation engines(CRDEs). This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.