Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived ...Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.展开更多
Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic...Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.展开更多
The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass ...The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.展开更多
The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed meth...The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.展开更多
The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete p...The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.展开更多
Within the seasonal-annual timeseale,there exists an angular momentum conservative exchange relationship be- tween the solid earth and the atmosphere,and their angular momentum exchange not only can cause variations i...Within the seasonal-annual timeseale,there exists an angular momentum conservative exchange relationship be- tween the solid earth and the atmosphere,and their angular momentum exchange not only can cause variations in length-of-day(LOD)but also can express anomalies in atmospheric general circulation.Therefore,their angular mo- mentum exchange mechanism should be introduced into the general circulation model. Considering the angular momentum anomalous exchange caused by the air-earth interface friction effect,a whole-layer atmospheric motion equation is derived in this paper including the earth spin anomalous friction force parameterized by using the change in the earth rotation rate.Through analysing the equation,it shows that the magni- tude of the earth spin anomalous friction force is the same as that of Coriolis force on seasonal-annual timescale.展开更多
The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational f...The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body os- cillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the up- stroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small neg- ative horizontal force, whilst in the upstroke, the body an- gle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizon- tal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-mass- specific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.展开更多
In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of th...In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.展开更多
The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equa...The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.展开更多
This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.
This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and...This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method.展开更多
In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia. This equation is the generalization of e...In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia. This equation is the generalization of equations of motion for the corresponding thick elastic plate, and it can be degenerated into several types of equations for various special cases.展开更多
A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C. A. Murray[1]
With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical s...With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed展开更多
In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the...In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.展开更多
On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the thi...On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.展开更多
This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in ves...This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in vestigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D Alambert-Le range, Hamilton-Ostrogradski and Gauss.展开更多
We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the firs...We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.展开更多
A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This mode...A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This model includes much more physiological factors. It couples the interaction of blood flow with mechanical factors such as the displacement, deformation, strain and stress etc. of the curved blood vessel. It is of great importance for investigating the circulation rules of the cardiovascular system and the nonlinear pulse wave propagation in curved blood vessels.展开更多
If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restric...If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.展开更多
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA17010105)National Key Research and Development Program(Grant No.2018YFC1507104)+2 种基金Science and Technology Development Plan Project of Jilin Province(20180201035SF)Flexible Talents Introducing Project of Xinjiang(2019)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(EarthLab)。
文摘Research on vertical motion in mesoscale systems is an extraordinarily challenging effort.Allowing for fewer assumptions,a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system(nonhydrostatic equilibrium)and the isobaric coordinate system(hydrostatic equilibrium),respectively.The terms on the right-hand side of the equations,which comprise the Q vector,are composed of three factors:dynamic,thermodynamic,and mass.A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation(Qz)and the diagnostic variable in the generalized Omega equation(Qp)using high-resolution model data.The results show that the horizontal distribution of the Qz-vector divergence at 5.5 km is roughly similar to the distribution of the Qp-vector divergence at 500 hPa,and that both relate well to the composite radar reflectivity,vertical motion,and hourly accumulated precipitation.The Qz-vector divergence is more effective in indicating weak precipitation.In vertical cross sections,regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors.The temporal evolutions of vertically integrated Qz-vector divergence and Qp-vector divergence are generally similar.Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.
基金Project supported by the National Natural Science Foundation of China (Nos.40175014, 90411006)the Science Foundation of Shanghai Municipal Commission of Science and Technology(No.02DJ14032)
文摘Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.
基金the Pre-Research Fund during the“13th Five-Year Plan” (No. 41417060101)。
文摘The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.
文摘The paper addresses the thermophoretic motion(TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries(KdV) equation. The generalized uni?ed method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and threesoliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.
文摘The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.
基金This work is supported by the National Natural Science Foundation of China(No.493752477)the Doctorial Program Foundation of the Institution of Higher Education.
文摘Within the seasonal-annual timeseale,there exists an angular momentum conservative exchange relationship be- tween the solid earth and the atmosphere,and their angular momentum exchange not only can cause variations in length-of-day(LOD)but also can express anomalies in atmospheric general circulation.Therefore,their angular mo- mentum exchange mechanism should be introduced into the general circulation model. Considering the angular momentum anomalous exchange caused by the air-earth interface friction effect,a whole-layer atmospheric motion equation is derived in this paper including the earth spin anomalous friction force parameterized by using the change in the earth rotation rate.Through analysing the equation,it shows that the magni- tude of the earth spin anomalous friction force is the same as that of Coriolis force on seasonal-annual timescale.
基金supported by the National Natural Science Foundation of China(11232002)the Ph.D.Student Foundation of Chinese Ministry of Education(30400002011105001)
文摘The forward flight of a model butterfly was stud- ied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body os- cillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the up- stroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small neg- ative horizontal force, whilst in the upstroke, the body an- gle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizon- tal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-mass- specific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.
文摘In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.
文摘The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.
文摘This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.
文摘This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method.
文摘In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia. This equation is the generalization of equations of motion for the corresponding thick elastic plate, and it can be degenerated into several types of equations for various special cases.
文摘A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C. A. Murray[1]
文摘With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed
基金Project supported by the Science and Technology Program of Xi’an City,China(Grant No.CXY1352WL34)
文摘In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.
基金Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006).
文摘On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.
文摘This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in vestigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D Alambert-Le range, Hamilton-Ostrogradski and Gauss.
文摘We applied the method of Thermomechanical Dynamics (TMD) to a low-temperature Stirling engine, and the dissipative equation of motion and time-evolving physical quantities are self-consistently calculated for the first time in this field. The thermomechanical states of the heat engine are in Nonequilibrium Irreversible States (NISs), and time-dependent thermodynamic work W(t), internal energy E(t), energy dissipation or entropy Q<sub>d</sub>(t), and temperature T(t), are precisely studied and computed in TMD. We also introduced the new formalism, Q(t)-picture of thermodynamic heat-energy flows, for consistent analyses of NISs. Thermal flows in a long-time uniform heat flow and in a short-time heat flow are numerically studied as examples. In addition to the analysis of time-dependent physical quantities, the TMD analysis suggests that the concept of force and acceleration in Newtonian mechanics should be modified. The acceleration is defined as a continuously differentiable function of Class C<sup>2</sup> in Newtonian mechanics, but the thermomechanical dynamics demands piecewise continuity for acceleration and thermal force, required from physical reasons caused by frictional variations and thermal fluctuations. The acceleration has no direct physical meaning associated with force in TMD. The physical implications are fundamental for the concept of the macroscopic phenomena in NISs composed of systems in thermal and mechanical motion.
基金Project supported by the National Natural Science Foundation of China(No.19872009)the Foundation of University Key Teachers by the Ministry of Education(No.GG-831-10005-1497)
文摘A geometric model of curved blood vessels is established based on some reasonable hypotheses; the nonlinear motion mechanics model of the curved blood vessel is established according to basic mechanics laws. This model includes much more physiological factors. It couples the interaction of blood flow with mechanical factors such as the displacement, deformation, strain and stress etc. of the curved blood vessel. It is of great importance for investigating the circulation rules of the cardiovascular system and the nonlinear pulse wave propagation in curved blood vessels.
基金National Natural Science Foundation of China (50178065), 973 Program (2002CB412706), National Social Com-monweal Research Foundation (2002DIB30076) and Joint Seismological Science Foundation (101066).
文摘If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.