The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the ...The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.展开更多
The relay propagation of Gaussian-Schell-model in turbulent atmosphere along a slant path is studied in this paper. Based on the extended Huygens-Fresnel principle and a quadratic approximation, an analytical formula ...The relay propagation of Gaussian-Schell-model in turbulent atmosphere along a slant path is studied in this paper. Based on the extended Huygens-Fresnel principle and a quadratic approximation, an analytical formula of average intensity for Gaussian-Schell-model beams in turbulent atmosphere along a slant path is derived, and some special cases are discussed. From the study and the comparison with the direct propagation, we can see that the relay propagation has an advantage over the direct propagation. When the altitude of the target is low, the peak intensity of relay propagation is much larger than that of direct propagation. However, because of the limitation of the relay system aperture for relay propagation and the variation of coherence length for direct propagation, the difference in peak intensity between the two propagations decreases with the increase of the target altitude.展开更多
Here a Gaussian Shell Model Array (GSMA) beam is used to investigate the propagation characteristics in the jet engine exhaust region. It has great significance to improve various optical systems for wide application ...Here a Gaussian Shell Model Array (GSMA) beam is used to investigate the propagation characteristics in the jet engine exhaust region. It has great significance to improve various optical systems for wide application in trapping cold atoms, creating gratings, and atmospheric optical communication. We calculate analytical formulas for the spectral density (SD) and the propagation factors M<sub>x</sub>2</sup> and M<sub>y</sub>2</sup> of a GSMA beam. The influence of inner scale of turbulence in the jet engine exhaust region on its power spectrum has been also analyzed. According to these results, the influence of turbulence in a jet engine exhaust on a GSMA beam has been reduced by changing the parameters of light source and turbulence. For example, it is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence to increase the source coherence length, the root-mean-squared (rms) beam width, the wavelength or reduce the outer scale of turbulence.展开更多
Traditional methods focus on the ultimate bending moment of glulam beams and the fracture failure of materials with defects,which usually depends on empirical parameters.There is no systematic theoretical method to pr...Traditional methods focus on the ultimate bending moment of glulam beams and the fracture failure of materials with defects,which usually depends on empirical parameters.There is no systematic theoretical method to predict the stiffness and shear distribution of glulam beams in elastic-plastic stage,and consequently,the failure of such glulam beams cannot be predicted effectively.To address these issues,an analytical method considering material nonlinearity was proposed for glulam beams,and the calculating equations of deflection and shear stress distribution for different failure modes were established.The proposed method was verified by experiments and numerical models under the corresponding conditions.Results showed that the theoretical calculations were in good agreement with experimental and numerical results,indicating that the equations proposed in this paper were reliable and accurate for such glulam beams with wood material in the elastic-plastic stage ignoring the influence of mechanic properties in radial and tangential directions of wood.Furthermore,the experimental results reported by the previous studies indicated that the method was applicable and could be used as a theoretical reference for predicting the failure of glulam beams.展开更多
The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft ro...The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft robotics,flexible electronics,and biomedicine.Theoretical investigations on large deformations of HMS structures are significant foundations of their applications.This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams.A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact(GE)beam model.The singularity-free governing equations for the three-dimensional(3D)large deformations of an HMS beam are first derived,and then solved with the Galerkin discretization method and the trustregion-dogleg iterative algorithm.The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones.The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples.It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field.The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.展开更多
We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger ...We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.展开更多
We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law ...We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.展开更多
The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigate...The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.展开更多
The scintillation index(SI) of a Gaussian–Schell model(GSM) beam in a moderate-to-strong anisotropic nonKolmogorov turbulent atmosphere is developed based on the extended Rytov theory. The on-axis SI in a marine atmo...The scintillation index(SI) of a Gaussian–Schell model(GSM) beam in a moderate-to-strong anisotropic nonKolmogorov turbulent atmosphere is developed based on the extended Rytov theory. The on-axis SI in a marine atmosphere is higher than that in a terrestrial atmosphere, but the off-axis SI exhibits the opposite trend. The on-axis SI first increases and then begins to decrease and saturate as the turbulence strength increases. Turbulence inner and outer scales have different effects on the on-axis SI in different turbulent fluctuation regions. The anisotropy characteristic of atmospheric turbulence leads to the decline in the on-axis SI, and the rise in the off-axis SI. The on-axis SI can be lowered by increasing the anisotropy of turbulence, wavelength, and source partial coherence before entering the saturation attenuation region. The developed model may be useful for evaluating ship-to-ship/shore free-space optical communication system performance.展开更多
Ionic Polymer-Metal Composite (IPMC) can work as an actuator by applying a few voltages.A thick IPMC actuator,whereNafion-117 membrane was synthesized with polypyrrole/alumina composite filler,was analyzed to verify t...Ionic Polymer-Metal Composite (IPMC) can work as an actuator by applying a few voltages.A thick IPMC actuator,whereNafion-117 membrane was synthesized with polypyrrole/alumina composite filler,was analyzed to verify the equivalent beamand equivalent bimorph beam models.The blocking force and tip displacement of the IPMC actuator were measured with a DCpower supply and Young’s modulus of the IPMC strip was measured by bending and tensile tests respectively.The calculatedmaximum tip displacement and the Young’s modulus by the equivalent beam model were almost identical to the correspondingmeasured data.Finite element analysis with thermal analogy technique was utilized in the equivalent bimorph beam model tonumerically reproduce the force-displacement relationship of the IPMC actuator.The results by the equivalent bimorph beammodel agreed well with the force-displacement relationship acquired by the measured data.It is confirmed that the equivalentbeam and equivalent bimorph beam models are practically and effectively suitable for predicting the tip displacement,blockingforce and Young’s modulus of IPMC actuators with different thickness and different composite of ionic polymer membrane.展开更多
This paper deals with the free vibration analysis of circular alumina(Al2O3)nanobeams in the presence of surface and thermal effects resting on a Pasternak foundation. The system of motion equations is derived using H...This paper deals with the free vibration analysis of circular alumina(Al2O3)nanobeams in the presence of surface and thermal effects resting on a Pasternak foundation. The system of motion equations is derived using Hamilton's principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equations which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.展开更多
Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of th...Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.展开更多
A beam approximation method for dynamic analysis of launch vehicles modelled as stiffened cylindrical shells is proposed.Firstly,an initial beam model of the stiffened cylindrical shell is established based on the cro...A beam approximation method for dynamic analysis of launch vehicles modelled as stiffened cylindrical shells is proposed.Firstly,an initial beam model of the stiffened cylindrical shell is established based on the cross-sectional area equivalence principle that represents the shell skin and its longitudinal ribs as a beam with annular cross-section,and the circumferential ribs as lumped masses at the nodes of the beam elements.Then,a fine finite element model(FE model)of the stiffened cylindrical shell is constructed and a modal analysis is carried out.Finally,the initial beam model is improved through model updating against the natural frequencies and mode shapes of the fine FE model of the shell.To facilitate the comparison between the mode shapes of the fine FE model of the stiffened shell and the equivalent beam model,a weighted nodal displacement coupling relationship is introduced.To prevent the design parameters used in model updating from converging to incorrect values,a pre-model updating procedure is added before the proper model updating.The results of two examples demonstrate that the beam approximation method presented in this paper can build equivalent beam models of stiffened cylindrical shells which can reflect the global longitudinal,lateral and torsional vibration characteristics very well in terms of the natural frequencies.展开更多
An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span.The clamped face sheets are simplifie...An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span.The clamped face sheets are simplified as a single-degree-of-freedom(SDOF)system,and the core is idealized using the rigid-perfectly-plastic-locking(RPPL)model.Reflection of incident shock wave is considered by incorporating the bending/stretching resistance of the front face sheet and compaction of the core.The model is validated with existing analytical predictions and FE simulation results,with good agreement achieved.Compared with existing analytical models,the proposed model exhibits superiority in two aspects:the deformation resistance of front face sheet during shock wave reflection is taken into account;the effect of pulse shape is considered.The practical application range of the proposed model is therefore wider.展开更多
The paper investigated the equivalent continuum modeling of beam-like repetitive truss structures considering the flexibility of joints,which models the contact between the truss member and joint by spring-damper with...The paper investigated the equivalent continuum modeling of beam-like repetitive truss structures considering the flexibility of joints,which models the contact between the truss member and joint by spring-damper with six directional stiffnesses and dampings.Firstly,a two-node hybrid joint-beam element was derived for modeling the truss member with flexible end joints,and a condensed model for the repeating element with flexible joints was obtained.Then,the energy equivalence method was adopted to equivalently model the truss structure with flexible joints and material damping as a spatial viscoelastic anisotropic beam model.Afterwards,the equations of motion for the equivalent beam model were derived and solved analytically in the frequency domain.In the numerical studies,the correctness of the presented method was verified by comparisons of the natural frequencies and frequency responses evaluated by the equivalent beam model with the results of the finite element method model.展开更多
Based on the (Ⅰ) of the present work, the behavior of shear beam model at crack initiation stage and at instable propagation stage was studied. The prime results include: 1) discriminant equation which clarifies the ...Based on the (Ⅰ) of the present work, the behavior of shear beam model at crack initiation stage and at instable propagation stage was studied. The prime results include: 1) discriminant equation which clarifies the mode of instability, snap_back or snap_through, was established; 2) analytical solution was given out for the double shear beam and the load_displacement diagram for monotonic loading was presented for a full process; and 3) the problem of the energy release induced by instability was discussed.展开更多
Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidi...Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidification, analyze the interaction between shell and molten steel, and compare the temperature distribution under different technological conditions. The results indicate that high superheating degree can lengthen the liquid-core depth and make the crack and breakout possible, so suitable superheating should be controlled within 35 ℃ according to the simulation results. Casting speed which is one of the most important technological parameters of improving production rate, should be controlled between 0.85 m/min and 1.05 m/min and the caster has great potential in the improvement of blank quality.展开更多
As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crac...As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton's principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.展开更多
The analytical expression of off-axis hollow Gaussian–Schell model vortex beam(HGSMVB)generated by anisotropic Gaussian–Schell model source is first introduced.The evolution properties of off-axis HGSMVB propagating...The analytical expression of off-axis hollow Gaussian–Schell model vortex beam(HGSMVB)generated by anisotropic Gaussian–Schell model source is first introduced.The evolution properties of off-axis HGSMVB propagating in turbulent atmosphere are analyzed.The results show that the off-axis HGSMVB with smaller coherence length or propagating in stronger turbulent atmosphere will evolve from dark hollow beam into Gaussian-like beam with a larger beam spot faster.The beams with different values of integer order N or the position for hollow and vortex factor R will have almost the same Gaussian-like spot distribution at the longer propagation distance.展开更多
基金National Natural Science Foundation of China under Grant No.51879191。
文摘The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.
文摘The relay propagation of Gaussian-Schell-model in turbulent atmosphere along a slant path is studied in this paper. Based on the extended Huygens-Fresnel principle and a quadratic approximation, an analytical formula of average intensity for Gaussian-Schell-model beams in turbulent atmosphere along a slant path is derived, and some special cases are discussed. From the study and the comparison with the direct propagation, we can see that the relay propagation has an advantage over the direct propagation. When the altitude of the target is low, the peak intensity of relay propagation is much larger than that of direct propagation. However, because of the limitation of the relay system aperture for relay propagation and the variation of coherence length for direct propagation, the difference in peak intensity between the two propagations decreases with the increase of the target altitude.
文摘Here a Gaussian Shell Model Array (GSMA) beam is used to investigate the propagation characteristics in the jet engine exhaust region. It has great significance to improve various optical systems for wide application in trapping cold atoms, creating gratings, and atmospheric optical communication. We calculate analytical formulas for the spectral density (SD) and the propagation factors M<sub>x</sub>2</sup> and M<sub>y</sub>2</sup> of a GSMA beam. The influence of inner scale of turbulence in the jet engine exhaust region on its power spectrum has been also analyzed. According to these results, the influence of turbulence in a jet engine exhaust on a GSMA beam has been reduced by changing the parameters of light source and turbulence. For example, it is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence to increase the source coherence length, the root-mean-squared (rms) beam width, the wavelength or reduce the outer scale of turbulence.
基金support from High-Level Natural ScienceFoundation of Hainan Province of China (Grant No. 2019RC055)National Natural Science Foundation ofChina (Grant No. 51808176) and the Project Funded by the National First-Class Disciplines (PNFD).
文摘Traditional methods focus on the ultimate bending moment of glulam beams and the fracture failure of materials with defects,which usually depends on empirical parameters.There is no systematic theoretical method to predict the stiffness and shear distribution of glulam beams in elastic-plastic stage,and consequently,the failure of such glulam beams cannot be predicted effectively.To address these issues,an analytical method considering material nonlinearity was proposed for glulam beams,and the calculating equations of deflection and shear stress distribution for different failure modes were established.The proposed method was verified by experiments and numerical models under the corresponding conditions.Results showed that the theoretical calculations were in good agreement with experimental and numerical results,indicating that the equations proposed in this paper were reliable and accurate for such glulam beams with wood material in the elastic-plastic stage ignoring the influence of mechanic properties in radial and tangential directions of wood.Furthermore,the experimental results reported by the previous studies indicated that the method was applicable and could be used as a theoretical reference for predicting the failure of glulam beams.
基金Project supported by the National Key Research and Development Program of China(No.2018YFA0703200)the National Natural Science Foundation of China(Nos.52205594 and51820105008)+1 种基金the China National Postdoctoral Program for Innovative Talents(No.BX20220118)the China Postdoctoral Science Foundation(No.2021M701306)。
文摘The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft robotics,flexible electronics,and biomedicine.Theoretical investigations on large deformations of HMS structures are significant foundations of their applications.This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams.A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact(GE)beam model.The singularity-free governing equations for the three-dimensional(3D)large deformations of an HMS beam are first derived,and then solved with the Galerkin discretization method and the trustregion-dogleg iterative algorithm.The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones.The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples.It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field.The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12274230,91950102,and 11834004)the Funding of Nanjing University of Science and Technology (Grant No.TSXK2022D005)the Postgraduate Research&Practice Innovation Program of Jiangsu Province of China (Grant No.KYCX230443)。
文摘We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Natural Sciences and Engineering Research Council of Canada(No.NSERC RGPIN-2023-03227)。
文摘We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.
文摘The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.
基金Project supported by the Open Research Fund of State Key Laboratory of Pulsed Power Laser Technology(Grant No.SKL2016KF05)the Key Industrial Innovation Chain Project in Industrial Domain,China(Grant No.2017ZDCXL-GY-06-02)+1 种基金the Huawei Innovation Research Program,China(Grant No.HO2017050001AG)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(Grant No.61621005)
文摘The scintillation index(SI) of a Gaussian–Schell model(GSM) beam in a moderate-to-strong anisotropic nonKolmogorov turbulent atmosphere is developed based on the extended Rytov theory. The on-axis SI in a marine atmosphere is higher than that in a terrestrial atmosphere, but the off-axis SI exhibits the opposite trend. The on-axis SI first increases and then begins to decrease and saturate as the turbulence strength increases. Turbulence inner and outer scales have different effects on the on-axis SI in different turbulent fluctuation regions. The anisotropy characteristic of atmospheric turbulence leads to the decline in the on-axis SI, and the rise in the off-axis SI. The on-axis SI can be lowered by increasing the anisotropy of turbulence, wavelength, and source partial coherence before entering the saturation attenuation region. The developed model may be useful for evaluating ship-to-ship/shore free-space optical communication system performance.
基金supported by the Defense Acquisition Program Administration (DAPA)the Agency for Defense Development (ADD) in Korea+1 种基金the Korea Research Foundation (KRF-2006-005-J03301)the National Research Foundation (Grant number: 2009-0083068).
文摘Ionic Polymer-Metal Composite (IPMC) can work as an actuator by applying a few voltages.A thick IPMC actuator,whereNafion-117 membrane was synthesized with polypyrrole/alumina composite filler,was analyzed to verify the equivalent beamand equivalent bimorph beam models.The blocking force and tip displacement of the IPMC actuator were measured with a DCpower supply and Young’s modulus of the IPMC strip was measured by bending and tensile tests respectively.The calculatedmaximum tip displacement and the Young’s modulus by the equivalent beam model were almost identical to the correspondingmeasured data.Finite element analysis with thermal analogy technique was utilized in the equivalent bimorph beam model tonumerically reproduce the force-displacement relationship of the IPMC actuator.The results by the equivalent bimorph beammodel agreed well with the force-displacement relationship acquired by the measured data.It is confirmed that the equivalentbeam and equivalent bimorph beam models are practically and effectively suitable for predicting the tip displacement,blockingforce and Young’s modulus of IPMC actuators with different thickness and different composite of ionic polymer membrane.
文摘This paper deals with the free vibration analysis of circular alumina(Al2O3)nanobeams in the presence of surface and thermal effects resting on a Pasternak foundation. The system of motion equations is derived using Hamilton's principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equations which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.
文摘Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.
基金the National Natural Science Foundation of China(11672060,11672052).
文摘A beam approximation method for dynamic analysis of launch vehicles modelled as stiffened cylindrical shells is proposed.Firstly,an initial beam model of the stiffened cylindrical shell is established based on the cross-sectional area equivalence principle that represents the shell skin and its longitudinal ribs as a beam with annular cross-section,and the circumferential ribs as lumped masses at the nodes of the beam elements.Then,a fine finite element model(FE model)of the stiffened cylindrical shell is constructed and a modal analysis is carried out.Finally,the initial beam model is improved through model updating against the natural frequencies and mode shapes of the fine FE model of the shell.To facilitate the comparison between the mode shapes of the fine FE model of the stiffened shell and the equivalent beam model,a weighted nodal displacement coupling relationship is introduced.To prevent the design parameters used in model updating from converging to incorrect values,a pre-model updating procedure is added before the proper model updating.The results of two examples demonstrate that the beam approximation method presented in this paper can build equivalent beam models of stiffened cylindrical shells which can reflect the global longitudinal,lateral and torsional vibration characteristics very well in terms of the natural frequencies.
基金supported by the National Natural Science Foundation of China (Grants 11972185, 11802221, 11472208, and 11472209)the China Postdoctoral Science Foundation (Grant 2016M600782)+2 种基金the Postdoctoral Scientific Research Project of Shaanxi Province (Grant 2016BSHYDZZ18)the Zhejiang Provincial Natural Science Foundation of China (Grant LGG18A020001)the Natural Science Basic Research Plan in Shaanxi Province of China (Grant 2018JQ1078)
文摘An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span.The clamped face sheets are simplified as a single-degree-of-freedom(SDOF)system,and the core is idealized using the rigid-perfectly-plastic-locking(RPPL)model.Reflection of incident shock wave is considered by incorporating the bending/stretching resistance of the front face sheet and compaction of the core.The model is validated with existing analytical predictions and FE simulation results,with good agreement achieved.Compared with existing analytical models,the proposed model exhibits superiority in two aspects:the deformation resistance of front face sheet during shock wave reflection is taken into account;the effect of pulse shape is considered.The practical application range of the proposed model is therefore wider.
基金This work was supported by the National Natural Science Foundation of China(Grants 11702146,11732006 and 11827801)the Equipment Pre-research Foundation(Grant 6140210010202).
文摘The paper investigated the equivalent continuum modeling of beam-like repetitive truss structures considering the flexibility of joints,which models the contact between the truss member and joint by spring-damper with six directional stiffnesses and dampings.Firstly,a two-node hybrid joint-beam element was derived for modeling the truss member with flexible end joints,and a condensed model for the repeating element with flexible joints was obtained.Then,the energy equivalence method was adopted to equivalently model the truss structure with flexible joints and material damping as a spatial viscoelastic anisotropic beam model.Afterwards,the equations of motion for the equivalent beam model were derived and solved analytically in the frequency domain.In the numerical studies,the correctness of the presented method was verified by comparisons of the natural frequencies and frequency responses evaluated by the equivalent beam model with the results of the finite element method model.
基金the EU project(INCO-Compernicus,ERBIC 15 CT970706)Research Foundation for Youth Scientist of Northeastern University,Shenyang,china(856049)
文摘Based on the (Ⅰ) of the present work, the behavior of shear beam model at crack initiation stage and at instable propagation stage was studied. The prime results include: 1) discriminant equation which clarifies the mode of instability, snap_back or snap_through, was established; 2) analytical solution was given out for the double shear beam and the load_displacement diagram for monotonic loading was presented for a full process; and 3) the problem of the energy release induced by instability was discussed.
文摘Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidification, analyze the interaction between shell and molten steel, and compare the temperature distribution under different technological conditions. The results indicate that high superheating degree can lengthen the liquid-core depth and make the crack and breakout possible, so suitable superheating should be controlled within 35 ℃ according to the simulation results. Casting speed which is one of the most important technological parameters of improving production rate, should be controlled between 0.85 m/min and 1.05 m/min and the caster has great potential in the improvement of blank quality.
基金Supported by National Natural Science Foundation of China(Grant Nos.51035008,51304019)National Science Foundation of USA(Grant Nos.CMMI-1000830,CMMI-1229532)+1 种基金the University of Maryland Baltimore County Directed Research Initiative Fund ProgramFundamental Research Funds for the Central Universities,China(Grant No.FRF-TP-14-123A2)
文摘As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton's principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.
基金Natural Science Foundation of Jilin Province,China(Grant No.20180101031JC)the Jilin Provincial Science Foundation for Basic Research,China(Grant No.2019C040-7).
文摘The analytical expression of off-axis hollow Gaussian–Schell model vortex beam(HGSMVB)generated by anisotropic Gaussian–Schell model source is first introduced.The evolution properties of off-axis HGSMVB propagating in turbulent atmosphere are analyzed.The results show that the off-axis HGSMVB with smaller coherence length or propagating in stronger turbulent atmosphere will evolve from dark hollow beam into Gaussian-like beam with a larger beam spot faster.The beams with different values of integer order N or the position for hollow and vortex factor R will have almost the same Gaussian-like spot distribution at the longer propagation distance.