The system dynamics model has been done. The contracting process of thecurved-surface of the rubber disc is analyzed carefully, which is the main research aspect of theelastodynamics in the system. The coupling equati...The system dynamics model has been done. The contracting process of thecurved-surface of the rubber disc is analyzed carefully, which is the main research aspect of theelastodynamics in the system. The coupling equation of the 'elastic surface and fluid' is resolvedby inverse resolution method. The main characteristics of the system, for instance, thedeparting-tube velocity, with which a carrier is to depart a launch tube, are estimated throughresolving the simulation model of the system dynamics. The simulation is based on some knownparameters and the experiment outcome of the elasticity modulus of a special rubber. On the otherhand, the influences on the system characteristics accompanying with the changing of some systemparameters are discussed. Finally, the conclusions are given that the elastodynamic system has asuperior performance and that the system deserves to be developed further as a kind of launchdevice.展开更多
To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used a...To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.展开更多
This paper presents a theoretical solution for the basic equation of axisymmetric problems in elastodynamics.The solution is composed of a quasi-static solution which satisfies inhomogeneous boundary conditions and a ...This paper presents a theoretical solution for the basic equation of axisymmetric problems in elastodynamics.The solution is composed of a quasi-static solution which satisfies inhomogeneous boundary conditions and a dynamic solution which satisfies homogeneous boundary conditions.After the quasi-static so- lution has been obtained an inhomogeneous equation for dynamic solution is found from the basic equation. By making use of eigenvalue problem of a corresponding homogeneous equation,a finite Hankel transform is defined.A dynamic solution satisfying homogeneous boundary conditions is obtained by means of the finite Hankel transform and Laplace transform.Thus,an exact solution is obtained.Through an example of hollow cylinders under dynamic load,it is seen that the method,and the process of computing are simple,effective and accurate.展开更多
A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the gove...A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.展开更多
This article is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain x 〉 0, t 〉 0. The number of boundary conditi...This article is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain x 〉 0, t 〉 0. The number of boundary conditions, to be prescribed at the boundary x = 0,depends on the number of characteristics entering the domain. Because our system is nonlinear, the characteristic speeds depends on the unknown and the direction of the characteristics curves are known apriori. As it is well known, the boundary condition has to be understood in a generalised way. One of the standard way is using vanishing viscosity method. We use this method to construct solution for a particular class of initial and boundary data, namely the initial and boundary datas that lie on the level sets of one of the Riemann invariants.展开更多
The effect of magnetic field on the plane vibrations for an elastodynamic orthotropic sphere is studied. Equations of elastodynamic problems of the orthotropic hollow sphere in terms of displacement are solved. The nu...The effect of magnetic field on the plane vibrations for an elastodynamic orthotropic sphere is studied. Equations of elastodynamic problems of the orthotropic hollow sphere in terms of displacement are solved. The numerical results of the frequency equations in the presence of magnetic field are discussed and shown graphically. Compar-isons are made with the result in the presence and absence of magnetic field in the case of orthotropic sphere. The results show that the effect of magnetic field is very pronounced.展开更多
Under the small deformation assumption this paper shows the existence of solution for the system of elastic dynamics with the general nonlinear constitutive laws, and the existence of classical solution can be found u...Under the small deformation assumption this paper shows the existence of solution for the system of elastic dynamics with the general nonlinear constitutive laws, and the existence of classical solution can be found under weaker conditions.展开更多
Elastodynamic analysis of an anisotropic liquid-saturated porous medium is made to study a deformation problem of a transversely isotropic liquid-saturated porous medium due to mechanical sources. Certain physical pro...Elastodynamic analysis of an anisotropic liquid-saturated porous medium is made to study a deformation problem of a transversely isotropic liquid-saturated porous medium due to mechanical sources. Certain physical problems are of the nature, in which the deformation takes place only in one direction, e.g., the problem relating to deformed structures and columns. In soil mechanics, an assumption of only vertical subsidence is often invoked and this leads to the one dimensional model of poroelasticity. By consid- ering a model of one-dimensional deformation of the anisotropic liquid-saturated porous medium, variations in disturbances are observed with reference to time and distance. The distributions of displacements and stresses are affected due to the anisotropy of the medium, and also due to the type of sources causing the disturbances.展开更多
All step-by-step integration methods available at present for structural dynamic analysis use the displacement, velocity, and acceleration vectors computed at a previous interval for evaluating those at an advanced ti...All step-by-step integration methods available at present for structural dynamic analysis use the displacement, velocity, and acceleration vectors computed at a previous interval for evaluating those at an advanced time step. Hence, an accumulated error will be definitely introduced after such integration. This paper presents a novel time-domain-advance integration method for transient elastodynamic problems in which the exact initial conditions are strictly satisfied for the solutions for each time step. In this way, the accumu- lated error can be eliminated and the approximate solutions will converge to the exact ones uniformly on the whole time domain. Therefore. the new method is more accurate. When applying to a structural dynamic problem, the present mehtod does not have to use the initial acceleration as is required by most other algorithms and the corresponding computation can be avoided. The present method is simple in representation, easy to be programmed, and especially suitable for accurate analyses of long-time problems. The comparison of numerical results with exact ones shows that the present method is much more accurate than some most widely used algorithms.展开更多
An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except...An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson＇s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler＇s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material （FGM） hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.展开更多
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrica...According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.展开更多
This paper presents an analytical method of solving the elastodynamic problem of a solid sphere. The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous ...This paper presents an analytical method of solving the elastodynamic problem of a solid sphere. The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous compound boundary conditions and a dynamic solution satisfying the homogeneous compound boundary conditions. By utilizing the variable transform, the dynamic equation may be transformed into Bassel equation. By defining a finite Hankel transform, we can easily obtain the dynamic solution for the inhomogeneous dynamic equation. Thereby, the exact elastodynamic solution for a solid sphere can be obtained. From results carried out, we have observed that there exists the dynamic stress-focusing phenomenon at the center of a solid sphere under shock load and it results in very high dynamic stress-peak.展开更多
The variation of new Gurtin-type region-wise variational principles results in continuous conditions, boundary conditions, all equations and relations in linear thermopiezoelectric elastodynamics. Gurtin-type region-w...The variation of new Gurtin-type region-wise variational principles results in continuous conditions, boundary conditions, all equations and relations in linear thermopiezoelectric elastodynamics. Gurtin-type region-wise variational principles comprise very important parts of linear thermopiezoelectric elastodynamics, and can fully characterize the initial-boundary-value problem in linear thermopiezoelectric elastodynamics.展开更多
In recent years, a lot of writers have used Cagniard-de Hoop's method[1][] to solve some problems of elastic wave. But it is a difficult and complicated task to change the path of integration when we use this meth...In recent years, a lot of writers have used Cagniard-de Hoop's method[1][] to solve some problems of elastic wave. But it is a difficult and complicated task to change the path of integration when we use this method. A differential transform by A.Ungar[3,6] can obviate this difficulty. In this paper, weuse Ungar 's differential transform to solve a case of Lamb's problem [1][2]展开更多
The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary elem...The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.展开更多
The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial diff...The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering;however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq?with regular distribution of nodes nt=55. After, the results are presented with fixed values of?as?and aq?for different time-step.展开更多
In this paper the existence of solution to finite elastodynamics constrainted by mixed boundary conditions is derived when the hyperpotential and its gradient (for Green's strain) satisfy adequate conditions.
Distinguished from parallel-axis gear systems,the revolution of the carrier brings out the pass effect of the planet gear.Compared with the phenomenological descriptions in conventional studies,this paper aims to prov...Distinguished from parallel-axis gear systems,the revolution of the carrier brings out the pass effect of the planet gear.Compared with the phenomenological descriptions in conventional studies,this paper aims to provide more abundant physical information and the elastodynamics mechanism of the pass effect of the planet gear.To this end,a continuous-discrete model of helical planetary gears is proposed.Considering both the in-plane and out-of-plane vibration,a semi-analytical model is established to simulate the elastic ring gear.The elastic and the lumped parameter submodels are synthesized using the moving elastic coupling boundary.The simulated modal and dynamic characteristics are verified using a planetary gear test rig.Based on the proposed dynamic model,the pass effect of the planet gear,the effects of bolt constraint,and the out-of-plane vibration of helical planetary gears are investigated.It is revealed that the“realistic rotation”strategy adopted in the proposed dynamic model can better reflect the physical essence of the pass effect of the planet gear compared with the“pseudo rotation”strategy utilized in the traditional model.展开更多
The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an ...The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.展开更多
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electroma...According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.展开更多
基金This project is supported by Warship/Ship Research Youth Foundation of CSIC (No.99QJ08).
文摘The system dynamics model has been done. The contracting process of thecurved-surface of the rubber disc is analyzed carefully, which is the main research aspect of theelastodynamics in the system. The coupling equation of the 'elastic surface and fluid' is resolvedby inverse resolution method. The main characteristics of the system, for instance, thedeparting-tube velocity, with which a carrier is to depart a launch tube, are estimated throughresolving the simulation model of the system dynamics. The simulation is based on some knownparameters and the experiment outcome of the elasticity modulus of a special rubber. On the otherhand, the influences on the system characteristics accompanying with the changing of some systemparameters are discussed. Finally, the conclusions are given that the elastodynamic system has asuperior performance and that the system deserves to be developed further as a kind of launchdevice.
基金Project(Kfkt2013-12)supported by Open Research Fund of Key Laboratory of High Performance Complex Manufacturing of Central South University,ChinaProject(2014002)supported by the Open Fund of Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures,ChinaProject(51375013)supported by the National Natural Science Foundation of China
文摘To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.
文摘This paper presents a theoretical solution for the basic equation of axisymmetric problems in elastodynamics.The solution is composed of a quasi-static solution which satisfies inhomogeneous boundary conditions and a dynamic solution which satisfies homogeneous boundary conditions.After the quasi-static so- lution has been obtained an inhomogeneous equation for dynamic solution is found from the basic equation. By making use of eigenvalue problem of a corresponding homogeneous equation,a finite Hankel transform is defined.A dynamic solution satisfying homogeneous boundary conditions is obtained by means of the finite Hankel transform and Laplace transform.Thus,an exact solution is obtained.Through an example of hollow cylinders under dynamic load,it is seen that the method,and the process of computing are simple,effective and accurate.
基金The project supported by the National Natural Science Foundation of China (10172075 and 10002016)
文摘A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.
文摘This article is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain x 〉 0, t 〉 0. The number of boundary conditions, to be prescribed at the boundary x = 0,depends on the number of characteristics entering the domain. Because our system is nonlinear, the characteristic speeds depends on the unknown and the direction of the characteristics curves are known apriori. As it is well known, the boundary condition has to be understood in a generalised way. One of the standard way is using vanishing viscosity method. We use this method to construct solution for a particular class of initial and boundary data, namely the initial and boundary datas that lie on the level sets of one of the Riemann invariants.
文摘The effect of magnetic field on the plane vibrations for an elastodynamic orthotropic sphere is studied. Equations of elastodynamic problems of the orthotropic hollow sphere in terms of displacement are solved. The numerical results of the frequency equations in the presence of magnetic field are discussed and shown graphically. Compar-isons are made with the result in the presence and absence of magnetic field in the case of orthotropic sphere. The results show that the effect of magnetic field is very pronounced.
文摘Under the small deformation assumption this paper shows the existence of solution for the system of elastic dynamics with the general nonlinear constitutive laws, and the existence of classical solution can be found under weaker conditions.
文摘Elastodynamic analysis of an anisotropic liquid-saturated porous medium is made to study a deformation problem of a transversely isotropic liquid-saturated porous medium due to mechanical sources. Certain physical problems are of the nature, in which the deformation takes place only in one direction, e.g., the problem relating to deformed structures and columns. In soil mechanics, an assumption of only vertical subsidence is often invoked and this leads to the one dimensional model of poroelasticity. By consid- ering a model of one-dimensional deformation of the anisotropic liquid-saturated porous medium, variations in disturbances are observed with reference to time and distance. The distributions of displacements and stresses are affected due to the anisotropy of the medium, and also due to the type of sources causing the disturbances.
文摘All step-by-step integration methods available at present for structural dynamic analysis use the displacement, velocity, and acceleration vectors computed at a previous interval for evaluating those at an advanced time step. Hence, an accumulated error will be definitely introduced after such integration. This paper presents a novel time-domain-advance integration method for transient elastodynamic problems in which the exact initial conditions are strictly satisfied for the solutions for each time step. In this way, the accumu- lated error can be eliminated and the approximate solutions will converge to the exact ones uniformly on the whole time domain. Therefore. the new method is more accurate. When applying to a structural dynamic problem, the present mehtod does not have to use the initial acceleration as is required by most other algorithms and the corresponding computation can be avoided. The present method is simple in representation, easy to be programmed, and especially suitable for accurate analyses of long-time problems. The comparison of numerical results with exact ones shows that the present method is much more accurate than some most widely used algorithms.
文摘An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson＇s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler＇s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material （FGM） hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.
基金Project supported by the National Natural Science Foundation of China(No.10172097)the Doctoral Foundation of Ministry of Education of China(No.20030558025)
文摘According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.
文摘This paper presents an analytical method of solving the elastodynamic problem of a solid sphere. The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous compound boundary conditions and a dynamic solution satisfying the homogeneous compound boundary conditions. By utilizing the variable transform, the dynamic equation may be transformed into Bassel equation. By defining a finite Hankel transform, we can easily obtain the dynamic solution for the inhomogeneous dynamic equation. Thereby, the exact elastodynamic solution for a solid sphere can be obtained. From results carried out, we have observed that there exists the dynamic stress-focusing phenomenon at the center of a solid sphere under shock load and it results in very high dynamic stress-peak.
文摘The variation of new Gurtin-type region-wise variational principles results in continuous conditions, boundary conditions, all equations and relations in linear thermopiezoelectric elastodynamics. Gurtin-type region-wise variational principles comprise very important parts of linear thermopiezoelectric elastodynamics, and can fully characterize the initial-boundary-value problem in linear thermopiezoelectric elastodynamics.
文摘In recent years, a lot of writers have used Cagniard-de Hoop's method[1][] to solve some problems of elastic wave. But it is a difficult and complicated task to change the path of integration when we use this method. A differential transform by A.Ungar[3,6] can obviate this difficulty. In this paper, weuse Ungar 's differential transform to solve a case of Lamb's problem [1][2]
基金This project is supported by National Natural Science Foundation of China
文摘The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.
文摘The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering;however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq?with regular distribution of nodes nt=55. After, the results are presented with fixed values of?as?and aq?for different time-step.
文摘In this paper the existence of solution to finite elastodynamics constrainted by mixed boundary conditions is derived when the hyperpotential and its gradient (for Green's strain) satisfy adequate conditions.
基金supported by the National Natural Science Foundation of China(Grant No.12272219)the National Science and Technology Major Project(Grant No.J2019-IV-0018-0086)the National Key Laboratory of Science and Technology on Helicopter Transmission(Grant No.HTL-O-21G02)。
文摘Distinguished from parallel-axis gear systems,the revolution of the carrier brings out the pass effect of the planet gear.Compared with the phenomenological descriptions in conventional studies,this paper aims to provide more abundant physical information and the elastodynamics mechanism of the pass effect of the planet gear.To this end,a continuous-discrete model of helical planetary gears is proposed.Considering both the in-plane and out-of-plane vibration,a semi-analytical model is established to simulate the elastic ring gear.The elastic and the lumped parameter submodels are synthesized using the moving elastic coupling boundary.The simulated modal and dynamic characteristics are verified using a planetary gear test rig.Based on the proposed dynamic model,the pass effect of the planet gear,the effects of bolt constraint,and the out-of-plane vibration of helical planetary gears are investigated.It is revealed that the“realistic rotation”strategy adopted in the proposed dynamic model can better reflect the physical essence of the pass effect of the planet gear compared with the“pseudo rotation”strategy utilized in the traditional model.
基金supported by the National Natural Science Foundation of China(Grant No.10571118)the Shanghai Leading Academic Discipline Project(Grant No.Y0103).
文摘The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.
基金the National Natural Science Foundation of China ( Grant No. 10172097) the Scientific Foundation of the Ministry of Education of China for Doctoral Program ( Grant No. 20030558025).
文摘According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.
