The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equa...There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.展开更多
In this article, two numerical techniques, namely, the homotopy perturbation and the matrix approach methods have been proposed and implemented to obtain an approximate solution of the linear fractional differential e...In this article, two numerical techniques, namely, the homotopy perturbation and the matrix approach methods have been proposed and implemented to obtain an approximate solution of the linear fractional differential equation. To test the effectiveness of these methods, two numerical examples with known exact solution are illustrated. Numerical experiments show that the accuracy of these methods is in a good agreement with the exact solution. However, a comparison between these methods shows that the matrix approach method provides more accurate results.展开更多
In this paper, we analyze the Galerkin approximation of parabolic integro-differential equation. A probability computational method for the equation is proposed.The method is based on the backward Euler scheme,the lef...In this paper, we analyze the Galerkin approximation of parabolic integro-differential equation. A probability computational method for the equation is proposed.The method is based on the backward Euler scheme,the left rectangle rule and the probability transfer matrices.展开更多
The firing accuracy of a tank gun is affected significantly by the flexural motion of the barrel.For the purpose of satisfying the requirement of efficiently and accurately dynamic analysis and optimization of the tan...The firing accuracy of a tank gun is affected significantly by the flexural motion of the barrel.For the purpose of satisfying the requirement of efficiently and accurately dynamic analysis and optimization of the tank gun barrel to ensure it has good dynamic characteristics and firing accuracy,the high-fidelity dynamic model of a tank gun barrel is developed according to the transfer matrix method for multibody system which has features of high degree of stylization and high computational speed.The transfer matrix of the non-uniform Euler-Bernoulli beam(NU-EB beam)is deduced from governing differential equations of motion utilizing the differential transform method.The orthogonality of augmented eigenvectors for the NU-EB beam is proven which can be used for its exact dynamics response analysis using the modal method.In allusion to the tank gun barrel with non-uniform cross-section,the barrel is modeled as a combination of several uniform and non-uniform transverse vibrating Euler-Bernoulli beams.The overall transfer equation and matrix of the tank gun barrel are established according to the automatic deduction theorem of the overall transfer equation of multibody system.The present method is proven to be effective by comparing the computational results to those in published literatures.The vibration characteristics of a tank gun barrel with a non-uniform cross-section are analyzed accurately and are verified by the modal test.展开更多
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
基金Supported by National Natural Science Foundation of China(Grant No.51175422)
文摘There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.
文摘In this article, two numerical techniques, namely, the homotopy perturbation and the matrix approach methods have been proposed and implemented to obtain an approximate solution of the linear fractional differential equation. To test the effectiveness of these methods, two numerical examples with known exact solution are illustrated. Numerical experiments show that the accuracy of these methods is in a good agreement with the exact solution. However, a comparison between these methods shows that the matrix approach method provides more accurate results.
文摘In this paper, we analyze the Galerkin approximation of parabolic integro-differential equation. A probability computational method for the equation is proposed.The method is based on the backward Euler scheme,the left rectangle rule and the probability transfer matrices.
基金This work was supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK20190438)the National Natural Science Foundation of China(Grant No.11902158).
文摘The firing accuracy of a tank gun is affected significantly by the flexural motion of the barrel.For the purpose of satisfying the requirement of efficiently and accurately dynamic analysis and optimization of the tank gun barrel to ensure it has good dynamic characteristics and firing accuracy,the high-fidelity dynamic model of a tank gun barrel is developed according to the transfer matrix method for multibody system which has features of high degree of stylization and high computational speed.The transfer matrix of the non-uniform Euler-Bernoulli beam(NU-EB beam)is deduced from governing differential equations of motion utilizing the differential transform method.The orthogonality of augmented eigenvectors for the NU-EB beam is proven which can be used for its exact dynamics response analysis using the modal method.In allusion to the tank gun barrel with non-uniform cross-section,the barrel is modeled as a combination of several uniform and non-uniform transverse vibrating Euler-Bernoulli beams.The overall transfer equation and matrix of the tank gun barrel are established according to the automatic deduction theorem of the overall transfer equation of multibody system.The present method is proven to be effective by comparing the computational results to those in published literatures.The vibration characteristics of a tank gun barrel with a non-uniform cross-section are analyzed accurately and are verified by the modal test.
