The transverse vibration of an axially moving string supported by a viscoelastic foundation is analysed using the complex modal method. The equation of motion is developed using the generalized Hamilton principle. The...The transverse vibration of an axially moving string supported by a viscoelastic foundation is analysed using the complex modal method. The equation of motion is developed using the generalized Hamilton principle. The exact closed-form solution of eigenvalues and eigen- functions are obtained. The governing equation is represented in a canonical state space form defined by two matrix differential operators, and the eigenfunctions and adjoint eigenfunctions are proved to be orthogonal with respect to each operator. This orthogonality is applied so that the response to arbitrary external excitations and initial conditions can be expressed in modal expansion. Numerical examples are presented to validate the proposed approach.展开更多
It is pointed out that the damping matrix deduced by active members in the finite element vibration equation of a truss adaptive structure generally can not be decoupled, which leads to the difficulty in the process o...It is pointed out that the damping matrix deduced by active members in the finite element vibration equation of a truss adaptive structure generally can not be decoupled, which leads to the difficulty in the process of modal analysis by classical superposition method. This paper focuses on the computational method of the dynamic response for truss adaptive structures. Firstly, a new technique of state vector approach is applied to study the dynamic response of truss adaptive structures. It can make the coeffic lent matrix of first derivative of state vector a symmetric positive definite matrix, and particularly a diagonal matrix provided that mass matrix is derived by lumped method, so the coefficient matrix of the first derivative of state vector can be exactly decomposed by CHOLESKY method. In this case, the proposed technique not only improves the calculation accuracy, but also saves the computing time. Based on the procedure mentioned above, the mathematical formulation for the system response of truss adaptive structures is systematically derived in theory. Thirdly, by using FORTRAN language, a program system for computing dynamic response of truss adaptive structures is developed. Fourthly, a typical 18 bar space truss adaptive structure has been chosen as test numerical examples to show the feasibility and effectiveness of the proposed method. Finally, some good suggestions, such as how to choose complex mode shapes practically in determining the dynamic response are also given. The new approach can be extended to calculate the dynamic response of general adaptive structures.展开更多
In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilto...In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton＇s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.展开更多
The objective of this paper is to investigate the dynamic characteristics of two adjacent building structures interconnected by viscoelastic dampers under seismic excitations. The computational procedure for an analyt...The objective of this paper is to investigate the dynamic characteristics of two adjacent building structures interconnected by viscoelastic dampers under seismic excitations. The computational procedure for an analytical model including the system model formulation, complex modal analysis and seismic time history analysis is presented for this purpose. A numerical example is also provided to illustrate the analytical model. The complex modal analysis is conducted to determine the optimal damping ratio, the optimal damper stiffness and the optimal damper damping of the viscoelastic dampers for each mode of the system. For the damper stiffness and damping with optimal values, the responses can be categorized into underdamped and critically damped vibrations. Furthermore, compared to the viscous dampers with only the energy dissipation mechanism, the viscoelastic dampers with both the energy dissipation and redistribution mechanisms are more effective for increasing the damping ratio of the system. The seismic time history analysis is conducted to assess the effectiveness of the viscoelastic dampers for vibration control. Based on the optimal damping ratio, the optimal damper stiffness, the optimal damper damping of the viscoelastic dampers for a certain mode of the system, and the viscoelastic dampers can be used to effectively suppress the root-mean-square responses as well as the peak responses of the two adjacent buildings.展开更多
基金Project supported by the State Key Program of National Natural Science of China(No.11232009)the National Natural Science Foundation of China(Nos.11372171 and 11422214)
文摘The transverse vibration of an axially moving string supported by a viscoelastic foundation is analysed using the complex modal method. The equation of motion is developed using the generalized Hamilton principle. The exact closed-form solution of eigenvalues and eigen- functions are obtained. The governing equation is represented in a canonical state space form defined by two matrix differential operators, and the eigenfunctions and adjoint eigenfunctions are proved to be orthogonal with respect to each operator. This orthogonality is applied so that the response to arbitrary external excitations and initial conditions can be expressed in modal expansion. Numerical examples are presented to validate the proposed approach.
基金supported by National Natural Science Foundation of China (Grant No. 10472007)
文摘It is pointed out that the damping matrix deduced by active members in the finite element vibration equation of a truss adaptive structure generally can not be decoupled, which leads to the difficulty in the process of modal analysis by classical superposition method. This paper focuses on the computational method of the dynamic response for truss adaptive structures. Firstly, a new technique of state vector approach is applied to study the dynamic response of truss adaptive structures. It can make the coeffic lent matrix of first derivative of state vector a symmetric positive definite matrix, and particularly a diagonal matrix provided that mass matrix is derived by lumped method, so the coefficient matrix of the first derivative of state vector can be exactly decomposed by CHOLESKY method. In this case, the proposed technique not only improves the calculation accuracy, but also saves the computing time. Based on the procedure mentioned above, the mathematical formulation for the system response of truss adaptive structures is systematically derived in theory. Thirdly, by using FORTRAN language, a program system for computing dynamic response of truss adaptive structures is developed. Fourthly, a typical 18 bar space truss adaptive structure has been chosen as test numerical examples to show the feasibility and effectiveness of the proposed method. Finally, some good suggestions, such as how to choose complex mode shapes practically in determining the dynamic response are also given. The new approach can be extended to calculate the dynamic response of general adaptive structures.
基金Project supported by the State Key Program of the National Natural Science Foundation of China(No.11232009)the National Natural Science Foundation of China(Nos.11372171 and 11422214)
文摘In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton＇s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.
文摘The objective of this paper is to investigate the dynamic characteristics of two adjacent building structures interconnected by viscoelastic dampers under seismic excitations. The computational procedure for an analytical model including the system model formulation, complex modal analysis and seismic time history analysis is presented for this purpose. A numerical example is also provided to illustrate the analytical model. The complex modal analysis is conducted to determine the optimal damping ratio, the optimal damper stiffness and the optimal damper damping of the viscoelastic dampers for each mode of the system. For the damper stiffness and damping with optimal values, the responses can be categorized into underdamped and critically damped vibrations. Furthermore, compared to the viscous dampers with only the energy dissipation mechanism, the viscoelastic dampers with both the energy dissipation and redistribution mechanisms are more effective for increasing the damping ratio of the system. The seismic time history analysis is conducted to assess the effectiveness of the viscoelastic dampers for vibration control. Based on the optimal damping ratio, the optimal damper stiffness, the optimal damper damping of the viscoelastic dampers for a certain mode of the system, and the viscoelastic dampers can be used to effectively suppress the root-mean-square responses as well as the peak responses of the two adjacent buildings.
