This paper considers one computational method of the eigenvalues approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy in...This paper considers one computational method of the eigenvalues approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and acc...展开更多
In this paper, the method of semi-active control with variable damper is presented to deal with the relatively poor transversal seismic condition of bridge. Based on the LQR control algorithm the control effectiveness...In this paper, the method of semi-active control with variable damper is presented to deal with the relatively poor transversal seismic condition of bridge. Based on the LQR control algorithm the control effectiveness for transverse vibration of pier-beam structure of bridge are discussed. Taking the structure as a multiple-degree of freedom system, the calculating model of structure-variable damper system is set up and the differential equation is derived, combined with practical example the control system is simulated and studied by various semi-active control algorithms and passive strategy with MATLAB. The results show that the semi-active control with variable damper can decrease the transverse vibration effectively and the control effect is obvious.展开更多
In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilto...In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3:1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3:1 internal resonances.展开更多
This paper analyzes the physical meaning of the active and reactive power flow in the finite L-shaped beams and studies the active vibration control of the structures based on the active and reactive power flow.The tr...This paper analyzes the physical meaning of the active and reactive power flow in the finite L-shaped beams and studies the active vibration control of the structures based on the active and reactive power flow.The traveling wave approach is used to calculate the structural dynamic responses.Because the error of control force is inevitable in practical applications,the effects of the error of control force on the control results are studied.The study indicates that the error of control force has pronounced influence on the control results of the acceleration and reactive power flow.It is obvious that the reactive power flow can represent the vibration strength component of the complex intensity,and the active power flow strongly depends on the structural damping of the finite beams.展开更多
文摘This paper considers one computational method of the eigenvalues approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and acc...
文摘In this paper, the method of semi-active control with variable damper is presented to deal with the relatively poor transversal seismic condition of bridge. Based on the LQR control algorithm the control effectiveness for transverse vibration of pier-beam structure of bridge are discussed. Taking the structure as a multiple-degree of freedom system, the calculating model of structure-variable damper system is set up and the differential equation is derived, combined with practical example the control system is simulated and studied by various semi-active control algorithms and passive strategy with MATLAB. The results show that the semi-active control with variable damper can decrease the transverse vibration effectively and the control effect is obvious.
基金supported by the National Outstanding Young Scientists Foundation of China (Grant No. 10725209)the National Natural Science Foundation of China (Grant No. 90816001)+3 种基金Shanghai Subject Chief Scientist Project (Grant No. 09XD1401700)Innovation Foundation for Graduates of Shanghai University (Grant No. A.16-0401-08-005)Shanghai Leading Academic Discipline Project (Grant No. S30106)the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0844)
文摘In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3:1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3:1 internal resonances.
基金supported by the National Natural Science Foundation of China (Grant Nos.10672017, 10632020 and 11002045)
文摘This paper analyzes the physical meaning of the active and reactive power flow in the finite L-shaped beams and studies the active vibration control of the structures based on the active and reactive power flow.The traveling wave approach is used to calculate the structural dynamic responses.Because the error of control force is inevitable in practical applications,the effects of the error of control force on the control results are studied.The study indicates that the error of control force has pronounced influence on the control results of the acceleration and reactive power flow.It is obvious that the reactive power flow can represent the vibration strength component of the complex intensity,and the active power flow strongly depends on the structural damping of the finite beams.
