The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial mot...The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.展开更多
An approach is presented to investigate the nonlinear vibration of stiffened plates.A stiffened plate is divided into one plate and some stiffeners,with the plate considered to be geometrically nonlinear,and the stiff...An approach is presented to investigate the nonlinear vibration of stiffened plates.A stiffened plate is divided into one plate and some stiffeners,with the plate considered to be geometrically nonlinear,and the stiffeners taken as Euler beams.Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system.Besides,the effect caused by boundary movement is transformed into equivalent excitations.The first approximation solution of the non-resonance is obtained by means of the method of multiple scales.The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method.The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS.Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance.In addition,the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out.Some nonlinear vibration characteristics of stiffened plates are obtained,which are useful for engineering design.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No.10472060）
文摘The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.
基金supported by the China Postdoctoral Science Foundation(Grant No.2013M540656)the Fundamental Research Funds for the Central Universities,South China University of Technology(Grant No.2013ZB0023)the National Natural Science Foundation of China(Grant No.11132002)
文摘An approach is presented to investigate the nonlinear vibration of stiffened plates.A stiffened plate is divided into one plate and some stiffeners,with the plate considered to be geometrically nonlinear,and the stiffeners taken as Euler beams.Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system.Besides,the effect caused by boundary movement is transformed into equivalent excitations.The first approximation solution of the non-resonance is obtained by means of the method of multiple scales.The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method.The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS.Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance.In addition,the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out.Some nonlinear vibration characteristics of stiffened plates are obtained,which are useful for engineering design.
