Based on the Coriolis acceleration and the Lagrangian strain formula, a gen- eralized equation for the transverse vibration system of convection belts is derived using Newton＇s second law. The method of multiple scal...Based on the Coriolis acceleration and the Lagrangian strain formula, a gen- eralized equation for the transverse vibration system of convection belts is derived using Newton＇s second law. The method of multiple scales is directly applied to the govern- ing equations, and an approximate solution of the primary parameter resonance of the system is obtained. The detuning parameter, cross-section area, elastic and viscoelastic parameters, and axial moving speed have a significant influences on the amplitudes of steady-state response and their existence boundaries. Some new dynamical phenomena are revealed.展开更多
Lagrange-Maxwell＇s equation is extended firstly. With the theory of electromechanical analytical dynamics, the magnetic complement energy in air gap of generator is acquired. The torsional vibration differential equa...Lagrange-Maxwell＇s equation is extended firstly. With the theory of electromechanical analytical dynamics, the magnetic complement energy in air gap of generator is acquired. The torsional vibration differential equations with periodic coefficients of rotor shafting of generator which is in the state of.magnetic saturation are established. It is shown that the magnetic saturation may cause double frequency electromagnetic moment. By means of the averaging method, the first approximate solution and corresponding solution of the primary parametric resonance is obtained. The characteristics and laws of the primary parametric resonance excited by the electromagnetism are analyzed and some of new phenomena are revealed.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supported by the Natural Science Foundation of Hebei Province (No. A200900997)
文摘Based on the Coriolis acceleration and the Lagrangian strain formula, a gen- eralized equation for the transverse vibration system of convection belts is derived using Newton＇s second law. The method of multiple scales is directly applied to the govern- ing equations, and an approximate solution of the primary parameter resonance of the system is obtained. The detuning parameter, cross-section area, elastic and viscoelastic parameters, and axial moving speed have a significant influences on the amplitudes of steady-state response and their existence boundaries. Some new dynamical phenomena are revealed.
文摘Lagrange-Maxwell＇s equation is extended firstly. With the theory of electromechanical analytical dynamics, the magnetic complement energy in air gap of generator is acquired. The torsional vibration differential equations with periodic coefficients of rotor shafting of generator which is in the state of.magnetic saturation are established. It is shown that the magnetic saturation may cause double frequency electromagnetic moment. By means of the averaging method, the first approximate solution and corresponding solution of the primary parametric resonance is obtained. The characteristics and laws of the primary parametric resonance excited by the electromagnetism are analyzed and some of new phenomena are revealed.
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.
