弹性接触支撑梁横向振动动力学建模研究

Study on Dynamic Modeling of Transverse Vibration of Elastic-contact Supporting Beams

考虑弹性梁与支撑弹簧之间的接触行为,建立三支撑弹性接触梁的分段线性动力学模型。采用假定振型法给出接触支撑梁的横向位移方程,推导得到梁和接触状态下的支撑弹簧的动能和势能,通过能量变分原理推导得到接触支撑梁的振动微分方程。利用Runge-Kutta法求解梁在简谐激励下的时域、频域响应。理论计算结果与有限元法的计算结果吻合良好,验证了方法的准确性。然后借助分岔图分析表明不同的激励幅值、激励频率和弹簧刚度系数会使接触支撑梁产生性质不同的周期运动或混沌运动,从而影响接触支撑梁的非线性振动特性。

A piecewise linear dynamic model of the three-support elastic contact beam is established by considering the contact behavior between the elastic beam and the support spring.The mode assumption method is used to give the transverse displacement equation of the contact supporting beam,and the kinetic energy and potential energy of the supporting spring beneath the beam in the contact state are derived.The vibration differential equation of the contact supporting beam is derived through the energy variation principle.The Runge-Kutta method is used to solve the time and frequency domain responses of the beam under harmonic excitation.The theoretical calculation results are in a good agreement with those of the finite element method,which verifies the accuracy of the method.With the help of bifurcation diagram analysis,it is shown that different excitation amplitude,excitation frequency,and spring stiffness coefficient can cause the contact supporting beam to have varying periodic or chaotic motions,which will affect the nonlinear vibration characteristics of the contact supporting beams.