移动荷载作用下非线性基础梁内共振分析

研究了有限长弹性基础上梁在移动载荷作用下的内共振响应.建立了移动集中力激励的非线性粘弹性基础支承的有限长Euler-Bernoulli梁模型,并对非线性偏微分方程进行离散,在第三阶固有频率与第一阶固有频率成三倍关系时,采用多尺度方法导出了3:1内共振的可解性条件,研究了有无移动载荷时基础阻尼和非线性刚度对梁内共振条件下自由振动响应和受迫振动响应的影响规律.在此基础上,应用Lyapunov第一方法确定了系统的稳定性条件.

Internal Resonance Analysis of Nonlinear Foundation Beams under Moving Loads

The internal external resonance response of a beam on a finite length elastic foundation under moving loads is studied. A finite length Euler Bernoulli beam model supported on a nonlinear viscoelastic foundation excited by a moving concentrated force is established, and the nonlinear partial differential equation is discretized. When the third order natural frequency and the first order natural frequency are three times related, the solvability condition for 3:1 internal resonance is derived by using a multiscale method. The effects of foundation damping and nonlinear stiffness on the free vibration response and forced vibration response of a beam under internal resonance conditions with or without moving loads are studied. On this basis, the stability conditions of the system are determined by using the first Lyapunov method.