轴向变速黏弹性Rayleigh梁非线性参数振动稳态响应

研究非线性轴向运动黏弹性Rayleigh梁因速度周期变化产生的亚谐波共振。轴向运动速度在平均速度附近做简谐周期性脉动。通过取物质导数的Kelvin本构关系描述Rayleigh梁的黏弹性。运用多尺度近似解析方法，构建轴向运动Rayleigh梁的非线性偏微分方程的可解性条件，分析参数振动稳态响应的振幅与扰动速度频率关系。并运用微分求积方法直接离散非线性Rayleigh梁的控制方程，以验证近似解析方法分析。通过数值算例，分析了系统参数对稳态响应曲线的影响。

Steady state response of nonlinear vibration of an axially accelerating viscoelastic Rayleigh beam

The sub-harmonic resonance of an axially accelerating nonlinear viscoelastic Rayleigh beam was investigated via an approximate analytical method and verified via the differential quadrature method.The mathematical model of transverse vibration of an infinitesimal beam was established with variation calculus.The axial speed was characterized as a simple harmonic variation about the constant mean speed.The solvable conditions of parametric vibration for sub-harmonic resonance were established via the method of multiple scales.Therefore,the steady state periodic response was presented for an accelerating viscoelastic Rayleigh beam with simple supports boundary conditions.With numerical examples the effects of the nonlinear coefficient and the viscoelastic coefficient on the steady state response were studied individually.The differential governing equation for transverse vibration of an axially moving slender Rayleigh beam was numerically solved via the differential quadrature method.The numerical calculations confirmed the analytical results.Numerical examples demonstrated that the approximate analytical results have rather high precision.