摘要
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。
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 Rayleigb 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.
出处
《振动与冲击》
EI
CSCD
北大核心
2012年第5期135-138,共4页
Journal of Vibration and Shock
基金
国家杰出青年科学基金(10725209)
国家自然科学基金项目(10902064)
上海市教育委员会科研创新项目(12YZ028)
上海市重点学科建设项目(S30106)
上海市青年科技启明星计划(11QA1402300)资助
关键词
Rayleigh梁
非线性
黏弹性
稳态响应
多尺度方法
Rayleigh beam
parametric resonance
nonlinear
multi-scale method
differential quadrature method
