摘要
研究非线性轴向变速黏弹性Rayleigh梁的参激振动问题。梁的本构关系使用Kelvin黏弹性模型描述,并且取全导数。基于广义哈密顿原理,导出轴向运动Rayleigh梁的非线性控制方程。考虑轴向速度在平均速度的基础上有简谐变化。运用直接多尺度法近似求解控制方程,并考虑轴向速度变化频率接近任意两阶固有频率之和时而发生的组合参激共振。依据可解性条件,得到振幅频率方程。通过对数值例子的分析,得到梁的刚度、扭转刚度以及平均速度对稳态响应的影响。
Parametric resonance of nonlinear axiallymoving viscoelastic beam is investigated.The constitutive relation of the beam is characterized by the Kelvin viscoelastic model with total derivative taken.According togeneralized hamiltonian principle,governing equation of nonlinear axially moving Rayleigh beam is derived.The axial speed harmonically variesnear the mean speed.The direct multi-scale method is used to approximate the governing equation,and the varying frequency of the axial speed is close to summation of any two natural frequencies.According to the solvability condition,the amplitude frequency equation is obtained.Use solvability conditions to obtain amplitude frequency equation.Numerical examples show effects on steady-state response of nonlinear axially moving beam with stiffness,torsion rigidity and mean speed.
作者
王波
钱伟
蒋敏
WANG Bo;QIAN Wei;JIANG Min(School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai 201418,China)
出处
《机械设计与制造》
北大核心
2019年第6期33-36,41,共5页
Machinery Design & Manufacture
基金
国家自然科学基金项目(11202136)
关键词
轴向运动Rayleigh梁
黏弹性
多尺度法
组合参数共振
稳态响应
Axially Moving Rayleigh Beam
Viscoelastic
Method of Multiple Scales
Summation Parametric Resonance
Steady-State Respons