摘要
研究了轴向运动黏弹性Rayleigh梁的非线性受迫振动。运用广义Hamilton原理推导出梁和边界条件的非线性控制方程。通过复模态法计算固有频率和模态函数。运用多尺度法获得主共振的稳态响应,根据Routh-Hurwitz分析稳态响应的稳定性,同时得到粘性阻尼,力和非线性系数的影响曲线。如果存在不稳定区域,通过增加粘性阻尼或减小力可使稳态响应的稳定。运用微分求积法对轴向黏弹性梁的受迫振动进行数值分析,并与多尺度分析进行对比,以此来证明了多尺度法的结果的正确性。
Nonlinear forced vibration is investigated for an axially moving viscoelastic Rayleigh beam.The nonlinear governing equation of beam and boundary condition are derived on the basis of the generalized Hamilton principle.The natural frequency and mode are calculated via complex-mode method.The method of multiple scales is provided to obtain the steady-state responses for primary resonance.Stability of the steady-state response is analyzed in accordance with Routh-Hurwitz criterion.The numerical illustrations represent the effects of viscous damping,force and nonlinear coefficients.If there is an unstable region,the steady state response can be stabilized by increasing the viscous damping or reducing the force.The differential quadrature method is proposed numerically to analyze the forced vibration of axially accelerating viscoelastic beams and made a comparison with the analysis of multiple scales to prove the results of the multi-scale method.
作者
王波
蒋敏
WANG Bo;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
2020年第4期62-65,共4页
Machinery Design & Manufacture
基金
国家自然科学基金项目(11202136)。
关键词
Rayleigh梁
受迫振动
广义Hamilton原理
多尺度法
微分求积法
Rayleigh Beam
Forced Vibration
The Generalized Hamilton Principle
The Method of Multiple Scales
The Differential Quadrature Method
