内共振作用下轴向运动黏弹性梁横向受迫振动

摘要

研究内共振与外部激励共同作用下,轴向运动黏弹性梁横向非线性振动的稳态响应.在运动梁动力学建模中采用Kelvin本构关系,并取物质时间导数.首次将直接多尺度法应用到轴向运动连续体的内共振研究.通过直接对连续体的偏微分-积分控制方程运用多尺度法,建立内共振条件下的横向非线性受迫共振的可解性条件.并通过稳定性分析,得到稳态响应解的稳定边界.另外还考察了参数对响应的影响.运用数值仿真验证了近似解析方法的正确性及有效性.%The transverse nonlinear forced vibration of an axially moving viscoelastic beam with a three-to-one internal resonance was analytically and numerically studied here.The beam material obeys Kelvin constitution relation model with material time derivatives adopted.For the first time,the multi-scale method was used to study the internal resonance of the axially moving continuous beam.The solvability condition for the transverse nonlinear forced vibration of the beam was derived under the internal resonance condition.The stable boundary for the beam's steady-state response solution was obtained with the stability analysis.The effects of the system parameters on the beam's steady-state response were examined.Finally,the correctness and effectiveness of the proposed approximate analytical method were verified with numerical simulations.