变形对夹层圆板非线性振动影响及其周期解.pdfVIP

辽宁工程技术大学学报(自然科学版) 第 31 卷第 l 期 2012 年 2 月 Vo 1. 31 No.l Joumal of Liaoning Technical University (Natural Science ) Feb. 2012 文章编号: 1 ∞8-0562(2012)0 1-0077-04 变形对夹层圆板非线性振动影响及其周期解 张秀礼 (河北建材职业技术学院机电工程系，闸北秦皇岛 066004) 摘 要2 为了解决载荷作用下夹层圆板非线性振动的大挠度方程求解问题，采用基于空间模态假设和变分法，导 出时间模态的控制方程.果用伽辽金法推导出静挠度和动挠度稿合作用下夹层圆板的非线性动力方程，从而求解 出解的时间模态的渐进表达式最后采用Lindestedt-Poincare 摄动法求解中心点附近的周期解并绘制出幅频特性 曲线.结果表明z 当横向激扰使夹层圆板产生较大幅度的受迫振动的同时，由于载荷作用下变形的存在，其产生 的附加动挠度就会与变形产生非线性精合现象，因而由此产生的变形必将影响夹层圆板的动力学特性.该成果对 非线性振动问题的研究具有一定的参考价值和指导意义. 关键词z 夹层圃板:非线性:变形:振动z 载荷:周期解:幅频特性:挠度 中图分类号: 0322 文献标志码:A Impact and periodical solutions on nonlinear vibration of circular composite plate with distortion ZHANG Xiuli (Department of Mechanical and Electrical Engineering, Hebei Vocational Technical College of Building Materials , Qinhuangdao 066004, China) Abstract: In order to solve the nonlinear oscillation large deflection equation of circular sandwich plate with loading, an 描sumption and variational method based on space mode are used to obtain control equation with time mode. Using Galerkins method, a nonlinear dynamic equation of circular sandwich plate under static deflection and dynamic deflection coupling action is derived, therefore，也e expression with time mode is obtained. Also, the periodical solutions of nonlinear vibration are obtained by using Lindstedt-Poincare perturbation methods and the curve of amplitude-仕equency is plotted. When there is a large lateral vibration in the circular sandwich plate , due ωexis由19 distortion, there will be some additional dynamic deflection coupling with distortion. Therefor毡， the disto