中心有刚体质量的环形薄板的非线性强迫振动  

Nonlinear Forced Vibration of Annular Plates With a Concentric Rigid Mass

作　　者：陈殿云[1,2] 任宝生[1,2] 

机构地区：[1]洛阳工学院 [2]西安交通大学

出　　处：《应用力学学报》1996年第4期88-94,共7页Chinese Journal of Applied Mechanics

基　　金：河南省自然科学基金

摘　　要：本文研究中心带有刚体质量外部固定铰支或活动铰支的环形薄板的非线性强迫振动。考虑板的弯曲变形、面内位移和几何非线性，用哈米尔顿原理建立板的运动方程，用Ｋａｎｔｏｒｏｖｉｃｈ平均法消去时间变量，然后用数值积分求得非线性振动的振幅随激振力的大小及激振力的频率而变化的关系。求解过程中用打靶法逐步改进未知参量，以保证边界条件的满足。最后讨论薄膜力、激振力的分布。This paper investigates nonlinear forced vibration of annular plates, whose inner edge is connected with a concentric rigid mass and the outer edge is movably or immovably hinged. The effects of bending deformation, in plane motion and geometric nonlinearity are considered and the governing equations of motion are obtained by using Hamiltons principle. The Kantorovich averaging method is used to eliminate the time variable from the equations of motion. Numerical integration is employed to obtain the solutions of the equations. To assure satisfaction of boundary conditions, shooting method is utilized to improve the iteration vector. Responses of several differently distributed exciting forces are selected to be calculated and plotted in the figures. It has been found that the membrane forces of the plate with immovable hinged edge are much biger than those of the plate with movable hinged edge, and that, the nearer to the center of the plate the exciting forces concentrate, the larger the vibration magnitudes of the plates.

关 键 词：环形板 非线性 强迫振动 数值积分 打靶法 

分 类 号：O322[理学—一般力学与力学基础]