样条函数双向迭代法分析薄板的振动特性

本文将康特洛维奇方法推广应用于板的几何非线性振动特性分析,也适用于线性振动特性分析。将振型函数展开为双向B 样条函数的级数,由哈密顿原理导出两组特征方程。这种方法大大地减少了所需要的计算机内存和计算时间,可在微机上进行运算。通过算例表明,该方法具有很高的计算速度和精度,可推广应用于非规则板和柱壳的线性及非线性振动特性分析。

Analysing the Characteristics of Geometric Nonlinear Vibration of Thin Plate with Spline and Bidirectional Iteration

In this paper,Kantorovich method is extended to analyse the characteristicsof geometric nonlinear vibration of plates,as well as to analyse that of linearvibration.The function of vibration mode is expanded into a series of bidirec-tional B-Splines.Two groups of eigenequations are obtained with Hamilton'sprinciple.The computer storage capacity will be largely reduced,and the time ofcalculation significantly saved.The calculation may be carried out on a microcomputer.The calculation examples show that the method has the advantage ofhigh calculation speed and precision.It can be extended for analysing thecharacteristics of linear and nonlinear vibration of irregular plates and cylindricalshells.