非线性振动分析中的正交函数法

Nonlinear Oscillation Analysis by an Orthogonal Function Method

本文根据谐波平衡法假设周期解的基本思想，提出了一种分析非线性振动特性的正交函数法。将位移展开为谐波的级数形式，根据线性模态和三角级数的正交性导出了一组形式简单的特征方程。有效地解决了平方非线性系统存在漂移项的困难，算例表明：本文方法精度高，收敛快，工作量小。

In this paper, an orthogonal function method is presented based on the idea to suppose periodic solution with the method of harmonic balance. The displace- ment is expressed in the form of trigonometric functions, a group of simplified eigenequations are obtained by the use of orthogonarity of trigonometric functions and linear modes. The method overcomes the difficulty of a drift term existing in systems with quadratic nonlinearities. The calculation examples show that the method has the advantages of high calculation precision, high convergence speed and little calculation work.