研究强非线性振动问题的最简规范形方法  

Research on Strongly Nonlinear Dynamic System by Simplest Normal Form Method

作　　者：张琪昌[1] 王炜[1] 郝淑英[2] 

机构地区：[1]天津大学,天津300072 [2]天津理工大学,天津300191

出　　处：《应用力学学报》2008年第4期698-702,741,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10372068);博士点基金(20060056005)

摘　　要：提出了一种应用最简规范形理论研究强非线性振动问题稳态渐近解的方法。最简规范形理论可以有效地化简传统规范形中的高阶项成分,复规范形方法的特点是简化矩阵分析的繁杂性,引入待定瞬时固有频率法则是将规范形理论的适用范围拓展至用于获取强非线性振动问题的稳态渐近解。结合上述特点,本文的改进方法克服了原有待定瞬时固有频率法在处理高阶传统规范形问题上遇到的计算复杂性问题。数值结果也表明本文方法更为简便、有效且具有更高的计算精度。New approach for the asymptotic solutions of strongly nonlinear oscillation system is presented with the simplest normal form method (SNF). The merit of the SNF method enables to reduce the highest order in conventional normal form (CNF) expression, the merit of complex normal form avoids the lengthy matrix deduction, and merit of introducing the undecided instantaneous fundamental frequency expands the normal form theory to the field of strongly nonlinear dynamic system for the accurate asymptotic solution. By all these merits, the new method solves the difficulty of handling the high order conventional normal form terms in the former research. The numerical results show that the new method is easier, more efficient and more accurate.

关 键 词：最简规范形 传统规范形 强非线性 渐近解 

分 类 号：O322[理学—一般力学与力学基础]