Analytical solution for general nonlinear continuous systems in a complex form

被引：10

作者：

Hosseini, S. A. A. ^{[1
]}

Zamanian, M. ^{[1
]}

机构：

[1] Tarbiat Moallem Kharazmi Univ, Fac Engn, Tehran, Iran

来源：

APPLIED MATHEMATICAL MODELLING | 2013年 / 37卷 / 03期

关键词：

Perturbation method; Method of multiple scales; Complex partial differential equations; General nonlinear continuous systems; 3-TO-ONE INTERNAL RESONANCES; CUBIC NONLINEARITIES; ROTATING SHAFT; FORCED VIBRATIONS;

D O I：

10.1016/j.apm.2012.03.042

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, the method of multiple scales is used to study free vibrations and primary resonances of geometrically nonlinear spatial continuous systems with general quadratic and cubic nonlinear operators in a complex form. It is found that in the free vibrations of general continuous systems in a complex form, both forward and backward modes are excited. This situation is in contrast to the primary resonances in which only forward modes are excited. Consequently, one may determine the form of solution before applying the multiple scales method to the equation. This analysis is applicable to general continuous systems with gyroscopic and Coriolis effects and includes many nonlinear problems as a special case. As an example of application of this general solution, free vibrations and primary resonances of a simply supported rotating shaft with stretching nonlinearity are considered. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1163 / 1169

页数：7

共 22 条

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