An analytical study of the non-linear vibrations of cylindrical shells

被引：28
|
作者：
Mahmoudkhani, S. [1 ]
Navazi, H. M. [1 ]
Haddadpour, H. [1 ]
机构：
[1] Sharif Univ Tech, Dept Aerosp Engn, Tehran, Iran
来源：
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2011年 / 46卷 / 10期
关键词：
Multiple scales; Primary resonance; Companion mode; Cylindrical shell; Functionally graded; FLEXURAL VIBRATION; FORCED VIBRATIONS; PLATES; FLUID;
D O I：
10.1016/j.ijnonlinmec.2011.07.012
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The primary resonance response of simply supported circular cylindrical shells is investigated using the perturbation method. Donnell's non-linear shallow-shell theory is used to derive the governing partial differential equations of motion. The Galerkin technique is then employed to transform the equations of motion into a set of temporal ordinary differential equations. Considering only the primary resonance case, the method of multiple scales is used to study the periodic solutions and their stability. The necessary and sufficient conditions for appearance of the so-called companion mode are also discussed. To this end, a range of the possible multi-mode solution is obtained for response and excitation amplitudes and also excitation frequency as a function of damping, geometry and material properties of the shell. Parametric studies are performed to illustrate the effect of different values of thickness, length and material composition on the possibility of the companion mode participation in primary resonance response. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1361 / 1372
页数：12
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