Nonlinear normal modes for vibratory systems under harmonic excitation
Nonlinear normal modes for vibratory systems under harmonic excitation
复制标题
DOI：
10.1016/j.jsv.2005.01.009
复制
发表时间：
2005-12-20
影响因子：
4.7
通讯作者：
Shaw, SW
中科院分区：
文献类型：
--
作者：
Jiang, D;Pierre, C;Shaw, SW
本文考虑用数值构造的不变流形来确定非线性振动系统在简谐激励下的响应。这种方法是作者先前发展的自由振动的非线性简正模(NNM)公式的扩展，其中一个模拟激励的辅助系统被用来增强运动方程。以这种方式，激励被简单地视为附加的系统状态，从而产生具有额外自由度(DOF)的系统，其响应是已知的。然后通过通常的NNM程序确定强迫系统的降阶模型，并使用基于Galerkin的有效求解方法来数值构造伴随不变流形。通过对一个简单的具有立方非线性的两自由度质量-弹簧系统和一个具有12自由度的离散化梁模型的频率响应的计算来说明这一技术。结果表明，该方法在接近共振的频率范围内提供了非常准确的响应。(C)2005爱思唯尔有限公司。保留所有权利。
This paper considers the use of numerically constructed invariant manifolds to determine the response of nonlinear vibratory systems that are subjected to harmonic excitation. The approach is an extension of the nonlinear normal mode (NNM) formulation previously developed by the authors for free oscillations, wherein an auxiliary system that models the excitation is used to augment the equations of motion. In this manner, the excitation is simply treated as an additional system state, yielding a system with an extra degree-of-freedom (dof), whose response is known. A reduced-order model for the forced system is then determined by the Usual NNM procedure, and an efficient Galerkin-based solution method is used to numerically construct the attendant invariant manifolds. The technique is illustrated by determining the frequency response for a simple 2-dof mass-spring system with cubic nonlinearities, and for a discretized beam model with 12 dof. The results show that this method provides very accurate responses over a range of frequencies near resonances. (c) 2005 Elsevier Ltd. All rights reserved.