Research Papers

Multiharmonic Response Analysis of Systems With Local Nonlinearities Based on Describing Functions and Linear Receptance

[+] Author and Article Information
F. Wei

Department of Space Engineering and Applied Mechanics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001, Chinaweifei1983@gmail.com

G. T. Zheng

School of Aerospace, Tsinghua University, P. O. Box 20, Beijing 100084, China

J. Vib. Acoust 132(3), 031004 (Apr 22, 2010) (6 pages) doi:10.1115/1.4000781 History: Received February 27, 2009; Revised September 11, 2009; Published April 22, 2010; Online April 22, 2010

Direct time integration methods are usually applied to determine the dynamic response of systems with local nonlinearities. Nevertheless, these methods are computationally expensive to predict the steady state response. To significantly reduce the computational effort, a new approach is proposed for the multiharmonic response analysis of dynamical systems with local nonlinearities. The approach is based on the describing function (DF) method and linear receptance data. With the DF method, the kinetic equations are converted into a set of complex algebraic equations. By using the linear receptance data, the dimension of the complex algebraic equations, which should be solved iteratively, are only related to nonlinear degrees of freedom (DOFs). A cantilever beam with a local nonlinear element is presented to show the procedure and performance of the proposed approach. The approach can greatly reduce the size and computational cost of the problem. Thus, it can be applicable to large-scale systems with local nonlinearities.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

An 18DOFs cantilever with a local nonlinear element

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Figure 2

Fundamental response of X17 for cubic stiffness nonlinearity

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Figure 3

Fundamental response of X17 for Coulomb damping

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Figure 4

Comparison for fundamental harmonic responses of X17 obtained by the current method and the fixed-interface CMS reduction method

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Figure 5

Comparison for fundamental harmonic and multiharmonic responses of X17

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Figure 6

Response of X17 for fundamental harmonic, multiharmonic, and the Newmark method



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