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A Unique Formulation of Piecewise Exact Method to Analyze a Nonlinear Spring System under Harmonic Excitation

Published online by Cambridge University Press:  01 December 2014

P.-S. Xie  and
P.-J. Shih
P.-S. Xie
Affiliation:
School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou, China
P.-J. Shih*
Affiliation:
Department of Civil and Environmental Engineering, National University of Kaohsiung, Kaohsiung, Taiwan
*
* Corresponding author ([email protected]
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Abstract

This paper introduces a unique, efficient, and exact formulation for solving a single-degree-of-freedom system with nonlinear stiffness under a harmonic loading. This formulation is one kind of the piecewise exact method, and its benefit lies in providing the closed-form exact solution in each displacement segment. Since the exact solution is given in each segment, the continuity between two segments can be confirmed. Consequently, no instability errors affect the analysis. To determine the exact solutions in these segments, this research develops a technique that shifts the equilibrium points of the piecewise linear segments, which are discretized from a nonlinear stiffness curve, to new equilibrium points in order to satisfy the typical linear exact solution. Thus, positive- and negative-stiffness linear segments can be solved with this technique. This formulation saves roughly 60% of the calculation time (error < 10−10) as compared to the numerical approximation.

Keywords

Piecewise exact methodNonlinear springStep-by-step procedureThe newmark explicit method
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 3 , June 2015 , pp. 337 - 344
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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