Archive of Applied Mechanics

, Volume 89, Issue 11, pp 2265–2279 | Cite as

Analytical approximate solutions for asymmetric conservative oscillators

  • Weijia Liu
  • Baisheng WuEmail author
  • Xin Chen
  • Weidong Zhu


This paper focuses on the construction of analytical approximate solutions for an asymmetric conservative single-degree-of-freedom oscillator. First, based on the asymmetric oscillator, two symmetric ones are introduced; then, the second-order Newton iteration method and the harmonic balance method are applied to the two oscillators, respectively; finally, the analytical approximate solutions of the asymmetric oscillator are constructed and expressed by the oscillation amplitudes. Each iterative step needs the Fourier series representations of the restoring force functions and their first and second derivatives, of the two symmetric oscillators. Using only one iterative step can obtain accurate analytical approximate solution valid for a large range of oscillation amplitudes. Two examples are presented to illustrate use and high accuracy of the proposed approach.


Conservative oscillator Asymmetric nonlinearity Analytical approximation Second-order Newton iteration Harmonic balance 



The work was supported by the National Natural Science Foundation of China (Grant No. 11672118) and the Department of Education of Guangdong Province of China (Grant No. 2017KQNCX059).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electro-Mechanical EngineeringGuangdong University of TechnologyGuangzhouPeople’s Republic of China
  2. 2.Department of Mechanical EngineeringUniversity of Maryland, Baltimore CountyBaltimoreUSA

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