Multi-level residue harmonic balance solution for the nonlinear natural frequency of axially loaded beams with an internal hinge

Hasan, Abu; Rahman, Mohammad Shaifur; Lee, Y. Y.; Leung, A.Y.T.

doi:10.1080/15376494.2016.1227492

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2020

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“…Consequently, the quest for accurate behavior of the nonlinear dynamical systems led to the development of many analytical approximations. In the literature, several analytical approximate methods are found such as perturbation, 7,8 homotopy analysis, 9,10 homotopy perturbation, 11,12 variational iteration, 13,14 harmonic balance (HBM), [15][16][17][18] etc.…”

Section: Introductionmentioning

confidence: 99%

A modified harmonic balance method for solving forced vibration problems with strong nonlinearity

Ullah

Rahman

Uddin

2020

Journal of Low Frequency Noise, Vibration and Active Control

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In this paper, a modified harmonic balance method is presented to solve nonlinear forced vibration problems. A set of nonlinear algebraic equations appears among the unknown coefficients of harmonic terms and the frequency of the forcing term. Usually a numerical method is used to solve them. In this article, a set of linear algebraic equations is solved together with a nonlinear one. The solution obtained by the proposed method has been compared to those obtained by variational and numerical methods. The results show good agreement with the results obtained by both methods mentioned above.

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