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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 8/2017

10-05-2017 | Original

Higher-order approximate analytical solutions to nonlinear oscillatory systems arising in engineering problems

Authors: Mostafa Mohammadian, Mehdi Akbarzade

Published in: Archive of Applied Mechanics | Issue 8/2017

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Abstract

In the current paper, a powerful approximate analytical approach namely the global residue harmonic balance method (GRHBM) is proposed for obtaining higher-order approximate frequency and periodic solution of nonlinear conservative oscillatory systems arising in engineering problems. The proposed method has a main difference with other traditional harmonic balance methods such that the residual errors obtained in pervious order approximation are used in the present one. Comparison of the obtained results with the exact and numerical solution as well as well-known analytical methods such as Hamiltonian approach, Max–Min approach, variational approach, and He’s amplitude–frequency formulation reveals the correctness and usefulness of the GRHBM. It is shown that the results are valid for different values of system parameters and both small and large amplitudes. Hence, the method can be easily applied to other strongly nonlinear conservative oscillatory systems. Furthermore, using the obtained analytical expressions, the effect of amplitude and system parameters on nonlinear frequency is studied.
previous article A dynamic stiffness method for analysis of thermal effect on vibration and buckling of a laminated composite beam
next article Effect of dislocation absorption by surfaces on strain hardening of single crystalline thin films

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Appendix
Available only for authorised users
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Metadata
Title
Higher-order approximate analytical solutions to nonlinear oscillatory systems arising in engineering problems
Authors
Mostafa Mohammadian
Mehdi Akbarzade
Publication date
10-05-2017
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 8/2017
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-017-1252-y

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