Continuous Systems with Odd Nonlinearities: A General Solution Procedure

Mehmet Pakdemirli; Hakan Boyacı; Mehmet Yılmaz

doi:10.3390/mca2020085

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Article

1 August 1997

Continuous Systems with Odd Nonlinearities: A General Solution Procedure

and

Department of Mechanical Engineering, Celal Bayar University, 45140 Muradiye, Manisa, Turkey

Authors to whom correspondence should be addressed.

Math. Comput. Appl.1997, 2(2), 85-90;https://doi.org/10.3390/mca2020085

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Abstract

A generalized equation of motion with odd nonlinearities is considered. The nonlinearities of cubic and fifth order are represented in the form of arbitrary operators. The equation of motion, in its general form, may model a class of partial differential equations encountered in vibrations of continuous systems. Approximate analytical solutions are sought using the method of multiple scales, a perturbation technique. Forced vibrations with viscous damping are considered. Frequency-response relation is derived in its most general form. Finally, an application to a specific problem is given.

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