A generalized approach to coupled nonlinear vibrations of continuous systems
type: Item
instance of: scholarly article
title: A generalized approach to coupled nonlinear vibrations of continuous systems
zbMATH Open document ID: 0920.73216
published in: Mathematical \& Computational Applications
publication date: 1999-03-02T00:00:00Z
review text: Summary: We propose a mathematical model which covers many practical vibration problems for continuous systems. The equations of motion consist of two nonlinearly coupled partial differential equations. The quadratic and cubic nonlinearities as well as the linear part of the equations are represented by arbitrary operators. A perturbation approach (method of multiple time scales) has been applied directly to partial differential equations. The responses as well as the amplitude and phase modulation equations are found for the primary resonances of the external excitation and for the one-to-one internal resonances between the natural frequencies of the equations. The coefficients of amplitude and phase modulation equations are calculated in their most general form. Results are then applied to nonlinear cable vibrations for small sag-to-span ratios.
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 1229957
zbMATH Keywords: quadratic nonlinearities
zbMATH Keywords: method of multiple time scales
zbMATH Keywords: amplitude modulation
zbMATH Keywords: cubic nonlinearities
zbMATH Keywords: perturbation approach
zbMATH Keywords: phase modulation
zbMATH Keywords: primary resonances
zbMATH Keywords: one-to-one internal resonances
zbMATH Keywords: cable vibrations
author: Mehmet Pakdemirli
author: Hakan Boyacı
MaRDI profile type: Publication
full work available at URL: mca2030141
OpenAlex ID: W2346655770
DOI: 10.3390/MCA2030141
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description: scientific article; zbMATH DE number 1229957