Continuous systems with odd nonlinearities: A general solution procedure
type: Item
instance of: scholarly article
title: Continuous systems with odd nonlinearities: A general solution procedure
zbMATH Open document ID: 0913.73043
author: Mehmet Yılmaz
author: Mehmet Pakdemirli
author: Hakan Boyacı
published in: Mathematical \& Computational Applications
publication date: 1999-03-02T00:00:00Z
review text: Summary: We consider a general equation of motion with odd nonlinearities. The nonlinearities of third and fifth order are represented in the form of arbitrary operators. The equation of motion, in its general form, can model a class of partial differential equations describing vibrations of continuous systems. Approximate analytical solutions are sought using the method of multiple scales and a perturbation technique. Forced vibrations with viscous damping are considered, and frequency-response relation is derived in its most general form. Finally, we give an application to a specific problem.
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 1229962
zbMATH Keywords: approximate analytical solutions
zbMATH Keywords: forced vibrations
zbMATH Keywords: nonlinearities of third and fifth order
zbMATH Keywords: method of multiple scales
zbMATH Keywords: perturbation technique
zbMATH Keywords: viscous damping
zbMATH Keywords: frequency-response relation
MaRDI profile type: Publication
full work available at URL: mca2020085
OpenAlex ID: W2368679239
DOI: 10.3390/MCA2020085
description: scientific article; zbMATH DE number 1229962