Nonlinear oscillations with multiple forcing terms
type: Item
instance of: scholarly article
title: Nonlinear oscillations with multiple forcing terms
zbMATH Open document ID: 0627.70020
DOI: 10.1016/0020-7462(87)90035-7
author: George C. Atallah
author: James F. Geer
published in: International Journal of Non-Linear Mechanics
publication date: 1987-01-01T00:00:00Z
review text: The problem of determining the transient response of a nonlinear oscillator of the form ü\(+u=\epsilon f(u,\dot u)+E(t)\) is studied by the method of multiple time scales, using the symbolic computation system MACSYMA, when the excitation E(t) consists of a finite number of harmonic forcing terms. Here \(\epsilon\) is a small parameter and f(u,\D{u}) is a nonlinear function of its arguments. In particular, the Van der Pol and Duffing oscillators are studied in detail. It is found that when the forcing frequencies are not close to each other or close to the primary resonance of the system, then the response of the system is analogous to the behavior when only one forcing term is present. However, when the forcing frequencies are close to each other or close to the primary resonance, then the behavior is quite different, exhibiting certain oscillations not observed in the case of one forcing term.
Mathematics Subject Classification ID: 70K30
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 4020537
zbMATH Keywords: transient response
zbMATH Keywords: nonlinear oscillator
zbMATH Keywords: symbolic computation system
zbMATH Keywords: MACSYMA
zbMATH Keywords: Duffing oscillators
describes a project that uses: MACSYMA
MaRDI profile type: Publication
full work available at URL: 0020-7462(87)90035-7
OpenAlex ID: W2056378772
description: scientific article; zbMATH DE number 4020537