The mathematical principles of vibration reductor
type: Item
instance of: scholarly article
title: The mathematical principles of vibration reductor
zbMATH Open document ID: 0604.70048
DOI: 10.1007/BF01898225
author: Ting-he Lu
author: Jun Jin
author: Yong-zhen Hang
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1986-01-01T00:00:00Z
review text: The vibration reductor is modelled in this paper by the system of equation: \[ \ddot x_ 1+\phi (\dot x_ 1)+k_ 1(x_ 1-x_ 2)=0,\quad \ddot x_ 2+c\dot x_ 1+k_ 2(x_ 2-x_ 1)=0. \] \(x_ 1\) is the coordinate of the (one-dimensional) motion of the machine, \(x_ 2\) is that of the coupled vibration reductor. \(k_ 1\), c, \(k_ 2\) are constants. No particular statement is made about the function \(\phi\) (ẋ\({}_ 1)\). The aim of the paper is to choose the above constants so that the zero solution of the given equations is globally asymptotically stable. Four cases of certain inequalities must be studied. To this end some lemmas of Plies are used.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70J99
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 3976444
zbMATH Keywords: vibration reductor
zbMATH Keywords: coupled vibration reductor
zbMATH Keywords: zero solution
zbMATH Keywords: globally asymptotically stable
reviewed by: Á. P. Bosznay
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01898225
OpenAlex ID: W2044118048
description: scientific article; zbMATH DE number 3976444