Mathematical model of a multisectional vibration unit
type: Item
instance of: scholarly article
zbMATH Open document ID: 1074.70524
author: V. P. Nisons'kyj
author: I. I. Gerega
author: V. M. Shopa
publication date: 2001-11-04T00:00:00Z
Mathematics Subject Classification ID: 70E55
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 70H03
zbMATH DE Number: 1668326
zbMATH Keywords: vibrational machine
zbMATH Keywords: elastic joint
zbMATH Keywords: generalized coordinate
zbMATH Keywords: Lagrange equations
zbMATH Keywords: nonlinear diferential equations
MaRDI profile type: Publication
title: Mathematical model of a multisectional vibration unit
published in: Dopovidi Natsional'noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky
review text: The studied unit consists of \(N\) vibrational machines mounted on a common basement framework. The machines are jointed by elastic joints. The technological load is installed on the supporting mass. Equations of motion of the system are written using the Lagrange principle. Generalized coordinates of the system are coordinates of bodies and angles of their rotation. Motion of the unit is represented by a system of nonlinear ordinary diferential equations. Nonlinearity is introduced by dynamic characteristics of the power source, by dry friction in contact zones and periodic collisions of the technological load with working units, by the Sommerfeld effect and by self-synchronization of systems with two or more power sources. An example of construction of the matrix of differential equations for a particular unit is presented.
description: scientific article; zbMATH DE number 1668326