The Melnikov criterion of instability for random rocking dynamics of a rigid block with an attached secondary structure
type: Item
instance of: scholarly article
title: The Melnikov criterion of instability for random rocking dynamics of a rigid block with an attached secondary structure
zbMATH Open document ID: 1197.74057
author: J. Blot
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-01-12T00:00:00Z
review text: The author investigates the dynamic behavior of a structure consisting of a rectangular symmetric rigid block (or a frame) with an attached chain of point masses coupled by linear viscoelastic suspensions and moving along the vertical axis of symmetry of the block. Assuming rigid foundation, large friction to prevent sliding, and the Newton restitution law at impact, the only possible response of the structure is rocking about the corners of the block accompanied by relative oscillations of the secondary structure. The problem of rocking is nonlinear even for the simple case of the planar response of a slender rigid uniform rectangular block on a flat rigid horizontal foundation. The nonlinearity is due to the impact occurring when the corner of rotation switches from one side of the block to the other. It is shown that under some non-restrictive assumptions, the rigid model is acceptable, but the condition of stability depends on the parameters of the secondary structure. Motion is excited by random acceleration of the ground; instability is associated with overturning of the overall structure. The condition of instability is constructed by the stochastic Melnikov method.
Mathematics Subject Classification ID: 74H50
Mathematics Subject Classification ID: 74H55
zbMATH DE Number: 5656669
zbMATH Keywords: stochastic systems
zbMATH Keywords: hybrid systems
zbMATH Keywords: Newton restitution law
zbMATH Keywords: impact
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2008.12.001
OpenAlex ID: W2038252231
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DOI: 10.1016/J.NONRWA.2008.12.001
description: scientific article; zbMATH DE number 5656669