The virtual friction of a sphere vibrating in an elastic medium
type: Item
instance of: scholarly article
title: The virtual friction of a sphere vibrating in an elastic medium
zbMATH Open document ID: 0656.73053
DOI: 10.1007/BF00281346
author: Piero Villaggio
published in: Archive for Rational Mechanics and Analysis
publication date: 1988-01-01T00:00:00Z
review text: The author studies a basic model of elasto-dynamic interaction: A rigid sphere is completely immerged in a surrounding isotropic linear elastic medium and oscillates harmonically. Two special cases are considered: Pure translational and pure rotational vibrations, respectively. A solution method due to Lamb is used for the calculation of the force (torque) which must be applied to the sphere in order to maintain the assumed translational (rotational) harmonic motion. This force (torque) consists of an elastic part and a virtual viscous (frictional) part. Additionally the energy lost due to the generation of elastic waves is calculated and conditions for the existence of aperiodic motions are established.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 4072539
zbMATH Keywords: soil-structure interaction
zbMATH Keywords: elasto-dynamic interaction
zbMATH Keywords: rigid sphere
zbMATH Keywords: completely immerged
zbMATH Keywords: surrounding isotropic linear elastic medium
zbMATH Keywords: oscillates harmonically
zbMATH Keywords: Pure translational
zbMATH Keywords: pure rotational vibrations
zbMATH Keywords: torque
zbMATH Keywords: energy lost
zbMATH Keywords: existence of aperiodic motions
reviewed by: Hans Bufler
MaRDI profile type: Publication
cites work: Q5838364
cites work: Q5784840
cites work: Q5804722
cites work: Isoperimetric Inequalities in Mathematical Physics. (AM-27)
cites work: Q5533735
cites work: Isoperimetric Inequalities and Their Applications
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description: scientific article; zbMATH DE number 4072539