Finite amplitude, free vibrations of an axisymmetric load supported by a highly elastic tubular shear spring
type: Item
instance of: scholarly article
title: Finite amplitude, free vibrations of an axisymmetric load supported by a highly elastic tubular shear spring
zbMATH Open document ID: 0840.73033
DOI: 10.1007/BF00041209
author: Millard F. Beatty
author: Rezaul A. Khan
published in: Journal of Elasticity
publication date: 1996-07-10T00:00:00Z
review text: The authors study free vibrational characteristics of a simple nonlinear mechanical system consisting of an axisymmetric rigid body supported by a highly elastic rubber tubular shear spring and subjected to axial, rotational, and coupled shearing motions. These elastic springs bonded on their inner and outer cylindrical surfaces to a rigid support are widely used in engineering structures as vibration isolation, shock suppression, and noise statement devices. Two classes of elastic tube materials are considered: a compressible material whose shear response is constant, and the incompressible Mooney-Rivlin material whose shear response is a quadratic function of the total amount of shear. For each material, the quasi-static elasticity problems are solved to determine the telescopic and gyratory shearing deformations needed to calculate the restoring force and torque exerted on the body. The motion of the tube itself and internal material damping is ignored. For the quadratic material, the free coupled shearing motion for which either the axial or the azimuthal shear deformation may be small is governed by a pair of equations of the Duffing and Hill types. The finite amplitude pure axial and pure rotational motions of the load are described by the classical nonlinear Duffing equation alone.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 753722
zbMATH Keywords: vibration isolation
zbMATH Keywords: compressible material
zbMATH Keywords: shear response
zbMATH Keywords: incompressible Mooney-Rivlin material
zbMATH Keywords: quasi-static elasticity problems
zbMATH Keywords: Duffing equation
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
cites work: Q3658881
cites work: Finite Amplitude Vibrations of a Body Supported by Simple Shear Springs
cites work: Finite amplitude, periodic motion of a body supported by arbitrary isotropic, elastic shear mountings
cites work: Stability of a body supported by a simple vehicular shear suspension system
cites work: Large elastic deformations of isotropic materials VI. Further results in the theory of torsion, shear and flexure
cites work: Axisymmetric finite anti-plane shear of compressible nonlinearly elastic circular tubes
cites work: Pure azimuthal shear of compressible non-linearly elastic circular tubes
cites work: Finite strain solutions for a compressible elastic solid
cites work: Finite deformations of compressible hyperelastic tubes subjected to circumferential shear
cites work: On free oscillations of elastic incompressible bodies in finite shear
cites work: Large shearing oscillations of incompressible nonlinearly elastic bodies
cites work: Simultaneous, finite, gyroscopic and radial oscillations of hyperelastic cylindrical tubes
cites work: Transverse deformations associated with rectilinear shear in elastic solids
cites work: Large amplitude oscillations of a tube of incompressible elastic material
cites work: On finite anti-plane shear for compressible elastic circular tube
cites work: Q5846205
cites work: Q4692663
cites work: Q5540675
cites work: Some general results in the theory of large elastic deformations
cites work: COMBINED AXIAL AND TORSIONAL SHEAR OF A TUBE OF INCOMPRESSIBLE ISOTROPIC ELASTIC MATERIAL
description: scientific article; zbMATH DE number 753722