Large shearing oscillations of incompressible nonlinearly elastic bodies

DOI10.1007/BF00041137zbMath0551.73017OpenAlexW2034332376MaRDI QIDQ800747

Stuart S. Antman, Zhongheng Guo

Publication date: 1984

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00041137

zbMATH Keywords

Mooney-Rivlin materialbifurcation theoryincompressibleisotropicrelation between amplitude and frequencyshearing oscillationsSturmian theory

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Vibrations in dynamical problems in solid mechanics (74H45) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Higher-order nonlinear hyperbolic equations (35L75) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (11)

Some exact dynamic solutions in nonlinear elasticity ⋮ Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations ⋮ Finite amplitude, periodic motion of a body supported by arbitrary isotropic, elastic shear mountings ⋮ Inhomogeneous deformations in finite thermo-elasticity ⋮ A numerical study of a rotationally degenerate hyperbolic system. I: The Riemann problem ⋮ Some inhomogeneous motions and deformations within the context of a non- linear elastic solid ⋮ On an inhomogeneous deformation of a generalized neo-Hookean material ⋮ Finite azimuthal shear motions of a transversely isotropic compressible elastic and prestressed tube ⋮ Weakly Nonlinear Oscillations Superimposed on Finite Circumferential Shear of a Compressible, Nonlinear, Viscoelastic, Isotropic Material ⋮ Boundary layers in finite thermoelasticity ⋮ Finite amplitude, free vibrations of an axisymmetric load supported by a highly elastic tubular shear spring

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The equilibrium and post-buckling behavior of an elastic curve governed by a non-convex energy
• The elastica and the problem of the pure bending for a non-convex stored energy function
• The implicit function theorem and the global methods of cohomology
• Existence of solitary waves in higher dimensions
• Superlinear Sturm-Liouville problems
• Some aspects of nonlinear eigenvalue problems
• Some Bifurcation Theory for k -Set Contractions
• Nonlinear eigenvalue problems for the whirling of heavy elastic strings
• Shearing motions and the formation of shocks in an elastic circular tube
• Travelling waves in hyperelastic rods
• A theory for imperfect bifurcation via singularity theory
• Nonlinear Sturm-Liouville problems
• Perturbed bifurcation theory

This page was built for publication: Large shearing oscillations of incompressible nonlinearly elastic bodies