Lie symmetry analysis and approximate solutions for nonlinear radial oscillations of an incompressible Mooney-Rivlin cylindrical tube

DOI10.1006/JMAA.2000.6748zbMath0976.34034OpenAlexW2067628320MaRDI QIDQ1570202

D. P. Mason, N. Roussos

Publication date: 23 October 2000

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6748

zbMATH Keywords

finite elasticitysymmetry breakingfirst integralLie point symmetriesnonlinear superpositionlimiting oscillations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Nonlinear elasticity (74B20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Applications of Lie groups to the sciences; explicit representations (22E70) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (5)

On Non-Linear Radial Oscillations of an Incompressible, Hyperelastic Spherical Shell ⋮ Radial oscillations of thin cylindrical and spherical shells: investigation of Lie point symmetries for arbitrary strain-energy functions ⋮ Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations ⋮ Nonlinear radial oscillations of a transversely isotropic hyperelastic incompressible tube ⋮ Small amplitude quasi-periodic solutions for the forced radial vibrations of cylindrical shells with incompressible materials

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