Similarity representation of wave propagation in a nonlinear viscoelastic rod on a group theoretic basis

DOI10.1016/0307-904X(86)90060-0zbMath0606.73029OpenAlexW2026888543MaRDI QIDQ1084912

Waclaw Frydrychowicz, Mansa C. Singh

Publication date: 1986

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0307-904x(86)90060-0

zbMATH Keywords

invariancesimilarity transformationsboundary and initial conditionsmultiparameter dimensional group of transformationsnonlinear viscoelastic rodordinary nonlinear boundary value problemset of simultaneous nonlinear partial differential equationsSimilarity representationvelocity impact

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Waves in solid mechanics (74J99)

Related Items

Riemann invariants-like solutions for a class of rate-type materials ⋮ A method for determining exact solutions to a class of nonlinear models based on introduction of differential constraints ⋮ A moving boundary hyperbolic problem for a stress impact in a bar of rate-type material ⋮ Discontinuous solutions of nonlinear wave phenomena by similarity approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Group theoretic analysis and similarity solution for a nonlinear viscous rod subjected to time dependent velocity impact
• Group theoretic and similarity analysis of hyperbolic partial differential equations
• Similarity methods for differential equations
• Similarity solutions to some non-linear impact problems
• Some matrix aspects of generalized dimensional analysis
• Solution of Troesch's two-point boundary value problem by a combination of techniques
• Nonlinear partial differential equations in engineering. Vol. II
• Dispersion of free harmonic waves in fiber- reinforced composites.

This page was built for publication: Similarity representation of wave propagation in a nonlinear viscoelastic rod on a group theoretic basis