Group theoretic analysis and similarity solution for a nonlinear viscous rod subjected to time dependent velocity impact

DOI10.1016/0165-2125(86)90019-3zbMath0575.73027OpenAlexW2041356881MaRDI QIDQ1064115

Waclaw Frydrychowicz, Mansa C. Singh

Publication date: 1986

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0165-2125(86)90019-3

zbMATH Keywords

creepquasilinearization methodWhittaker functionsNorton's lawsimilarity transformationssecond order equationsnonlinear rodsystem of nonlinear ordinary differential equationsauxiliary conditionsClosed form solutionsconstant velocity impactfour parameter dimensional group of transformations, absolute invariants of the grouplinear rodNonlinear case is solved by a numerical approachnonlinear viscous rodpower series for weakly nonlinear casetime dependent velocity impactUnidirectional wave motionweakly nonlinear rod

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Impact in solid mechanics (74M20) Other special methods applied to PDEs (35A25)

Related Items (2)

Similarity representation of wave propagation in a nonlinear viscoelastic rod on a group theoretic basis ⋮ Discontinuous solutions of nonlinear wave phenomena by similarity approach

Cites Work

• Group theoretic and similarity analysis of hyperbolic partial differential equations
• Some exact solutions for wave propagation in viscoelastic, viscoplastic and electrical transmission lines
• Continuation in shooting methods for two-point boundary value problems
• Similarity solutions to some non-linear impact problems
• Similarity solution for the problem of an impact on a nonlinear viscoplastic rod
• Some matrix aspects of generalized dimensional analysis
• Longitudinal Impact on Viscoplastic Rods—Linear Stress-Strain Rate Law
• Reduction of the Number of Variables in Systems of Partial Differential Equations, with Auxiliary Conditions
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