Acceleration wave propagation in hyperelastic rods of variable cross- section

DOI10.1016/0165-2125(82)90033-6zbMath0479.73023OpenAlexW2020353632MaRDI QIDQ1162194

Alan Jeffrey

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0165-2125(82)90033-6

zbMATH Keywords

generalized Riccati equationcomparison equationsexistence of thresholdsthree theoremstransport equation for wave intensitywave intensity become infinite

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Impact in solid mechanics (74M20) Waves in solid mechanics (74J99)

Related Items (15)

Invariant solutions and constitutive laws for a nonlinear elastic rod of variable cross-section ⋮ On the decoupling problem of general quasilinear first order systems in two independent variables ⋮ Lie group analysis and Riemann problems for a \(2\times 2\) system of balance laws ⋮ Equivalence transformations of quasilinear first order systems and reduction to autonomous and homogeneous form ⋮ Subsymmetries and their properties ⋮ On global solvability of one-dimensional quasilinear wave equations ⋮ Linearization of nonautonomous models describing fluid filled elastic tubes and nonlinear elastic rods with variable cross-section ⋮ Local and nonlocal symmetries for nonlinear telegraph equation ⋮ New conservation laws obtained directly from symmetry action on a known conservation law ⋮ On the existence of conservation law multiplier for partial differential equations ⋮ On the inverse variational problem for one class of quasilinear equations ⋮ Conservation laws for nonlinear telegraph equations ⋮ Reduction of nonhomogeneous quasilinear 2×2 systems to homogeneous and autonomous form ⋮ Comparing symmetries and conservation laws of nonlinear telegraph equations ⋮ Complete group classification of a class of nonlinear wave equations

Cites Work

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• Formation of shock waves in hyperelastic solids
• On the local and global behavior of acceleration waves
• On the local and global behavior of acceleration waves: Addendum, asymptotic behavior
• Kirchhoff’s problem for nonlinearly elastic rods
• On the breaking of water waves on a sloping beach of arbitrary shape
• 19.—Propagation of Weak Discontinuities in a Layered Hyperelastic Half-space
• 5.—Qualitative Aspects of the Spatial Deformation of Non-linearly Elastic Rods.
• Travelling waves in hyperelastic rods
• ONE-DIMENSIONAL NON-LINEAR WAVE PROPAGATION IN INCOMPRESSIBLE ELASTIC MATERIALS

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