Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods
From MaRDI portal
Publication:1811348
DOI10.1007/BF01182157zbMath1205.74081OpenAlexW2005506380MaRDI QIDQ1811348
Publication date: 10 June 2003
Published in: Acta Mechanica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01182157
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear waves in solid mechanics (74J30)
Related Items (23)
Weakly nonlinear long waves in a prestretched Blatz-Ko cylinder: solitary, kink and periodic waves ⋮ Non-existence of one-dimensional stress problems in solid-solid phase transitions and uniqueness conditions for incompressible phase-transforming materials ⋮ An asymptotic modeling and resolution framework for morphology evolutions of multiple-period post-buckling modes in bilayers ⋮ On constructing the analytical solutions for localizations in a slender cylinder composed of an incompressible hyperelastic material ⋮ Approximate modeling of wave processes in elastoplastic solids ⋮ Pitchfork and octopus bifurcations in a hyperelastic tube subjected to compression: Analytical post-bifurcation solutions and imperfection sensitivity ⋮ ANALYTICAL SOLUTIONS FOR THE POST-BUCKLING STATES OF AN INCOMPRESSIBLE HYPERELASTIC LAYER ⋮ Nonclassical Lie symmetry and conservation laws of the nonlinear time-fractional Korteweg–de Vries equation ⋮ Buckling and post-buckling of a compressible slab under combined axial compression and lateral load ⋮ Bifurcation to a corner-like formation in a slender nonlinearly elastic cylinder: asymptotic solution and mechanism ⋮ Phase transitions in a slender cylinder composed of an incompressible elastic material. I. Asymptotic model equation ⋮ Solitary waves in a slender tube composed of an incompressible nonlinear elastic material ⋮ Phase transitions induced by extension in a slender SMA cylinder: analytical solutions for the hysteresis loop based on a quasi-3D continuum model ⋮ Numerical simulation of propagation of solitary deformation waves in a compressible hyperelastic rod ⋮ Instabilities induced by phase transformation fronts coalescence during the phase transitions in a thin SMA layer: mechanism and analytical descriptions ⋮ Computing wrinkling and restabilization of stretched sheets based on a consistent finite-strain plate theory ⋮ The Gardner Equation in Elastodynamics ⋮ Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions ⋮ A developed damage constitutive model for circular steel tubes of reticulated shells ⋮ Corner instabilities in a slender nonlinearly elastic cylinder: analytical solutions and formation mechanism ⋮ Some interesting nonlinear dynamic behaviors of hyperelastic spherical membranes subjected to dynamic loads ⋮ Asmptoticaliy Approximate Model Equations for Weakly Nonlinear Long Waves in Compressible Elastic Rods and their Comparisons with Other Simplified Model Equations ⋮ On solitonic solutions for the hyperelastic rod equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlinear axisymmetric waves in compressible hyperelastic rods: Long finite amplitude waves
- On waves in slender elastic rods
- Nonlinear elastic waves in rods
- Nonlinear Waves in a Rod: Results for Incompressible Elastic Materials
- Solitary waves on nonlinear elastic rods. I
- Solitary-Wave Interactions in Elastic Rods
- Dispersive-dissipative solitons in nonlinear solids.
- Head-on collision between two solitary waves in a compressible Mooney-Rivlin elastic rod.
This page was built for publication: Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods
