Asmptoticaliy Approximate Model Equations for Weakly Nonlinear Long Waves in Compressible Elastic Rods and their Comparisons with Other Simplified Model Equations
From MaRDI portal
Publication:4467924
DOI10.1177/1081286503035199zbMath1167.74464OpenAlexW1988403756MaRDI QIDQ4467924
Publication date: 10 June 2004
Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1177/1081286503035199
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear waves in solid mechanics (74J30) Solitary waves in solid mechanics (74J35)
Related Items (22)
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 ⋮ Analytical study on the stress-induced phase or variant transformation in slender shape memory alloy samples ⋮ Buckling and post-buckling of a compressible slab under combined axial compression and lateral load ⋮ Phase transitions in a slender cylinder composed of an incompressible elastic material. I. Asymptotic model equation ⋮ Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and cubic nonlinearities ⋮ 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 ⋮ Weakly nonlinear waves propagating in hyperelastic cylindrical rod tranquility of compressible Murnaghan material ⋮ An analytical study on the instability phenomena during the phase transitions in a thin strip under uniaxial tension ⋮ 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 ⋮ Three kinds of nonlinear dispersive waves in elastic rods with finite deformation ⋮ Computing wrinkling and restabilization of stretched sheets based on a consistent finite-strain plate theory ⋮ On a three-dimensional axisymmetric boundary-value problem of nonlinear elastic deformation: asymptotic solution and exponentially small error ⋮ Corner instabilities in a slender nonlinearly elastic cylinder: analytical solutions and formation mechanism ⋮ Weakly-Nonlinear Solution of Coupled Boussinesq Equations and Radiating Solitary Waves ⋮ Solitons of dispersive wave steered from Navier-Bernoulli and Love's hypothesis in cylindrical elastic rod with compressible Murnaghan's materials ⋮ On Boussinesq-type models for long longitudinal waves in elastic rods ⋮ On solitonic solutions for the hyperelastic rod equation
Cites Work
- Unnamed Item
- Nonlinear axisymmetric waves in compressible hyperelastic rods: Long finite amplitude waves
- On waves in slender elastic rods
- Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
- Asymptotically approximate model equations for nonlinear dispersive waves in incompressible elastic rods
- Solitary waves in an inhomogeneous rod composed of a general hyperelastic material
- Nonlinear Waves in a Rod: Results for Incompressible Elastic Materials
- Solitary waves on nonlinear elastic rods. I
- Solitary-Wave Interactions in Elastic Rods
- Nonlinear travelling waves in a rod composed of a modified Mooney–Rivlin material. I. Bifurcation of critical points and the non–singular case
- Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
This page was built for publication: Asmptoticaliy Approximate Model Equations for Weakly Nonlinear Long Waves in Compressible Elastic Rods and their Comparisons with Other Simplified Model Equations
