Some nonlinear dispersive waves arising in compressible hyperelastic plates
نویسنده
چکیده
In this paper we study finite deformations in a pre-stressed, hyperelastic compressible plate. For small-amplitude nonlinear waves, we obtain equations that involve an amplitude parameter ε. Using an asymptotic perturbation technique, we derive a new family of two-dimensional nonlinear dispersive equations. This family includes the KdV, Kadomtsev-Petviashvili and Camassa-Holm equations.
منابع مشابه
H−perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation
We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R). In particular, the supersonic solitary shock w...
متن کاملOn the Integrability of a Class of Nonlinear Dispersive Wave Equations
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.
متن کاملGlobal Weak Solutions to a Generalized Hyperelastic-rod Wave Equation
We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.
متن کاملNonlinear transverse waves in deformed dispersive solids
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without recourse to a microstructure or a special geometry. As a result, nonlinear and dispersive waves can travel in the bulk of such solids, and special waves emerge, so...
متن کاملFinite amplitude elastic waves propagating in compressible solids.
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical stress tensor describing a Stokesian fluid and is commonly used in nonlinear acoustics. The aim of this research is to derive the corresponding general equat...
متن کامل