A composite hyperbolic equation for plate extension

Kaplunov

doi:10.1016/j.mechrescom.2019.06.008

A composite hyperbolic equation for plate extension

Kaplunov

Authors

Julius Kaplunov j.kaplunov@keele.ac.uk

Abstract

A fourth-order inhomogeneous hyperbolic equation modeling the symmetric motion of a thin elastic plate subject to shear stresses prescribed along its faces is derived. The shortened forms of this equation govern the quasi-front, i.e. dispersive wave-front of longitudinal waves and the Rayleigh wave front at long-wave, low-frequency and short-wave, high-frequency limits, respectively. Comparison with exact plane strain solutions for both free and forced vibrations demonstrates that the derived equation is also applicable over the intermediate region where a typical wave length is of order the plate thickness.

Acceptance Date	Jun 29, 2019
Publication Date	Jun 29, 2019
Journal	Mechanics Research Communications
Print ISSN	0093-6413
Publisher	Elsevier
Pages	64-67
DOI	https://doi.org/10.1016/j.mechrescom.2019.06.008
Keywords	elasticity, composite equation, asymptotic, plate extension, Rayleigh wave, quasi-front
Publisher URL	https://doi.org/10.1016/j.mechrescom.2019.06.008