A composite hyperbolic equation for plate extension

•Fourth-order composite equation for plate extension.•Quasi-front, Rayleigh wave-front.•Comparison with exact plane strain solution.•Pseudo-differential operator in the expression for the external load. A fourth-order inhomogeneous hyperbolic equation modeling the symmetric motion of a thin elastic...

Full description

Saved in:
Bibliographic Details
Published in:Mechanics research communications 2019-07, Vol.99, p.64-67
Main Authors: Erbaş, Barış, Kaplunov, Julius, Palsü, Melike
Format: Article
Language:English
Subjects:
Asymptotic
Composite equation
Elasticity
Plate extension
Quasi-front
Rayleigh wave
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•Fourth-order composite equation for plate extension.•Quasi-front, Rayleigh wave-front.•Comparison with exact plane strain solution.•Pseudo-differential operator in the expression for the external load. 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.
ISSN:0093-6413
1873-3972
DOI:10.1016/j.mechrescom.2019.06.008