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A composite hyperbolic equation for plate extension


A composite hyperbolic equation for plate extension Thumbnail



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
Keywords elasticity, composite equation, asymptotic, plate extension, Rayleigh wave, quasi-front
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