A composite hyperbolic equation for plate extension

Kaplunov

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.

Citation

Kaplunov. (2019). A composite hyperbolic equation for plate extension. Mechanics Research Communications, 64-67. https://doi.org/10.1016/j.mechrescom.2019.06.008

• 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