TY - JOUR

T1 - Long-Wave Vibrations and Long Waves in an Anisotropic Plate

AU - Morozov, N. F.

AU - Tovstik, P. E.

AU - Tovstik, T. P.

N1 - Publisher Copyright: © 2020, Allerton Press, Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - Abstract: Free vibrations and plane waves are analyzed in the linear approximation for a thin elastic, anisotropic infinite plate having constant thickness. A general anisotropy described by 21 elastic moduli is considered. It is assumed that the moduli of elasticity and density are independent in the tangential coordinates but can depend on the coordinate along the thickness of the plate. Multilayer and functionally gradient plates are also considered. Assuming that the wavelength significantly exceeds the thickness of the plate, an asymptotic power expansion is obtained for a small thickness parameter for a harmonic solution of the system using the three-dimensional equations in tangential coordinates provided by the elasticity theory. For fixed values of wave numbers, there are only three long-wave solutions available: one low-frequency bending and two shearing ones. Dispersion equations are obtained for these solutions with accuracy to the terms of the second order of smallness in the dimensionless thickness. Bending solutions are characterized by a strong dependence of frequency on the wavelength, while the tangential waves propagate with low dispersion. Particular types of anisotropy are considered.

AB - Abstract: Free vibrations and plane waves are analyzed in the linear approximation for a thin elastic, anisotropic infinite plate having constant thickness. A general anisotropy described by 21 elastic moduli is considered. It is assumed that the moduli of elasticity and density are independent in the tangential coordinates but can depend on the coordinate along the thickness of the plate. Multilayer and functionally gradient plates are also considered. Assuming that the wavelength significantly exceeds the thickness of the plate, an asymptotic power expansion is obtained for a small thickness parameter for a harmonic solution of the system using the three-dimensional equations in tangential coordinates provided by the elasticity theory. For fixed values of wave numbers, there are only three long-wave solutions available: one low-frequency bending and two shearing ones. Dispersion equations are obtained for these solutions with accuracy to the terms of the second order of smallness in the dimensionless thickness. Bending solutions are characterized by a strong dependence of frequency on the wavelength, while the tangential waves propagate with low dispersion. Particular types of anisotropy are considered.

KW - anisotropic heterogeneous plate

KW - dispersion equation

KW - harmonic vibrations

KW - plane waves

UR - http://www.scopus.com/inward/record.url?scp=85101776642&partnerID=8YFLogxK

U2 - 10.3103/S0025654420080166

DO - 10.3103/S0025654420080166

M3 - Article

AN - SCOPUS:85101776642

VL - 55

SP - 1253

EP - 1266

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 0025-6544

IS - 8

ER -