 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| Morozov N.F., Tovstik P.E., and Tovstik T.P., "Long-Wave Vibrations and Long Waves in an Anisotropic Plate," Mech. Solids. 55 (8), 1253-1266 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
8 |
Pages |
1253-1266 |
| DOI |
10.3103/S0025654420080166 |
| Title |
Long-Wave Vibrations and Long Waves in an Anisotropic Plate |
| Author(s) |
Morozov N.F. (Saint Petersburg State University, Saint Petersburg, 199034 Russia; Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, 199178Russia, morozov@nm1016.spb.edu)
Tovstik P.E. (Saint Petersburg State University, Saint Petersburg, 199034 Russia; Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, 199178Russia, peter.tovstik@mail.ru)
Tovstik T.P. (Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, 199178Russia, tovstik_t@mail.ru) |
| 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. |
| Keywords |
anisotropic heterogeneous plate, harmonic vibrations, plane waves, dispersion equation |
| Received |
17 March 2020 | Revised |
15 May 2020 | Accepted |
22 May 2020 |
| Link to Fulltext |
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