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- Publisher
- Springer Journals
- Copyright
- 2015 Pleiades Publishing, Ltd.
- ISSN
- 1063-7710
- eISSN
- 1562-6865
- DOI
- 10.1134/s106377101501008x
- Publisher site
- See Article on Publisher Site
Abstract
Abstract A new asymptotically exact solution is obtained for the problem of transverse vibrations of a rectangular orthotropic plate with free edges. The general solution to the vibration equation is constructed as the sum of Fourier series with unknown coefficients, which are related by a homogeneous quasi-regular infinite system of linear algebraic equations. Analysis of the infinite system makes it possible to determine the power-law asymptotics for a nontrivial solution to the system, which makes it possible to calculate the natural vibration frequencies and to construct the corresponding eigenmodes. Examples of numerical calculations for real materials are presented.
Journal
Acoustical Physics – Springer Journals
Published: Mar 1, 2015
Keywords: Acoustics