M.Ya.Barnyak, B.Soltannia A projection method for solving the problem on natural vibrations of the fixed plate |
Acoustic bulletin, Vol. 12 ¹ 1, (2009) |
| The paper deals with the problem on natural vibrations of the elastic plate with a fixed boundary. To solve this problem a projective method is suggested that is based on the Trefts method for solving the Dirichlet problems for the Helmholtz equation and r.m.s. value method for solving auxiliary spectral boundary problems with a parameter in the boundary condition. As a result, the solution has been developed that exactly satisfies the equation inside the domain and approximately (to within six-eight significant figures) - boundary conditions of the problem. As an example, the first 24 eigenvalues and eigenfunctions in the problem for the elliptic and superelliptic plates have been specified. |
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KEY WORDS: natural vibration, eigenfrequencies, elastic plate, a projection method |
| TEXT LANGUAGE: Russian |