V.V.Meleshko, S.O.Papkov Bending vibration of the rectangular elastic plates with free edges: from Chladni (1809) and Ritz (1909) to the present day |
Acoustic bulletin, Vol. 12 ¹ 4, (2009) |
| A classic problem on vibration of the plate with free edges has been considered. On the base of the superposition method, its solving has been reduced to a homogeneous quasiregular infinite system of linear algebraic equations. Plate's eigenfrequencies have been found using the sufficient condition for existence of a limited solution of a quasiregular system. The nontrivial solutions of the system corresponding to these frequencies have been constructed by analyzing the asymptotic behavior of the unknown values, that allow the obtaining of analytical representations for vibration eigenforms. The accuracy of satisfying of the homogeneous boundary conditions has been studied and theoretical data have been compared with the experimental ones. |
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KEY WORDS: thin plate, natural vibrations, Chladni’s figures, the Ritz method, infinite linear system, quasiregularity |
| TEXT LANGUAGE: Russian |