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Все рубрики - Наука - Доклады / reports
Доклады / reports
17.01.2007
Eigenfrequencies spectrum of piezoelectric plate of an arbitrary shape
S. S. Nedorezov, O. Yu. Shmaliy, EIGENFREQUENCIES SPECTRUM OF PIEZOELECTRIC PLATE OF AN ARBITRARY SHAPE, Proc. of CAOL 2003, Sept. 16-20, Alushta, Crimea, Ukraine. – P. 219-222.

Accurate calculation of the frequency spectrum of the piezoelectric resonator is important if its anharmonics are employed in the multimode oscillatory system or as sensors of environment. Yet, such knowledge allows for making steps ahead avoiding problems with the frequency jumps. During several decades, the mathematical theory of eigenvibrations in resonators has undergone great changes forwarded to serve engineering needs. Even so, determination of eigenfrequencies sometimes is not accurate and new mathematical models are still of great interest.

In this report, an analysis is given of the eigenvibrations of a convex piezoelectric plate of an arbitrary shape. It is shown that the frequency spectrum is determined by the curvature of the boundary surface at the point of a maximum. The formula is derived for the eigenfrequencies of the vibrations, assuming arbitrary orientation of the direction of major curvature of a surface with respect to the self axes of a piezoelectric plate. It is noticed that anisotropy of the piezoelectric surface affects essentially the frequency spectrum that may be used to optimize the resonator performance.
 
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