Shape optimization for the eigenfrequency of the plate
Copyright policy )Shape optimization for the eigenfrequency of the plate
Abstract In this paper, we consider an eigenvalue problem for the biharmonic operator that describes the transverse vibrations of the plate. Under the imposed boundary conditions, the eigenvalues of this operator are indeed eigenfrequencies of the clamped plate. The domain of the plate is taken variable and the domain functional, involving an eigenfrequency, is studied. A new formula for an eigenfrequency is proved, the first variation of the functional with respect to the domain is calculated, and the necessary condition for an optimal shape is derived. New explicit formulas are obtained for the eigenfrequency in the optimal domain in some particular cases.
- Azerbaijan National Academy of Sciences Azerbaijan
- Institute of Mathematics and Mechanics Azerbaijan
- Azerbaijan University Azerbaijan
- Baku State University Azerbaijan
clamped plate, support function, Optimization of shapes other than minimal surfaces, Methods involving semicontinuity and convergence; relaxation, domain variation, shape optimization, eigenvalue problem, Variational methods for eigenvalues of operators, eigenfrequency
clamped plate, support function, Optimization of shapes other than minimal surfaces, Methods involving semicontinuity and convergence; relaxation, domain variation, shape optimization, eigenvalue problem, Variational methods for eigenvalues of operators, eigenfrequency
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