Shape deformation for vibrating hinged plates

Davide Buoso; Pier Domenico Lamberti

doi:10.1002/mma.2858

Shape deformation for vibrating hinged plates

Davide Buoso, Pier Domenico Lamberti

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the biharmonic operator subject to homogeneous intermediate boundary conditions of Steklov-type. We prove an analyticity result for the dependence of the eigenvalues upon domain perturbation and compute the appropriate Hadamard-type formulas for the shape derivatives. Finally, we prove that balls are critical domains for the symmetric functions of multiple eigenvalues subject to volume constraint.

Original language	English
Pages (from-to)	237-244
Number of pages	8
Journal	Mathematical Methods in the Applied Sciences
Volume	37
Issue number	2
DOIs	https://doi.org/10.1002/mma.2858
Publication status	Published - 30 Jan 2014
Externally published	Yes

Keywords

biharmonic operator
domain perturbation
hinged plate
intermediate Steklov boundary conditions

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10.1002/mma.2858

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AB - We consider the biharmonic operator subject to homogeneous intermediate boundary conditions of Steklov-type. We prove an analyticity result for the dependence of the eigenvalues upon domain perturbation and compute the appropriate Hadamard-type formulas for the shape derivatives. Finally, we prove that balls are critical domains for the symmetric functions of multiple eigenvalues subject to volume constraint.

KW - biharmonic operator

KW - domain perturbation

KW - hinged plate

KW - intermediate Steklov boundary conditions

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DO - 10.1002/mma.2858

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

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Shape deformation for vibrating hinged plates

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Keywords

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