An analytically solvable eigenvalue problem for the linear elasticity equations. | Zendy

David Day | Zendy; Louis A. Romero | Zendy

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An analytically solvable eigenvalue problem for the linear elasticity equations.

Author(s) -

David Day,

Louis A. Romero

Publication year - 2004

Language(s) - English

Resource type - Reports

DOI - 10.2172/975249

Subject(s) - eigenvalues and eigenvectors , cuboid , eigenfunction , linear elasticity , isotropy , elasticity (physics) , mathematics , boundary value problem , computation , mathematical analysis , vibration , geometry , physics , finite element method , structural engineering , algorithm , engineering , quantum mechanics , thermodynamics

Analytic solutions are useful for code verification. Structural vibration codes approximate solutions to the eigenvalue problem for the linear elasticity equations (Navier's equations). Unfortunately the verification method of 'manufactured solutions' does not apply to vibration problems. Verification books (for example [2]) tabulate a few of the lowest modes, but are not useful for computations of large numbers of modes. A closed form solution is presented here for all the eigenvalues and eigenfunctions for a cuboid solid with isotropic material properties. The boundary conditions correspond physically to a greased wall

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