An analytically solvable eigenvalue problem for the linear elasticity equations.

Day, David Minot ; Romero, Louis Anthony

Sandia National Laboratories

关键词: Eigenfunctions;    Vibration-Mathematical Models.;    Elasticity;    Boundary Conditions;    Mechanical Vibrations Vibration-Mathematical Models.;   

DOI  :  10.2172/975249
RP-ID  :  SAND2004-3310
RP-ID  :  AC04-94AL85000
RP-ID  :  975249

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.