Integral identities for bi-Laplacian problems and their application to vibrating plates (Q383989)

The present paper deals with the bi-Laplacian eigenvalue problems for the Dirichlet, Navier, and simply supported boundary conditions. The simply supported boundary condition is converted into a simpler new one. Then the corresponding three boundary integral identities are derived for the Dirichlet, Navier, and simply supported boundary conditions, which are applied to plate vibration problems. It is proved that the first natural frequency of a simply supported plate strictly increases with Poisson's ratio.