  Vibrations of structures subjected to concentrated point loads have many
applications in mechanical engineering. Experiments are expensive and numerical
methods are often used for simulations. In this paper, we consider the plate
vibration with nonlinear dependence on the eigen-parameter. The problem is
formulated as the eigenvalue problem of a holomorphic Fredholm operator
function. The Bogner-Fox-Schmit element is used for the discretization and the
spectral indicator method is employed to compute the eigenvalues. The
convergence is proved using the abstract approximation theory of Karma.
Numerical examples are presented for validations.
