FREE VIBRATIONS OF A PARABOLOID SHELL

Abstract

The paper presents an application of the method of the generator function. The method is used in the analytic investigation of the free vibrations of a parabolic antenna dish, which is considered as a thin shell. For solving the differential equation system of the vibration problem, the method of the generator function is applied. This method is based on the generalization of determinants and cofactors of quadratic matrices. In an illustrative example the natural frequencies of the paraboloid are compared with those of a circular plate having the same radius and material properties as the paraboloid, and also with those of the circular plate resting on a fictitious elastic foundation.