A note on elliptical plate vibration modes as a bifurcation from circular plate modes

Abstract

The exact modes of vibration of a circular plate satisfy the geometrical boundary conditions of uniform elliptical plates in modified polar coordinates. In a previous investigation the exact modes of a clamped circular plate were used as shape functions in the Rayleigh-Ritz method to characterize the vibration of clamped elliptical plates. The mass and stiffness matrices were expressed in closed form and the resulting eigen value problems for the four mode categories of the elliptical plates were solved numerically. In the present investigation the computed variations of the plate frequencies with aspect ratio are used to study the similarities between the elliptical and circular plate modes. It is concluded that as the aspect ratio increases from unity, the axisymmetrical circular plate mode varies as a single elliptical plate mode, whereas the non-axisymmetrical circular plate mode splits up into two distinct elliptical plate modes.