Vibration analysis of rectangular plates with edge V-notches

Abstract

A method is presented for accurately determining the natural frequencies of plates having V-notches along their edges. It is based on the Ritz method and utilizes two sets of admissible functions simultaneously, which are (1) algebraic polynomials from a mathematically complete set of functions, and (2) corner functions duplicating the boundary conditions along the edges of the notch, and describing the stress singularities at its sharp vertex exactly. The method is demonstrated for free, square plates with a single V-notch. The effects of corner functions on the convergence of solutions are shown through comprehensive convergence studies. The corner functions accelerate convergence of results significantly. Accurate numerical results for free vibration frequencies and nodal patterns are tabulated for V-notched square plates having notch angle α=5° or 30° at different locations and with various notch depths. These are the first known frequency and nodal pattern results available in the published literature for rectangular plates with V-notches.