Vibration of Plates with Constrained V-Notches or Cracks

Abstract

This paper reports the first known free vibration solutions for thin circular plates with V-notches having various edge conditions. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets include: (1) mathematically complete algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained; and (2) corner functions which account for the bending moment singularities at the sharp re-entrant corner of the V-notch. Extensive convergence studies summarized herein confirm that the corner functions substantially enhance the convergence and accuracy of nondimensional frequencies for circular plates having a free circumferential edge and various combinations edge conditions of the V-notch. Accurate (five significant figures) frequencies are presented for clamped-free, clamped-hinged, and hinged-free notches for the spectra of notch angles (1°,5°,10°,30°,60°,90°), causing a re-entrant vertex corner of the radial edges. For very small notch angles, a