Influence of Stress Singularities on the Vibration of Rhombic Plates with V-Notches or Sharp Cracks

This study offers first known free vibration solutions for thin rhombic plates having V-notches or sharp cracks. A single-field energy-based Ritz procedure is employed with the dynamical energies derived from classical thin-plate theory. The normal displacement of the rhombic plates is approximated as a hybrid series of (i) admissible and mathematically complete algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained, and (ii) 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 rhombic plates having V-notches. Accurate frequencies are presented for notches for the spectra of notch angles and notch depths, causing a re-entrant vertex corner of the radial edges and for two different aspect ratios.