Free vibration analysis for V-notched Mindlin plates with free or clamped radial edges

The free vibration analysis for the moderately thick V-notched plate based on Mindlin’s first-order shear deformation theory is examined here. The Ritz method is employed with two sets of admissible functions assumed for the generalized displacement components to evaluate the frequency and mode shape of the V-notched plate, where the complete algebraic trigonometric polynomials and the singularity characteristic angular functions are chosen to guarantee the accuracy and convergence. The singularity characteristic angular functions of the V-notch are derived from the singularity characteristic equations, which are established by introducing the series asymptotic expansions of the generalized displacement components into the equilibrium equations and corresponding boundary conditions. It is found that the addition of the characteristic angular functions substantially enhances the convergence and accuracy of the calculated result of the frequency compared with the classical Ritz method. The influences of the notch opening angle, relative plate thickness and relative notch depth on the frequency of the V-notched Mindlin plate under the free and clamped radial boundary conditions are, respectively, investigated. It is found that the frequency increases with the increase in the opening angle and relative thickness. The frequency increases with the relative depth of the V-notch with the clamped radial edges, while the conclusion is on the contrary for the V-notch with free radial edges.