Analytical Solution for Free Vibration of Annular Mindlin Plate with a Circumferential Open Crack

Abstract

Mindlin plate theory is employed to obtain the free vibration response of an annular moderately thick plate with a circumferential open crack with fixed-free boundary conditions. To model the crack, a set of continuously distributed rotational springs are employed at the crack location. The corresponding spring stiffness value is a function of the crack depth and is given as a closed-form function. To obtain the vibration behaviour, the eigenvalue problem is solved to obtain the natural frequencies and mode shapes. The current method is verified by comparing the results with those obtained from finite element analysis. Through a parametric study, the effects of the crack depth and its radial location on the natural frequencies and mode shapes are investigated. The results show that for a constant crack depth, the reduction in natural frequency is a strong function of the radial location of the crack.

A Study on Mode Shape and Natural Frequency of Rotating Flexible Cracked Annular Thin Disk

“…Meanwhile, on the research of circumferential cracked disk, Pramod et al [18] investigated the natural frequencies of annular plates with circumferential cracks by finite element method. Derakhshan et al [19] researched the effect of crack radial location and its depth on the natural frequencies and mode shapes of an annular plate with a circumferential crack. Bahaloo et al [20] researched the transverse vibration and stability of rotating annular disk with a circumferential crack and found the phenomenon that the disk critical speed will decrease with the crack depth increasing and the crack radius decreasing.…”