Study of Vibration Characteristics of Cantilever Rectangular Plate with Side Crack

Abstract

In this paper, the vibration characteristics of the cantilever rectangular plate with side crack are studied in the way of analysis, which including natural frequency and mode shape. The influences of different parameters of crack, such as the locations and lengths of crack, to the vibration characteristics of the cantilever rectangular plate are investigated. The modal function of the crack plate consists two parts, which are (1) the modal function of intact cantilever rectangular plate from beam functions combination method and (2) corner functions presenting the discontinuity of displacement and slope along the crack. The natural frequencies and modal shapes can be obtained when taking the modal function into the method of Ritz. At last, the effects of the crack location and crack length on the vibration characteristics are investigated, and it could provide the theoretical basis for engineering application and the relevant study.

Instant Dynamic Response Measurements for Crack Monitoring in Metallic Beams

“…It can be safely estimated that the cracks may have effects on: the section modulus of the area around the crack, the deflection curve or energy content of the beam, mode values and mode shapes [3][4][5][6][7][8][9][10][11][12][13][14][15]. This can be verified from Timoshenko beam solution (as shown in Eq.…”

“…Crack initiation and propagation have also been studied with numerical and experimental approaches. The relation in between the relative length (i.e., crack distance from the fixed end with respect to the length of the specimen) to the depth ratio (i.e., crack depth with respect to the thickness of the specimen) was discussed in detail [25]. Mostly linear methods are used to detect crack behavior which is a non-linear phenomenon [26].…”

Prediction of Crack Depth and Fatigue Life of an Acrylonitrile Butadiene Styrene Cantilever Beam Using Dynamic Response

“…They have also studied crack initiation and propagation with numerical and experimental approaches. The relation in between the relative length (i.e., crack distance from the fixed end with respect to the length of the specimen) to the depth ratio (i.e., crack depth with respect to the thickness of the specimen) was discussed in detail [26][27][28][29]. Tommy J. George's [30] presented a method using a base exited plate resonating at high frequency.…”

Analysis of Vibration Natural Frequencies of Rotationally Restrained and Simply Supported Circular Plate with Weakened Interior Circle Due to an Angular Crack

“…Using the Rayleigh-Ritz method, Si et al [27][28][29] studied the free vibration behavior of a completely clamped cracked circular plate, a baffled cracked circular plate, and a cracked rectangular plate, respectively, considering the influence of water on one side. Chen et al [30] studied the vibration characteristics of a cantilever rectangular plate with side crack using Ritz method. Chen et al [31,32] performed mathematical analysis and numerical study of true and spurious eigenequations for free vibration of plates using the imaginary-part boundary element method (BEM).…”