Free Vibrations of Beams With a Single-Edge Crack

Natural frequencies for bending vibrations of Timoshenko cracked beams

“…Alternatively, simplified procedures are available with less computational effort. Among these simplified methods are those proposed by Christides and Barr [15] and Shen and Pierre [16,17]. In both cases, a crack function representing the perturbation in the stress field induced by the crack is considered.…”

Crack Detection in Beam using Sensitivity Coefficient of Modal Data

“…Christides [3] 등은 균열이 상, 하면에 대칭으로 존재 하고 단면이 일정한 오일러 보의 진동해석을 수행하였으며 Shen [4] 등은 균열 끝 부분의 응력 집중을 이용하여 구조물의 동특성을 얻 기 위해 2차원 유한요소법을 사용했다. Yang [5] 등은 열린 균열을 갖는 보가 진동하는 동안 균열이 구조물의 동특성에 어떤 영향을 주는 지 조사하기위해 수치적 모델을 제시하였고 Lin [6] 은 전달행 렬법을 사용하여 열린 균열을 갖는 단순보의 역 문제를 직접 계산 하였다.…”

A new continuous model for flexural vibration analysis of a cracked beam

“…The results are as follows: (15) In which the constants c 1 , c 2 , c 3 and c 4 will be as follows: (16) Now using equation (15) one can obtain the additional remote point rotation θ * as follows: (17) In equation (17) the parameter κ is a function of β. However comparing the finite element results with those obtained by this model shows that the parameter β has a very large value and accordingly it can be assumed that the parameter β is infinity.…”

“…In addition the resulted partial differential equation is complex and dependent on some constants which are unknown and must be calculated by correlating the analytically obtained results with those calculated by finite element in each case. Several researchers followed the Christides and Barr approach by modifying their method and gained some improvements [14][15][16][17][18]. However there still exists the inconsistency between strain and displacement fields which causes inaccuracy of the results especially in mode shapes and stress analysis.…”