Analysis of natural vibration characteristics of Timoshenko cracked beam based on transfer matrix method
Firstly,based on the transfer matrix method,the transfer matrices of a Timoshenko beam with arbitrary crack and Timoshenko beam without crack are derived.the crack section of the beam is assumed to be a mass free torsional spring.The matrix transfer relation between each beam segment and the crack section is established.Matlab is used to solve the equation.Secondly,the effect of crack location and relative depth on the natural vibration frequency of the simply supported beam with a single crack is discussed.The error is less than 1％compared with the results in the literature.Then,the finite element models of a cantilever beam and a beam fixed at both ends are established by ABAQUS,and the influence of the relative crack depth on the natural vibration frequency is analyzed.The calculated results are compared with the finite element results,and the error is less than 3.86％.Finally,the effect of the relative crack depth on the natural frequency of Timoshenko simply supported beams with different span to height ratios is studied.The maximum error between the calculated results and the literature is 4.56％,which verifies the validity and applicability of the proposed method.
transfer matrix methodtimoshenko cracked beamnatural frequency of vibrationmatlabABAQUS
万方数据
维普
