Analysis of Natural Vibration Characteristics of Modified Timoshenko Cracked Beam

Abstract

This study utilizes the transfer matrix method to analyze the modified Timoshenko beam with and without cracks. The massless torsional spring is assumed to represent the section where the crack is located. The matrix equation is simplified using boundary conditions and solved using MATLAB. Additionally, the influence of different crack depths and positions on the first three natural frequencies is compared to finite element analysis using three common types of beams as examples. The results indicate that increasing the crack depth leads to a decrease in the natural frequency of the beam. However, the impact on certain specific positions is insignificant, with a maximum error between the two methods not exceeding 2.73%. Furthermore, the study investigates the influence of crack depth on natural frequency under different span-to-height ratios. The findings reveal that increasing the span-to-height ratio reduces the influence of crack depth on natural frequency, thereby validating the proposed method and its applicability in modified Timoshenko cracked beams.