Vibration analysis of cracked Timoshenko beam under moving load with constant velocity and acceleration by spectral finite element method

This study describes spectral finite element (SFE) formulation and solution for vibration of cracked Timoshenko beam subjected to moving load. The crack is modeled by two massless springs at the crack position. The dynamic stiffness matrix of cracked beam together with both constant velocity and constant acceleration moving load vectors is evaluated for spectral elements in frequency-domain. The accuracy of results obtained from SFE formulation is compared with that of finite element (FE) method. The SFE results display remarkable superiority compared to FE ones in reducing the number of elements together with increasing numerical accuracy.