One of the most important problems facing structural and design engineers is the analysis of dynamic behavior of beams subjected to moving loads and masses. Moving objects have a great effect on dynamic stresses in such structures, and cause them to vibrate intensively, especially at high velocities. Euler-Bernoulli and Timoshenko theories are best modeling of beams in literatures. Crack is one of the most common defects in a structure, may result in a dangerous effect on the behavior of structures. It may also lead to improper structural performance which can eventually destroy the structure. In the literatures, two models of crack (open and breathing crack) are investigated. In this thesis, open crack is considered. The cracked beam is modeled as two segments connected by massless springs at the crack position. In this case, crack is modeled by a torsional spring in Euler-Bernoulli beam and torsional linear springs in Timoshenko beam. The dynamic behavior of structures has been studied by several analytical and numerical methods. The spectral element model is known to provide very accurate structural dynamic characteristics and involve partial differential equations of motion, displacement fields, shape functions and dynamic stiffness matrix. This method reduce the number of degree-of-freedom to resolve the computational and costs problems. In this thesis, frequency domain representation of moving load, extracting the dynamic stiffness matrix for cracked beam and spectral element model for moving mass problem is considered. The force vector for each spectral element is evaluated in frequency domain for moving load with constant velocity and acceleration. Spectral element model is developed for moving mass on beams by using an approximate model namely a stationary mass model (SM model). The SM model is based on adding a stationary concentrated mass (point mass) and equivalent to the moving mass at the beam center and then calculate the dynamic response due to a moving load equivalent to the weight of stationary concentrated mass. The accuracy of results obtained from spectral finite element formulation is compared with those of finite element (FE) method and analytical formulations, whenever available. The SFE results display remarkable superiority compared to FE results in reducing number of elements as well as increasing numerical accuracy . Keywords : Cracked beam, Euler-Bernoulli beam, Timoshenko beam, Moving mass, Spectral element method, Dynamic shape function, Dynamic stiffness matrix.
