Natural frequency analysis of Euler-Bernoulli beam subjected to moving mass

To analyze the natural frequencies of Euler-Bernoulli beam subjected to moving mass, based on the beam's governing function, the dynamic stiffness matrix and the shape function matrix of Euler-Bernoulli beam element were deducted by introducing the force and displacement boundary condition. The attached dynamic stiffness matrix which is caused by the moving mass' inertial force was developed by Furious Transformation. The dynamic stiffness matrix of the whole system was then set up, and the natural frequencies of Euler-Bernoulli beams subjected to moving mass were calculated through Wittrick-Williams algorithm. The method is validated in comparison with FEM results, and is proved of higher precision and smaller computing size. In addition, the rules of simple-supported or cantilever beams' natural frequencies varying against the velocity, density of moving concentrated mass were brought forth according to this method.