Analysis of the natural frequency of an axially moving beam with non-uniform velocity

An analysis on the natural frequencies of an axially moving beam with non-uniform velocity was conducted using the dynamic stiffness matrix method. The governing equations and force boundary conditions in the time domain were established via Hamilton's principle, and the governing equation and force boundary conditions in the frequency domain were then developed using the Furious Transformation. A dynamic stiffness matrix model for the beam was created by importing the displacement and force boundary conditions, after computing the governing equation in the frequency domain. The finite element model was created using the Hermite shape function. Then the model was evaluated by comparing results from literature, FEM results, and DSM results. It was concluded that DSM was more accurate and efficient than FEM. The relationships between natural frequency and the axial movement's velocity and acceleration, axial load, and boundary conditions were also summarized.