Dynamic characteristics analysis of variable cross-section beam under thermal vibration environment

A transverse asymmetric structural cantilever beam model is developed in the paper, based on Timoshenko beam theory, taking into account the shear deformation of the beam section and special boundary conditions. The semi-analytic solution and the vibration function of the circular frequency of this cantilever beam model are obtained by applying the transfer matrix method and the Newton-Raphson iteration method. The accuracy and effectiveness of the method are verified by comparing with the experimental data and the semi-analytic solutions obtained by other methods. The effects of the number of segments, temperature and thermal expansion coefficient on the obtained circular frequency results and vibration functions are analyzed, and the responses of different beam segment combination distribution forms under the same excitation state are explored. The results of this study can provide novel design insights for the design of beam structures in future projects.