Transverse Free Vibration of Non-Uniform Beams With Exponentially Varying Cross-Sections

Non-uniform beam structures are widely applied in various engineering fields, and the accurate estimation of modal parameters is significant to the design and optimization of non-uniform beams. This work aims to investigate the transverse free vibration of non-uniform beams with exponentially varying rectangular and circular cross-sections. When solving the governing equations for non-uniform beams in transverse free vibration, utilizing the Adomian Decomposition Method (ADM) can achieve semi-analytical expressions for natural frequencies and modal shape functions. To verify the efficiency of ADM, comparisons are made among the results obtained by the present proposed method, previous studies, the Finite-Element-Method (FEM) model and the experimental modal testing. Variations of natural frequencies and modal shapes under representative constraint boundary conditions are illustrated considering the effects of exponential factors. The results indicate that the modal parameters of non-uniform beams depend on the exponential factors significantly. Especially, for non-uniform beams with varying rectangular cross-sections, the exponential factor of the thickness direction has a greater impact on the modal parameters compared to the width direction. In addition, the positions of modal nodes and antinodes in non-uniform beams will shift compared to uniform beams due to the exponential non-uniformity.