Free vibration analysis of axially functionally graded tapered Timoshenko beams using differential transformation element method and differential quadrature element method of lowest-order

摘要

The present paper investigates the free vibration characteristics of Timoshenko beams whose cross-sectional profile and material properties vary along the beam axis with any arbitrary functions. Free vibration analysis of these beams is carried out through solving the governing differential equations of motion. Since the application of differential transformation method (DTM) does not necessarily converge to satisfactory results, an element-based differential transformation method, namely differential transformation element method (DTEM), is introduced which significantly enhances the accuracy of the results. Furthermore, differential quadrature element of the lowest order (DQEL) is introduced which is based on differential quadrature element method (DQEM). DQEL formulates the problem on the basis of the interpolation of the first differential of the functions; therefore, in contrast with DQEM higher differentials of functions are not employed in DQEL. The competency of DQEL and DTEM in free vibration analysis is verified through several numerical examples. The effects of taper ratio and material non-homogeneity on natural frequencies are investigated.