Longitudinal vibration of a beam with arbitrary section by differential transformation method

Since resonance of beams can fails them, analyze of longitudinal vibration of beams is an important accept of design them. Unfortunately, in account of complexities which appear in solving differential equation of longitudinal vibration of beams, with analytical methods, we can solve it in some special cases for section and boundary conditions. The differential transform is a numerical method for solving linear and some non linear, ordinary and partial differential equations. In this paper, this technique has been applied for solving differential equation of longitudinal vibration of beams witch cross section of area vary as an arbitrary function of length and boundary conditions. Natural circular frequencies and mode shapes have been calculated. The results have been compared with the exact solution which has been presented for some special cases. This omparison proves the accuracy of this technique.

Keywords:

Differential Transformation Method (DTM) , Longitudinal Vibration , Natural Circular Frequencies , Mode Shapes