Solving coupled differential eigenvalue problems using the differential transformation method numerical example: Dynamic analysis of multi-span beams

This paper presents an innovative application of the Differential Transformation Method (DTM) for solving differential equations, specifically addressing coupled eigenvalue problems in structural engineering. For this purpose, the free vibration analysis problem of multi-span beams with the most general support conditions, including translational and rotational springs at the connection to the ground, is selected as a structural and coupled eigenvalue problem and is solved using the DTM. The process of solving the problem is thoroughly described, and the results obtained from the DTM are compared and verified with the results from other methods in reliable sources. This comparison demonstrates DTM's efficiency, accuracy, and potential as an alternative method. Numerical results, including frequency values, are tabulated, and mode shapes for various multi-span beams are illustrated. Furthermore, a comprehensive parametric study is conducted, examining the effects of different support types-clamped, simple, and free-on multi-span beams. The numerical results and comparisons demonstrate that DTM is an accurate and capable method for solving coupled eigenvalue problems, comparable to most other differential problem-solving method.