Further Development of Series Expanded Transfer Matrix Method for Structural Dynamic Analysis of Complex Structures

Structural dynamic analysis of an arbitrary structure such as vehicle structure can conveniently be carried out using finite element method or other numerically oriented approaches. Analytical approach is usually preferred due to its elegance and convenience for parametric studies; however the usefulness of such an approach is limited for a class of geometries or problem setting only.

Following the method which was originally proposed by Barboni, Gaudenzi, Mannini and Santini, the author and colleagues have rederived and modified the well known transfer matrix method by expanding the governing differential equations for the structural state vector into a power series, which is related to the eigenvalues of the dynamic eigenvalue problem. The work is motivated by the need for an efficient procedure which possesses the elegance of analytical method, but yet well applicable for arbritrary and complex structure. The procedure has been applied to basic bending and torsional oscillation of prismatic beams, and the results are compared to analytical solutions as well as those obtained using finite element method. Next the problem of structure with arbitrary geometry is analysed. For this purpose, the bending oscillation of non-prismatic beam has been considered. Previous formulation can readily be applied for piecewise continuous approximation to the structure. In the present work, further development related to complex structures, in particular as related to the presence of joints, are elaborated and novel results are presented.