Dynamic analysis of planar closed-frame structures

An eigenanalysis problem concerning planar closed-frame structures is investigated. A hybrid analytical/numerical method is proposed that permits an efficient dynamic analysis of these structures. The method utilizes a numerical implementation of a transfer matrix solution to the analytical equation of motion. By using the Timoshenko beam theory, by analyzing the transverse and longitudinal motions of each segment simultaneously, and by considering the compatibility requirements across each frame angle, the undetermined variables of the entire frame structure system can be reduced to six. Then, by considering the relationship between the first segment and the last segment in the closed structure, the eigenvalues can be obtained by the existence of the non-trivial solutions. The main feature of this method is decreasing the dimensions of the matrix involved in the finite element methods and various other analytical methods.