Analysis of Vibration in L- and H-Shaped Planar Frame Structures Using Transfer Function

This paper analyzed the vibration of planar frame structures using the transfer function, which is obtained as the Laplace transform of Green’s function. The transfer function was used to represent the relationship between the excitation (including the initial and boundary conditions) and the response of the system; that is, it can determine the vibration response and stability of the system. The frame was divided into several joint blocks with substructures (beams). A state-space matrix form was used to represent the equation of motion in the beams. The compatibility between the joint blocks and beams allows us to establish the characteristic matrix of the frame, of which the determinant is the characteristic equation. With the eigenvalues obtained as the roots of the characteristic equation, one can establish the eigenfunction of the frame. The receptance of the structure with a single point excitation was also studied. The application of the transfer function to analysis of the L- and H-shaped planar frame structures was conducted in this paper. The results agree well with those published in the literature.