Transient Response Of Frames Subjected To Suddenly Applied Step Displacement With The Reverberation Ray Matrix

Recently Pao and his colleagues proposed a method to solve the transient response of trusses and frames under impact load: the method of reverberation ray matrix. This is a novel matrix method of obtaining transient response of trusses and frames in frequency domain with elastic wave approach. Based on wave propagation theory, the transient response of truss type structures is obtained. In this method the wave amplitudes are taken as basic unknowns. Scattering matrixes are derived from compatible condition of displacements and force equilibrium condition at each node, then they are assembled into a global matrix. Eventually, the transient responses such as the strain and the displacement can be solved in frequency domain and the time domain histories of these variables are produced by Inverse Fast Fourier Transformation.In this study, the author further developed the formulation of the method of reverberation matrix and improved the computer code. This work extends analysis and computer code to include the case of a structure subjected to suddenly applied displacement. The reliability of the method of reverberation ray matrix is verified by comparing the solution of a single beam subjected to right-end suddenly applied step displacement with Mindlin's solution. The transient response of a 17 bar frame subjected to suddenly applied step displacement is solved and the results are discussed. These results provide valuable information for engineering application.