A Study On The Transient Response Of Frames Subjected To Displacement Load With The Elastic Wave Approach

Recently based on elastic wave theory, Y.H. Pao and his colleagues proposed a method to solve the transient response of trusses and frames: the method of reverberation ray matrix. This is a novel matrix method of obtaining transient response of trusses and frames in frequency domain. First, it transformed the governing equation into frequency domain. The amplitudes of waves are taken as basic unknowns, and local scattering matrix can be formed with force equilibrium and displacement compatibility conditions at joints. All the basic unknowns can be solved by assembling the local matrices as a global one. Then the waves at any location can be obtained with propagation matrix. Transient response such as the internal force, strain and displacement can be obtained by superposing all of the waves at the same location. At last, we get the response of these variables in the time domain by the Inverse Fast Fourier Transformation.Based on elastic wave theory, the present study further develops the formulation of the MRRM as well as the computer source code to include the case of a structure subjected to applied impulse (step or half cycle sine wave) displacement load in terms of Euler-Bernoulli beam theory. The reliability of the reverberation ray matrix method is verified by comparing the solution of the transient internal forces and displacement responses of a simple supported beam subjected to right end applied half cycle sine wave displacement with FEM solution obtained by ANSYS and with the Mindlin's Solution. Then the transient response of a 17-bar frame subjected to apply step or impulse displacement is solved and the results are analyzed and discussed. It is found that, the solution of MRRM is superior to that of FEM when the response contains many high frequency components.