The method of reverberation-ray matrix is extended to investigate the transient response of a multi-span, continuous Timoshenko beam subject to a moving load. Dual local coordinate systems are introduced and the corresponding analytical solutions in the frequency domain are presented, with the particular solution derived by the dual Fourier transform. The transient responses are then obtained using the Fast Fourier Transform algorithm. To avoid the error due to the singularity (or near singularity) of the kernel of integral, the technique of Neumann series expansion is adopted for the undamped response of beams. Numerical results are compared with those obtained by the existing methods and a good agreement is observed. It is found that the present method is uniform in formulating for dynamic analysis of beam-typed structures with multi-branches and is especially suitable for calculating transient responses containing high-frequency components. Besides, no discretization error is involved as the method is completely based on continuum models.
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