Transient response analysis of balanced laminated composite beams by the method of reverberation-ray matrix

• MRRM is demonstrated to analyze the transient responses of balanced laminated beams.
• MRRM is verified by comparing the velocity response of a laminated cantilever beam with that of FEM.
• The solving process of MRRM is simpler and quicker than that by FEM.
• The velocity response of the cantilever beam with various axial–flexural coupling was analyzed by MRRM.
• The response amplitude increases with the increasing of axial–flexural coupling parameter.

This study extends the method of reverberation-ray matrix (MRRM) to analyze the transient response of a laminated composite beam subjected to an impulse force load. To validate the MRRM for this application, we first analyze the velocity response of a laminated cantilever beam model, then solve the transient responses of a laminated composite beam under a half-cycle pulse force and a rectangular pulse force using the MRRM. We present the reverberation-ray matrix of multi-reflected and scattered waves in the laminated composite beam, and analyze the influence of the impact load type and the axial–flexural coupling effects due to asymmetric ply stacking sequences. The effects of different beam models on the calculation results for transient responses are also emphasized. Compared with the finite element method, the proposed MRRM approach yields results that are in good agreement with previous findings, and the MRRM solution process is simpler, faster, and requires fewer computational elements.