Jiang, W., Bennett, A., Vlahopoulos, N., Castanier, M. et al., "A Reduced-Order Model for Evaluating the Dynamic Response of Multilayer Plates to Impulsive Loads," SAE Int. J. Passeng. Cars - Mech. Syst. 9(1):83-89, 2016, doi:10.4271/2016-01-0307.
Assessing the dynamic performance of multilayer plates subjected to impulsive loading is of interest for identifying configurations that either absorb energy or transmit the energy in the transverse directions, thereby mitigating the through-thickness energy propagation. A reduced-order modeling approach is presented in this paper for rapidly evaluating the structural dynamic performance of various multilayer plate designs. The new approach is based on the reverberation matrix method (RMM) with the theory of generalized rays for fast analysis of the structural dynamic characteristics of multilayer plates. In the RMM model, the waves radiated from the dynamic load are reflected and refracted at each interface between layers, and the waves within each layer are transmitted with a phase lag. These two phenomena are represented by the global scattering matrix and the global phase matrix, respectively. The product of these two matrices after some mathematical manipulations provides a reverberation matrix that represents the waves within the entire plate. The dynamic response of the plate is calculated by employing the generalized ray theory and an inverse Fourier Transformation. Free response results obtained by the new approach are shown to have good agreement with those obtained by a spectral finite element analysis. Then, different multilayer plate design configurations are ranked by evaluating the dynamic response with the new reduced-order model. These forced response results are validated successfully by comparison to the ranking obtained through much more computationally expensive finite element analysis results.