Dispersion of stress waves in one-dimensional semi-infinite, weakly coupled layered systems

An analytical study of the dispersion of transient stress waves in the first layer of a weakly coupled semi-infinite bi-layered system is carried out. The analysis is based on approximate Fourier transform inversions, and makes use of the fact that the weakly coupled system possesses small propagation zones (PZs) in the frequency domain. Low- and high-frequency asymptotic approximations to the transient waves are computed, taking into account frequency components of the transfer function in the first and second PZs, respectively. The derived analytic expressions are superpositions of non-oscillating terms and convolution integrals with decaying oscillatory kernels. It is shown that, depending on the frequency and the amplitude of the convolution kernels, the dispersed waves overshoot or undershoot the applied impulsive excitation. This result is of significant practical importance in the design of layered systems as stress attenuators.