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The inverse calculation of material parameters of a thin-layer system is investigated using transient elastic waves. The inverse problem is formulated as an optimization problem in which the norm of the discrepancies between the calculated and measured normal surface displacements is minimized through the simplex algorithm. The theoretical result is first solved using the Laplace transform and the transient response is then implemented analytically by Cagniard's method. In the experiment, the source time function is generated by the brittle fracture of a pencil lead on the surface of the thin-layer system, and a National Bureau of Standards (NBS) conical transducer is used to record the surface responses. To obtain reliable inverse results for material parameters, a two-step inverse calculation procedure is proposed. The recovered material parameters of the specimens agree well with the theoretical values and experimental results.

The transition from transient response to steady-state for a layered medium subjected to antiplane loadings is studied. The steady-state formula for a layered medium is derived and the solutions for a layered half-space are then expressed explicitly in the form of wave number integrals. The transient response solutions for a layered half-space are obtained by the convolution of time harmonic loading function with transient response formula derived analytically from an effective matrix method. Two layered half-spaces with different ratios of wave velocities in the layer and half-space are considered and investigated by means of extensive numerical results to show their quite different transition behavior. The numerical results indicate that transient responses will approach steady state after certain characteristic times when the transient effects die away. The transition phenomena and characteristic times are investigated in detail through the responses from near field to far field as well as from low frequency to high frequency.