An expression is derived for the temperature distribution in a semi-infinite translucent medium irradiated by a spatially uniform but time-varying pulse. When the pulse decays exponentially (as, for example, in the case of radiation from a pulsed laser), the temperature is expressed as a sum of complex error functions for which there exist rational approximations that are convenient for computing. The calculations are based on classical theory, and no resonant absorption is considered.

A numerical analog to the laws of conservation and momentum and the constitutive laws of piecewise-continuous materials is developed and shown to be able to describe the propagation of vibrational waves in a composite. The analog considers material strains of up to 30% to permit a first-order description of nonlinear plastic and viscoelastic response of metal syntactic foam composite T junctions to relatively large scale vibrational and acoustic excitations. The computations describe the propagation of direct stresses across the junction and the generation of shear stresses at the T junction corners. Results of propagation studies of Gaussian and sinusoidal wave packets across a T junction are discussed. Results are presented for selected T junction composites. The results of the numerical analog are discussed in terms of an extension of the classical dilatation-torsion wave theory extended to piecewise continuous materials. Techniques to minimize reflections of vibrations or acoustic excitations from T junctions are discussed.

A general solution is given to the uncoupled one-dimensional equations for the stress wave in a semi-infinite body due to an absorbed heat flux that is spatially uniform but varies in an arbitrary manner with time. The solution is in the form of a convolution integral that is applicable when both the thermal conductivity and the exponential absorption depth of the material are nonzero. Analytical results in terms of real and complex error functions are given for the cases where the flux is steady or varies in an impulsive, linear or exponential manner with time.

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