Discontinuities in integral-transform solutions

Abstract

Criteria are derived for the determination of the magnitude and the location of discontinuities of solutions in the form of definite integrals obtained by means of integral-transform techniques. The types of integrals arising with the Fourier sine or cosine transforms and those arising with the Laplace transforms are considered in detail. Applications of the theory arise particularly with problems of wave propagation, where interest is centered on the location of wave fronts and the magnitude of jumps there; two illustrative examples of such problems relating to Timoshenko beams are included.