Jerry H. Ginsberg
School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332
Without incorporation of weak shock theory or an explicit description of dissipation, a numerical evaluation of the distortion of finite amplitude planar waves generated by an arbitrary period excitation is extremely limited in its domain of validity. Prior descriptions of such waves using weak shock theory have apparently been restricted to the case of initially harmonic signals. The present study describes a computational algorithm combining the small signal version of Earnshaw's solution with weak shock theory implemented in the form of the ``equal area rule.'' The major steps in this algorithm are: (1) development of a nominal waveform at a specified location based on equal increments in the phase variable, (2) identification of (possibly multiple) shocks and the corresponding instants at which the equal area rule is satisfied, (3) coalescence of overlapping shocks associated with each of the harmonics contained in the initial signal, and (4) reconstruction of the shocked waveform using equal time increments in order to permit evaluations using FFT's. The presentation will describe the algorithm, and use a variety of test problems to illustrate the various manifestations of shocks.