### ASA 125th Meeting Ottawa 1993 May

## 4pPA11. Development of an algorithm for evaluating finite amplitude waves
resulting from arbitrary periodic excitation.

**Jerry H. Ginsberg
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*School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332
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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.