Resonance-behavior of non-linear one-dimensional gas vibrations analyzed by the Ritz-Galerkin method

Summary

The present paper concerns an approximate analysis of damped resonance vibrations in a closed cylindrical pipe with harmonic excitation at one pipe end. Earlier experiments made by Lettau have disclosed that such vibrations may be highly non-linear and may even include shock waves travelling back and forth. The analysis is based essentially on the socalled Ritz-Galerkin method. Emphasis is put on the mechanism of the analysis rather than on a strict mathematical justification hereof. The theoretical results are in close agreement with the experimental evidence. Further a criterion for the presence and absence of shocks is derived.

The present investigation was undertaken while the author, on leave from the Technical University of Denmark, was working as a Research Associate ar Stanford University in California on a Research Fellowship from International Cooperation Administration, Washington D. C. Thanks are due to all these institutions.

In particular the author wishes to express his sincere thanks to Professor K. Klotter, Division of Engineering Mechanics, Stanford University, for his kind encouragement of the work and valuable criticism.