1965-02-01

Matrix Treatment of Waves in Mechanical Systems 650822

The use of matrices in the mathematical solution of problems in mechanical engineering has become increasingly popular. The matrix formulation of the analysis is flexible and gives a broad and unified outlook on the problems discussed. In recent years it has been applied to the solution of torsional vibration problems, to the study analysis of mechanical filters, and to the study of the vibrations of beams and other structures. This paper is intended to show how the theory of wave propagation finds a very natural development in the language of matrices in mechanical systems that have concentrated or “lumped parameters” and also in systems that have continuously distributed parameters. Important concepts such as the propagation and attenuation parameters and surge and iterative impedances are shown to be intimately connected with the eigenvalues and eigenvectors of matrices.

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