Introduction

Abstract

It is likely that the early interest in vibrations was due to the development of musical instruments such as whistles and drums. In was in modern times, starting around 1583, when Galilei Galileo made his observations about the period of a pendulum, that the subject of vibrations attracted scientific scrutiny. In the 1600’s, strings were analyzed by Marin Mersenne and John Wallis; in the 1700’s, beams were analyzed by Leonhard Euler and Daniel Bernoulli and plates were analyzed by Sophie Germain; in the 1800’s, plates were analyzed by Gustav Kirchhoff and Simeon Poisson, and shells by D. Codazzi and A. E. H. Love. A complete historical development of the subject can be found in (Love, 1927). Lord Rayleigh’s book Theory of Sound, which was first published in 1877, is one of the early comprehensive publications on the subject of vibrations. Since the publication of his book, there has been considerable growth in the diversity of devices and systems that are designed with vibrations in mind: mechanical, electromechanical, biomechanical and biomedical, ships and submarines, and civil structures. Along with this explosion of interest in quantifying the vibrations of systems, came great advances in the computational and analytical tools available to analyze them.