Rayleigh's influence on engineering vibration theory

The first ten chapters of The Theory of Sound constitute an unprecedented exposition of vibration theory. This tour de force set the mold for the teaching of vibration for more than a century. The central core is linear modal analysis applied to lumped parameter systems and to strings, bars, beams, membranes, plates, and shells. In addition, there are preliminary investigations of nonlinear vibrations, parametrically excited vibrations, and random vibrations. Most of the textbooks on vibrations for engineers that have appeared in the past 50 years may be viewed as attempts to explain Rayleigh's idea to university students. Rayleigh's paradigm has served us well for a century but it appears that we are now on the threshold of major changes in the way vibration theory is taught. These changes are being driven by the tremendous advances in instrumentation and data processing facilities. The second coming of modal analysis (modal testing, really) is largely based on the concept of transfer functions. Although Rayleigh occasionally used the complex exponential and even computed a few transfer functions in passing, he did not attach any special significance thereto. It is interesting to speculate what Rayleigh would have done had he envisioned today's multichannel spectral analyzers. Other advances, unavailable to Rayleigh, which are currently entering vibration courses, are discussed.