A restatement of the principles of coincidence and resonance

• Published in: Journal of sound and vibration Vol. 25; no. 1; pp. 51 - 73
• Main Author: Yaneske, P.P.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 08.11.1972
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/0022-460X(72)90595-0

Coincidence and resonance are examined from a viewpoint that involves a wider interpretation of these phenomena than appears usual at present. A method is given which formulates the steady-state conditions under which maximal and minimal energy transfer may take place between any load form and any shape of system displacement. It is shown that the maximization conditions correspond to the load being present both “at the right time” and also “at the right place” in relation to the system displacement. If the first condition is described as resonance and the second by such a term as “coupled”, it is seen that neither the occurrence of both conditions together nor of the “coupled” condition alone is necessarily best described by the word coincidence. Cremer's coincidence appears as a special case of the “coupled” condition. The method is illustrated for particular load forms interacting with strings and rectangular thin plates for the sake of simplicity. An interpretation of the method in terms of correlation is also given.