The history of mechanical resonance -- from initial studies to autoresonance

A. S. Smirnov ; B. A. Smolnikov

Čebyševskij sbornik, Tome 23 (2022) no. 1, pp. 269-292.

Résumé

The paper traces the historical development process of one of the most important concepts of the mechanical oscillations theory – resonance, starting from the XVII century to the present day. It is noted that resonance is of great theoretical and practical importance, but there is no sufficiently strict and comprehensive definition for this term. The prehistory of resonance is mentioned and the initial studies associated with the works of Galileo Galilei, who first described resonance using the example of an ordinary pendulum, and Christiaan Huygens, who studied the phenomenon of sympathetic resonance using the example of two pendulums on a common beam support, are discussed. The leading role of orbital resonances in the XVIII-XIX centuries, that indicate the evolutionary maturity of the Solar system, is noted, and the internal resonances in terrestrial mechanics are analyzed using the example of double and spherical pendulums. The classical harmonic resonance is analyzed in detail, and it played a significant role in technology. The harmful role of resonance is demonstrated by the example of catastrophes with bridge structures. In addition, a classification of various types of resonance, which was formed in the XIX-XX centuries, is given. The term "autoresonance" associated with the name of A. A. Andronov was the last step in this chain. Autoresonance made it possible to effectively swing the system using feedbacks, thereby adapting the driving forces to the properties of the system itself. Several illustrative examples of autoresonance in pendulum systems are given. In conclusion, it is noted that autoresonances gradually began to take a serious place in robotics and biomechanics, and their use turned out to be the most important step into the world of optimal motion modes.

Détail

Keywords: acoustic resonance, sympathetic resonance, internal (structural) resonance, orbital (astronomical) resonance, harmonic (technical) resonance, antiresonance, superharmonic (ultraharmonic) resonance, subharmonic resonance, combinational (subultraharmonic) resonance, parametric resonance, self-oscillating (self-excited) resonance, autoresonance (controlled resonance), bioresonance, quasi-resonance, true resonance.

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