Affiliation:
1. Department of Applied Physics, California Institute of Technology, Pasadena, CA 91125
2. Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125
Abstract
I propose that there exists in natural and artificial environments a class of resonant oscillations that can be excited directly by a steady, zero-frequency force such as that of wind, water, electric field. A member of this class comprises two normally independent oscillating modes of a system, for example, a building or bridge, which, separately, cannot be driven by a zero-frequency force. Agreeing on terms of collaboration, the two modes engage in a joint oscillation powered by the steady zero-frequency force in which they drive each other, one directly and the other parametrically. I observed a bimodal vibration belonging to this class in a home shower where the two modes are the pendulum excursion and the torsional twisting of a freely suspended showerhead which break into a joint oscillation above a threshold value of the water flow rate. I advance a theoretical model which predicts and explains the main features of the observations. The model constitutes an extension to two modes of a proposal and demonstration in 1883 by Lord Rayleigh and Michael Faraday for the excitation of a single resonant mode by modulating a system parameter at twice the resonance frequency. The proposal is credited with the launching of parametric physics. The Experiments section of this report consists of three linked video clips photographed in the home shower which support the basic theoretical assumptions. The ubiquity of zero-frequency forces, such as that of wind, and their direct conversion to alternating on-resonance system vibrations endows the class with an amplified destructive potential with implications for structural stability.
Publisher
Proceedings of the National Academy of Sciences
Reference5 articles.
1. XXXIII. On maintained vibrations
2. Y. R. Shen, Principles of Nonlinear Optics (J. Wiley and Sons, New York, 1984), chap. 10.
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5. Numerous videos of the Tacoma bridge collapse can be found on UTube and on Wikipedia. For example: Tacoma Narrows Bridge Collapse “Galloping Gertie.” https://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_ (1940).
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1 articles.
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