In the 1960s, mathematicians Mark Kac and Lipman Bers asked, “Can one hear the shape
of a drum?” Put another way, can one infer the structural properties of a system from
its oscillatory response to stimulation? While it has been demonstrated that there
is no singular solution to this question when the system is completely unknown, the
information-rich oscillatory response of a system that is partially known can be used
to infer a trove of structural and dynamical properties. If a periodic force is applied
to a system at one of its resonant frequencies, the amplitude of the resulting vibrations
(oscillations) will have a local maximum (resonance state). Since the resonance state
is a function of a system’s properties (e.g., stiffness), the analysis of the system’s
oscillations during resonance has been widely used to assess the structural integrity
of physical systems (
1
). For example, by analyzing the oscillatory response of a steel beam to vibrations
applied at its resonant frequencies (resonance test), it is possible to detect and
localize incipient, visually undetectable cracks that, under shear stress, will cause
breakage.
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References
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Article info
Publication history
Accepted:
July 2,
2021
Received:
June 29,
2021
Identification
Copyright
Published by Elsevier Inc on behalf of Society of Biological Psychiatry.
