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.
- Adams R.
- Cawley P.
- Pye C.
- Stone B.
A vibration technique for non-destructively assessing the integrity of structures.
J Mech Engin Sci. 1978; 20: 93-100
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- A vibration technique for non-destructively assessing the integrity of structures.J Mech Engin Sci. 1978; 20: 93-100
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Accepted: July 2, 2021
Received: June 29, 2021
Published by Elsevier Inc on behalf of Society of Biological Psychiatry.