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Detecting and locating damage information from waves reflected off damage is a common practice in non-destructive structural health monitoring systems. Yet, the transmitted ultrasonic guided waves are affected by the physical and material properties of the structure and are often complicated to model mathematically. This calls for data-driven approaches to model the behaviour of waves, where patterns in wave data due to damage can be learned and distinguished from non-damage data. Recent works have used a popular dictionary learning algorithm, K-SVD, to learn an overcomplete dictionary for waves propagating in a metal plate. However, the domain knowledge is not utilized. This may lead to fruitless results in the case where there are strong patterns in the data that are not of interest to the domain. In this work, instead of treating the K-SVD algorithm as a black box, we create a novel modification by enforcing domain knowledge. In particular, we look at how regularizing the K-SVD algorithm with the one-dimensional wave equation affects the dictionary learned in the simple case of vibrating string. By adding additional non-wave patterns (noise) to the data, we demonstrate that the “wave-informed K-SVD” does not learn patterns which do not obey the wave equation hence learning patterns from data and not the noise.
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Dynamics of NEMS resonators across dissipation limits
The oscillatory dynamics of nanoelectromechanical systems (NEMS) is at the heart of many emerging applications in nanotechnology. For common NEMS, such as beams and strings, the oscillatory dynamics is formulated using a dissipationless wave equation derived from elasticity. Under a harmonic ansatz, the wave equation gives an undamped free vibration equation; solving this equation with the proper boundary conditions provides the undamped eigenfunctions with the familiar standing wave patterns. Any harmonically driven solution is expressible in terms of these undamped eigenfunctions. Here, we show that this formalism becomes inconvenient as dissipation increases. To this end, we experimentally map out the position- and frequency-dependent oscillatory motion of a NEMS string resonator driven linearly by a non-symmetric force at one end at different dissipation limits. At low dissipation (high Q factor), we observe sharp resonances with standing wave patterns that closely match the eigenfunctions of an undamped string. With a slight increase in dissipation, the standing wave patterns become lost, and waves begin to propagate along the nanostructure. At large dissipation (low Q factor), these propagating waves become strongly attenuated and display little, if any, resemblance to the undamped string eigenfunctions. A more efficient and intuitive description of the oscillatory dynamics of a NEMS resonator can be obtained by superposition of waves propagating along the nanostructure.
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- PAR ID:
- 10385924
- Date Published:
- Journal Name:
- Applied Physics Letters
- Volume:
- 121
- Issue:
- 2
- ISSN:
- 0003-6951
- Page Range / eLocation ID:
- 023506
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0100318
