Inverse Problems in Vibration
Abstract
This article concerns infinitesimal free vibrations of undamped elastic systems of finite extent. A review is made of the literature relating to the unique reconstruction of a vibrating system from natural frequency data. The literature is divided into two groups—those papers concerning discrete systems, for which the inverse problems are closely related to matrix inverse eigenvalue problems, and those concerning continuous systems governed either by one or the other of the Sturm–Liouville equations or by the Euler–Bernoulli equation for flexural vibrations of a thin beam.
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Given an eigenvalue spectrum satisfying Eq. (5), the corresponding coupling constants can be uniquely determined.
“Given an eigenvalue spectrum { E k } satisfying Eq. (5), the corresponding coupling constants { ω j , λ j } can be uniquely determined.”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [24]
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Quantum speed limit for perfect state transfer in one dimension
Yung, M.-H. (2006) · Physical Review A · doi:10.1103/physreva.74.030303 · Cited by 128 · see citing works
- Authors
- Gladwell, G. M. L.
- Affiliations
- University of Waterloo (CA)
- Corresponding author
- Gladwell, Graham M. L.
- Venue
- Applied Mechanics Reviews
- Publisher
- ASME International
- Published
- 1986-07-01
- Volume
- 39
- Issue
- 7
- Pages
- 1013-1018
- ISSN
- 0003-6900 (ISSN-L)
- 2379-0407
- OpenAlex
- W2090135779
- Cited by
- 439
- References
- 0
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 3 · 2023: 5 · 2022: 7 · 2021: 11 · 2020: 19 · 2019: 15 · 2018: 12 · 2017: 15 · 2016: 21 · 2015: 26 · 2014: 24 · 2013: 19 · 2012: 13
- FWCI
- 2.79
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Applied Mechanics Reviews (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
- Physical Sciences › Engineering › Control and Systems Engineering › Vibration and Dynamic Analysis
- Keywords
- inverse problems, free vibration, natural frequencies, elastic systems, discrete systems, Sturm-Liouville equation, Euler-Bernoulli beam, flexural vibration, system reconstruction
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