Article
| Title: | Spectral estimates of vibration frequencies of anisotropic beams (English) |
| Author: | Sabatini, Luca |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 68 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 15-33 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics. (English) |
| Keyword: | theory of beams |
| Keyword: | deformation of cross section |
| Keyword: | spectral geometry |
| Keyword: | comparison of spectra |
| MSC: | 35P15 |
| MSC: | 47A75 |
| MSC: | 74B05 |
| MSC: | 74K10 |
| idZBL: | Zbl 07655737 |
| idMR: | MR4541073 |
| DOI: | 10.21136/AM.2021.0057-21 |
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| Date available: | 2023-02-03T11:00:50Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151494 |
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| Reference: | [1] Bordoni, M.: An estimate for finite sums of eigenvalues of fiber spaces.C. R. Acad. Sci., Paris Sér. I 315 (1992), 1079-1083. Zbl 0761.53019, MR 1191493 |
| Reference: | [2] Bordoni, M.: Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds.Math. Ann. 298 (1994), 693-718. Zbl 0791.58094, MR 1268600, 10.1007/BF01459757 |
| Reference: | [3] Bordoni, M.: Spectral comparison between Dirac and Schrödinger operators.Rend. Mat. Appl., VII. Ser. 18 (1998), 181-196. Zbl 0919.58064, MR 1638207 |
| Reference: | [4] Brézis, H.: Analyse fonctionnelle. Théorie et applications.Collection Mathématiques Appliquées pour la Maîtrise. Masson, Paris (1983), French. Zbl 0511.46001, MR 0697382 |
| Reference: | [5] Picone, M., Fichera, G.: Trattato di analisi matematica.Tumminelli, Roma (1954), Italian. Zbl 0058.03803, MR 0106814 |
| Reference: | [6] Reed, M., Simon, B.: Methods of Modern Mathematical Physics. Vol. I: Functional Analysis.Academic Press, New York (1972). Zbl 0242.46001, MR 0493419, 10.1016/b978-0-12-585001-8.x5001-6 |
| Reference: | [7] Reed, M., Simon, B.: Methods of Modern Mathematical Physics. Vol. II: Fourier Analysis, Self-Adjointness.Academic Press, New York (1975). Zbl 0308.47002, MR 0493420 |
| Reference: | [8] Reed, M., Simon, B.: Methods of Modern Mathematical Physics. Vol. IV: Analysis of Operators.Academic Press, New York (1978). Zbl 0401.47001, MR 0493421 |
| Reference: | [9] Sabatini, L.: Estimation of vibration frequencies of linear elastic membranes.Appl. Math., Praha 63 (2018), 37-53. Zbl 06861541, MR 3763981, 10.21136/AM.2018.0316-16 |
| Reference: | [10] Sabatini, L.: Estimates of the Laplacian spectrum and bounds of topological invariants for Riemannian manifolds with boundary.An. Ştiinţ. Univ. "Ovidius" Constanţa, Ser. Mat. 27 (2019), 179-211. MR 3956406, 10.2478/auom-2019-0027 |
| Reference: | [11] Sabatini, L.: Estimates of the Laplacian spectrum and bounds of topological invariants for Riemannian manifolds with boundary II.An. Ştiinţ. Univ. "Ovidius" Constanţa, Ser. Mat. 28 (2020), 165-179. MR 4089855, 10.2478/auom-2020-0012 |
| Reference: | [12] Sabatini, L.: A linear theory of beams with deformable cross section.J. Math. Model. 9 (2021), 465-483. MR 4275997, 10.22124/jmm.2021.17932.1548 |
| Reference: | [13] Tikhonov, A. N., Samarskij, A. A.: Equazioni della fisica matematica.Mir, Roma (1981), Italian. Zbl 0489.35001 |
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