Truncated Bresse-Timoshenko beam with fractional Laplacian damping

被引：0

作者：

Rosario Miranda, Luiz Gutemberg ^{[1
]}

Raposo, Carlos Alberto ^{[2
]}

Siqueira Cordeiro, Sebastiao Martins ^{[3
]}

机构：

[1] Fed Univ Para, Fac Math, BR-68721000 Salinopolis, PA, Brazil

[2] Univ Fed Bahia, Dept Math, BR-40170110 Salvador, BA, Brazil

[3] Fed Univ Para, Dept Math, BR-68440000 Para, Brazil

来源：

CONTRIBUTIONS TO MATHEMATICS | 2023年 / 8卷

关键词：

fractional Laplacian damping; Timoshenko system; well-posedness; semigroups; TRANSVERSE VIBRATIONS; EXPONENTIAL STABILITY; STABILIZATION; EQUATION; DECAY;

D O I：

10.47443/cm.2023.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article focuses on a Timoshenko beam model introduced by Elishakoff. This model is free of the second frequency spectrum and solves the paradox of equal wave speeds, related to Timoshenko's model. Damping created by a fractional Laplacian is considered, which includes internal damping, Kelvin-Voigt damping, and intermediate damping. Exponential stability is shown without requiring any relationship between the system coefficients.

引用

页码：1 / 10

页数：10

共 26 条

[1] QUANTITATIVE ESTIMATES ON LOCALIZED FINITE DIFFERENCES FOR THE FRACTIONAL POISSON PROBLEM, AND APPLICATIONS TO REGULARITY AND SPECTRAL STABILITY
Akagi, Goro
Schimperna, Giulio
Segatti, Antonio
Spinolo, Laura, V
[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2018, 16 (04) : 913 - 961
[2] The hypothesis of equal wave speeds for stabilization of Timoshenko beam is not necessary anymore: the time delay cases
Almeida Junior, D. S.
Elishakoff, I
Ramos, A. J. A.
Rosario Miranda, L. G.
[J]. IMA JOURNAL OF APPLIED MATHEMATICS, 2019, 84 (04) : 763 - 796
[3] On the nature of dissipative Timoshenko systems at light of the second spectrum of frequency
Almeida Junior, D. S.
Ramos, A. J. A.
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2017, 68 (06):
[4] Thermoelastic Timoshenko system free of second spectrum
Apalara, Tijani A.
Raposo, Carlos A.
Ige, Aminat
[J]. APPLIED MATHEMATICS LETTERS, 2022, 126
[5] Atangana A, 2018, FRACTIONAL OPERATORS WITH CONSTANT AND VARIABLE ORDER WITH APPLICATION TO GEO-HYDROLOGY, P79, DOI 10.1016/B978-0-12-809670-3.00005-9
[6] Balakrishnan A.V., 1960, Pac. J. Math., V10, P419, DOI 10.2140/pjm.1960.10.419
[7] BRAVO J. C. V., 2020, TEMA (São Carlos), V21, P261, DOI 10.5540/tema.2020.021.02.0002610261
[8] Exponential stability for laminated beams with intermediate damping
Cabanillas, Victor R.
Raposo, Carlos A.
[J]. ARCHIV DER MATHEMATIK, 2022, 118 (06) : 625 - 635
[9] Elishakoff I., 2019, ZAMM Z. Angew. Math. Mech., V99, P1
[10] Who developed the so-called Timoshenko beam theory?
Elishakoff, Isaac
[J]. MATHEMATICS AND MECHANICS OF SOLIDS, 2020, 25 (01) : 97 - 116

← 1 2 3 →