EQUIVALENCE BETWEEN EXPONENTIAL STABILIZATION AND OBSERVABILITY INEQUALITY FOR MAGNETIC EFFECTED PIEZOELECTRIC BEAMS WITH TIME-VARYING DELAY AND TIME-DEPENDENT WEIGHTS

被引：10

作者：

Kong, Aowen ^{[1
]}

Nonato, Carlos ^{[2
]}

Liu, Wenjun ^{[1
]}

Dos Santos, Manoel Jeremias ^{[3
]}

Raposo, Carlos ^{[4
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China

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

[3] Fed Univ Para, Fac Exact Sci & Technol, Manoel de Abreu St S-N, BR-68440000 Abaetetuba, Para, Brazil

[4] Univ Fed Sao Joao del Rei, Dept Math, BR-36307352 Sao Joao Del Rei, MG, Brazil

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2022年 / 27卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Time dependent delay; exponential decay; piezoelectric beams; internal observability; TIMOSHENKO SYSTEM; ENERGY DECAY; WAVE-EQUATION; TERM; STABILITY; EXISTENCE; DYNAMICS;

D O I：

10.3934/dcdsb.2021168

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller with a time-varying delay. Under appropriate assumptions on the time-varying delay term and time-dependent weights, we obtain exponential stability estimates by using the multiplicative technique, and prove the equivalence between stabilization and observability.

引用

页码：2959 / 2978

页数：20

共 38 条

[1] Piezoelectric field enhancement in III-V core-shell nanowires
Al-Zahrani, Hanan Y. S.
Pal, Joydeep
Migliorato, Max A.
Tse, Geoffrey
Yu, Dapeng
[J]. NANO ENERGY, 2015, 14 : 382 - 391
[2] GLOBAL EXISTENCE AND ENERGY DECAY OF SOLUTIONS FOR A WAVE EQUATION WITH NON-CONSTANT DELAY AND NONLINEAR WEIGHTS
Barros, Vanessa
Nonato, Carlos
Raposo, Carlos
[J]. ELECTRONIC RESEARCH ARCHIVE, 2020, 28 (01): : 205 - 220
[3] Benaissa A, 2014, ELECTRON J QUAL THEO, P1
[4] Active control of a beam using a piezoceramic element
Blanguernon, A
Léné, F
Bernadou, M
[J]. SMART MATERIALS & STRUCTURES, 1999, 8 (01) : 116 - 124
[5] Existence and general stabilization of the Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms
Chen, Miaomiao
Liu, Wenjun
Zhou, Weican
[J]. ADVANCES IN NONLINEAR ANALYSIS, 2018, 7 (04) : 547 - 569
[6] Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics
Damjanovic, D
[J]. REPORTS ON PROGRESS IN PHYSICS, 1998, 61 (09) : 1267 - 1324
[7] Multidomain boundary integral formulation for piezoelectric materials fracture mechanics
Davì, G
Milazzo, A
[J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2001, 38 (40-41) : 7065 - 7078
[8] A Timoshenko beam model for cantilevered piezoelectric energy harvesters
Dietl, J. M.
Wickenheiser, A. M.
Garcia, E.
[J]. SMART MATERIALS AND STRUCTURES, 2010, 19 (05)
[9] Long-time dynamics for a nonlinear Timoshenko system with delay
Feng, Baowei
Yang, Xin-Guang
[J]. APPLICABLE ANALYSIS, 2017, 96 (04) : 606 - 625
[10] Long-time dynamics for a fractional piezoelectric system with magnetic effects and Fourier's law
Freitas, M. M.
Ramos, A. J. A.
Ozer, A. O.
Almeida Junior, D. S.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 280 : 891 - 927

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