Piezoelectric beams with magnetic effect and localized damping

Afilal, Mounir; Soufyane, Abdelaziz; Santos, Mauro de Lima

doi:10.3934/mcrf.2021056

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…In [24], a piezoelectric beam system with magnetic effects and delay term was considered and the existence of a global attractor was proved. Afilal et al [25] considered a one‐dimensional dissipative system of piezoelectric beams with magnetic effect and localized damping. They proved that the system is exponential stable using a damping mechanism acting only on one component and on a small part of the beam.…”

Section: Introductionmentioning

confidence: 99%

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

Al‐Gharabli,

Messaoudi

2023

Math Methods in App Sciences

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In this paper, we consider a piezoelectric beam model with nonlinear source terms and investigate the interaction between a viscoelastic damping and a nonlinear frictional damping. Under general assumptions on the relaxation function and the nonlinear feedback, we establish explicit formulae for the energy decay rates of this system and prove that the energy decays at a rate dictated by the weaker damping. Our results substantially improve some earlier related results in the literature.

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Section: Introductionmentioning

confidence: 99%

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

Al‐Gharabli,

Messaoudi

2023

Math Methods in App Sciences

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“…In fact, there exists a physical interpretation of this type of the system. For example, in 1D, system (1.1) represents the piezoelectric material with magnetic effect (see, for instance, [35][36][37][38][39][40][41][42] and the rich references therein). In this direction, system (1.1) can be considered as a restriction of piezoelectric material in the multidimensional case.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability and exact controllability of a system of coupled wave equations by second‐order terms (via Laplacian) with only one non‐smooth local damping

Akil,

Hajjej

2023

Math Methods in App Sciences

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The purpose of this work is to investigate the exponential stability of a second‐order coupled wave equations by Laplacian with one locally internal viscous damping. The strong stability is established by combining a unique continuation result and a Carleman estimate. Besides, the exponential stability is proved under (PMGC) condition on the damping region without any restriction on wave propagation speed (i.e., whether the two wave equations propagate at the same speed or not). The proof of this result relies on the frequency domain method combined with the multiplier techniques.

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“…It is worth mentioning that it is well known that piezoelectric beams without the magnetic effect, in which they are represented by a wave equation [13], are exactly observable [11] and exponentially stable [25]. Also, there exists a few results on piezoelectric material with different kind of dampings [1,24,20,19,15,17,2,3]. Recently, in [16], a nouvel infinite-dimensional models, by a through variational approach, are introduced to describe vibrations on a piezoelectric beam.…”

Section: Introductionmentioning

confidence: 99%

Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings

Akil¹,

Soufyane²,

Belhamadia³

2022

Preprint

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In this paper, we investigate the stabilization of a one-dimensional Lorenz piezoelectric (Stretching system) with partial viscous dampings. First, by using Lorenz gauge conditions, we reformulate our system to achieve the existence and uniqueness of the solution. Next, by using General criteria of Arendt-Batty, we prove the strong stability in different cases. Finally, we prove that it is sufficient to control the stretching of the center-line of the beam in x−direction to achieve the exponential stability. Numerical results are also presented to validate our theoretical result. Contents 1. Introduction 1 2. Reformulation and Wellposedness 3 3. Strong Stability 6 4. The stretching of the centreline of the beam in x−direction and electrical field component in (x and z)−direction are damped "(a, b, c) = (0, 0, 0)" 9 5. The electrical field component in (x and z)−direction are damped "a = 0 and (b, c) = (0, 0)" 12 6. The stretching of the centreline of the beam in x−direction and electrical field component in z−direction are damped "b = 0 and (a, c) = (0, 0)" 15 7. The stretching of the centreline of the beam in x−direction and electrical field component in x−direction are damped "c = 0 and (a, b) = (0, 0)" 16 8. The stretching of the centreline of the beam in x−direction only is damped and "a = 0 and (b, c) = (0, 0)" 19 9. Numerical Results 22 10. Conclusion 24 References 25

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Piezoelectric beams with magnetic effect and localized damping

Cited by 8 publications

References 18 publications

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

Exponential stability and exact controllability of a system of coupled wave equations by second‐order terms (via Laplacian) with only one non‐smooth local damping

Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings

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