Exponential stability for laminated beams with a frictional damping

Apalara, Tijani A.; Raposo, Carlos A.; Nonato, Carlos

doi:10.1007/s00013-019-01427-1

Cited by 30 publications

(8 citation statements)

References 17 publications

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“…where µ = ρ EI ω 2 1/4 is treated as the new spectral parameter of problem ( 7), (9). The general solution of ( 10) can be represented in the intervals of continuity of u(x) as…”

Section: Spectral Problemmentioning

confidence: 99%

“…Over the last few years, stability and stabilization problems for laminated beams and beam networks have received a lot of attention due to their rich theoretical context and engineering applications (see, e.g., [8][9][10][11] and references therein). Stability conditions for elastic structures formed by serially connected flexible beams with different types of boundary conditions are obtained and illustrated by numerical examples in [12,13].…”

Section: Introductionmentioning

confidence: 99%

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On the Eigenvalue Distribution for a Beam with Attached Masses

Kalosha,

Zuyev,

Benner

2020

Preprint

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We study a mathematical model of a hinged flexible beam with piezoelectric actuators and electromagnetic shaker in this paper. The shaker is modelled as a mass and spring system attached to the beam. To analyze free vibrations of this mechanical system, we consider the corresponding spectral problem for a fourthorder differential operator with interface conditions that characterize the shaker dynamics. The characteristic equation is studied analytically, and asymptotic estimates of eigenvalues are obtained. The eigenvalue distribution is also illustrated by numerical simulations under a realistic choice of mechanical parameters.

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“…where µ = ρ EI ω 2 1/4 is treated as the new spectral parameter of problem ( 7), (9). The general solution of ( 10) can be represented in the intervals of continuity of u(x) as…”

Section: Spectral Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Eigenvalue Distribution for a Beam with Attached Masses

Kalosha,

Zuyev,

Benner

2020

Preprint

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“…Raposo 9 proved that the exponential stability holds without any restriction on the parameters if the first two equations are also damped via frictional dampings. For other stability results related to frictional dampings, see previous studies 10–14 …”

Section: Introductionmentioning

confidence: 99%

“…For other stability results related to frictional dampings, see previous studies. [10][11][12][13][14] Recently, Raposo et al 15 proved that, without any restriction on the parameters, the polynomial stability holds under additional three dynamic boundary conditions. For the stability of laminated beams with Cattaneo's or Fourier's type heat conduction, we refer the readers to Alves et al 16 and Liu and Zhao 17 (see also Apalara, 18 Feng, 19 and Mukiawa et al 20 for other types of thermoelastic laminated beams).…”

Section: Introductionmentioning

confidence: 99%

Laminated Timoshenko beams with interfacial slip and infinite memories

Guesmia

Rivera

Sepúlveda

et al. 2021

Math Methods in App Sciences

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We study in this paper the well‐posedness and stability of three structures with interfacial slip and two infinite memories effective on the transverse displacement and the rotation angle. We consider a large class of kernels and prove that the system has a unique solution satisfying some regularity properties. Moreover, without restrictions on the values of the parameters, we show that the solution goes to zero at infinity and give an information on its speed of convergence in terms of the growth of kernels at infinity. A numerical analysis of the obtained theoretical results will be also given.

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“…For example, Raposo [28] introduced extra linear frictional damping terms in the first two equations of (1.1) in addition to structural damping, and proved exponential stability without further restrictions. Later Apalara et al [9] established that a single linear frictional damping in the effective rotation angle is sufficient for exponential decay in case of equal wave speeds. Similarly, in [2], the authors consider system (1.1) with structural damping, and prove that if it is coupled with boundary feedback controls acting through complementary displacements, then no further dissipation or restrictions on parameters are required for exponential decay, otherwise the assumption of equal wave speeds is necessary.…”

Section: Introductionmentioning

confidence: 99%