Asymptotic behavior of a laminated beam with nonlinear delay and nonlinear structural damping

Mpungu, Kassimu; Apalara, Tijani A.

doi:10.15672/hujms.947131

Cited by 4 publications

(2 citation statements)

References 44 publications

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“…Some previous research projects have provided examples related to our established assumptions and our stability results; see [4] for more details.…”

Section: Preliminaries and Position Of Problemmentioning

confidence: 99%

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Decay of a Thermoelastic Laminated Beam with Microtemperature Effects, Nonlinear Delay, and Nonlinear Structural Damping

Saber,

Yazid,

Ouchenane

et al. 2023

Mathematics

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This article deals with a non-classical model, namely a thermoelastic laminated beam along with microtemperature effects, nonlinear delay, and nonlinear structural damping, where the last two terms both affect the equation which depicts the dynamics of slip. With the help of convenient conditions in both weight delay and wave speeds, we demonstrate explicit and general energy decay rates of the solution. To attain our interests, we highlight useful properties regarding convex functions and apply a specific approach known as the multiplier technique, which enables us to prove the stability results. Our results here aim to show the impact of different types of damping by taking into account the interaction between them, which extends recent publications in the literature.

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“…Some previous research projects have provided examples related to our established assumptions and our stability results; see [4] for more details.…”

Section: Preliminaries and Position Of Problemmentioning

confidence: 99%

“…In the research of Mpungu and Apalara in [4], system (1) was taken into consideration. By including both nonlinear delay and nonlinear structural damping in the third equation, the authors managed to provide the general energy decay rates of the solutions, assuming that certain assumptions regarding the weight delay and wave speeds hold.…”

Section: Introductionmentioning

confidence: 99%

Decay of a Thermoelastic Laminated Beam with Microtemperature Effects, Nonlinear Delay, and Nonlinear Structural Damping

Saber,

Yazid,

Ouchenane

et al. 2023

Mathematics

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Uniform stability result of laminated beams with thermoelasticity of type Ⅲ

Apalara

Ige

Enyi

et al. 2023

MATH

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<abstract><p>In this work, we study the effect of heat conduction theories pioneered by Green and Naghdi, popularly called thermoelasticity of type Ⅲ, on the stability of laminated Timoshenko beams. Without the structural (interfacial slip) damping or any other forms of damping mechanisms, we establish an exponential stability result depending on the equality of wave velocities of the system. Our work shows that the thermal effect is strong enough to stabilize the system exponentially without any additional internal or boundary dampings. The result extends some of the developments in literature where structural damping (in addition to some internal or boundary dampings) is necessary to bring about exponential stability.</p></abstract>

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On the time decay for a thermoelastic laminated beam with microtemperature effects, nonlinear weight, and nonlinear time-varying delay

Djeradi,

Yazid,

Georgiev

et al. 2023

MATH

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<abstract><p>This article examines the joint impacts of microtemperature, nonlinear structural damping, along with nonlinear time-varying delay term, and time-varying coefficient on a thermoelastic laminated beam, where, the equation representing the dynamics of slip is affected by the last three mentioned terms. A general decay result was established regarding the system concerned given equal wave speeds and particular assumptions related to nonlinear terms.</p></abstract>

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Asymptotic behavior of a laminated beam with nonlinear delay and nonlinear structural damping

Cited by 4 publications

References 44 publications

Decay of a Thermoelastic Laminated Beam with Microtemperature Effects, Nonlinear Delay, and Nonlinear Structural Damping

Decay of a Thermoelastic Laminated Beam with Microtemperature Effects, Nonlinear Delay, and Nonlinear Structural Damping

Uniform stability result of laminated beams with thermoelasticity of type Ⅲ

On the time decay for a thermoelastic laminated beam with microtemperature effects, nonlinear weight, and nonlinear time-varying delay

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