Viscoelastic string-beam coupled vibro-impact system: modeling and dynamic analysis

Wu, Qiliang; Qi, Guoyuan

doi:10.1016/j.euromechsol.2020.104012

Cited by 12 publications

(9 citation statements)

References 65 publications

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“…For more literatures on polynomial decay results, we can also refer to previous studies [7][8][9][10]. In the same way, researchers have also obtained some exponential decay results of damping additive on a single wave/string in previous studies [11][12][13][14], which they have studied two-dimensional wave-plate and string-beam transmission systems, respectively. There are also some papers on the control of the stability of coupled systems by the dissipation mechanism of heat.…”

Section: Introductionmentioning

confidence: 89%

Stabilization for weakly coupled string–riser system with partial frictional damping

Zhang,

Liu

2023

Math Methods in App Sciences

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In this paper, we consider the stabilization of a 1‐D coupled string–riser system with partial frictional damping. The frictional damping is only distributed in the part of the string's or riser's domain, and its dissipative effect is transmitted to the other equation through the coupling. Firstly, we prove the existence and uniqueness result for solution of coupled system. Next, using a semigroup approach combined with the multipliers technique, we obtain that the two coupled systems are not exponentially stable, provide precise polynomial decay rates for their energy functionals, respectively, regardless of whether the friction damping only acts on the string equation or the riser equation, and give the optimality of polynomial decay rates. Finally, we compare the case of friction damping acting on string and riser equations simultaneously with the previous two cases. The results show that the case of friction damping acting on string and riser equations simultaneously is exponential stable, while the case of friction damping only acting on string or riser equations is polynomial stable and the decay result of friction damping only acts on the string equation is better than that only acts on the riser equation.

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Section: Introductionmentioning

confidence: 89%

Stabilization for weakly coupled string–riser system with partial frictional damping

Zhang,

Liu

2023

Math Methods in App Sciences

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“…As a result of shrinking the size of devices, an unavoidable problem could be the occurrence of chaotic motion leading to device stiction or malfunction. [41][42][43][44] So far, several works have shown the strong dependence of the normal Casimir force on the material optical properties and explored how these properties can be utilized to tune the actuation dynamics of devices that can exhibit transitions toward chaotic motion. [27][28][29][30] However, still unexplored is the actuation dynamic of devices under the influence of the lateral Casimir force by taking into account significant contrast in the material optical properties and conductivity of the interacting surfaces.…”

Section: Articlementioning

confidence: 99%

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics

Tajik

Masoudi

Sedighi

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In [6] the Faedo-Galerkin method was used to solve beam vibration equation with nonlinear tension, a viscoelastic damping and distributed delay term. Wu [7] studied the viscoelastic string-beam coupled system in detail. In [8], the one-dimensional finite element method and analytical method were used to study Euler-Bernoulli beams equations resting on multi-layered viscoelastic soil.…”

Section: Introductionmentioning

confidence: 99%

Hermite Finite Element Method for a Class of Viscoelastic Beam Vibration Problem

Tang¹,

Yin²

2021

ENG

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Beam equation can describe the deformation of beams and reflect various bending problems and it has been widely used in large engineering projects, bridge construction, aerospace and other fields. It has important engineering practice value and scientific significance for the design of numerical schemes. In this paper, a scheme for vibration equation of viscoelastic beam is developed by using the Hermite finite element. Based on an elliptic projection, the errors of semi-discrete scheme and fully discrete scheme are analyzed respectively, and the optimal L 2 -norm error estimates are obtained. Finally, a numerical example is given to verify the theoretical predictions and the validity of the scheme.

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Viscoelastic string-beam coupled vibro-impact system: modeling and dynamic analysis

Cited by 12 publications

References 65 publications

Stabilization for weakly coupled string–riser system with partial frictional damping

Stabilization for weakly coupled string–riser system with partial frictional damping

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics

Hermite Finite Element Method for a Class of Viscoelastic Beam Vibration Problem

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