Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity

Repka, Miroslav�; Sládek, J.; Sládek, V.

doi:10.3390/nano11113123

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…Laplace transform and Adomian decomposition method (LADM) was employed to investigate semi-analytical solutions of Euler–Bernoulli beam equation in order to describe a uniform flexible cantilever beam 5 . Repka et al 6 applied the Timoshenko beam model in the analysis of the flexoelectric effect for a cantilever beam under large deformations, and considered the geometric nonlinearity with von Kármán strains. Meanwhile, some methods, such as a homotopy analysis method 7 , a rational elliptic balance method 8 , an enriched multiple scales method 9 , and an improved homotopy analysis method 10 , 11 , etc., have been gradually developed to solve nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 99%

Chaotic vibration control of a composite cantilever beam

Liu,

Sun

2023

Sci Rep

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In this research, an adaptive control strategy adapted from fuzzy sliding mode control is established and applied in chaotic vibration control of a multiple-dimension nonlinear dynamic system of a laminated composite cantilever beam. The third order shearing effect on the vibration of the beam is considered in the nonlinear dynamic model establishment, and the Hamilton principle as well as the Galerkin method is employed. It is discovered that a multi-dimensional nonlinear dynamic system of the cantilever beam needs to be considered for accurate vibration estimation. Therefore, the control strategy appropriate for the chaotic vibration control of a multiple-dimension system of the laminated composite beam is necessary, and then proves to be effective in chaotic vibration control in numerical simulation.

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Section: Introductionmentioning

confidence: 99%

Chaotic vibration control of a composite cantilever beam

Liu,

Sun

2023

Sci Rep

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show abstract

“…Laplace transform and Adomian decomposition method (LADM) was investigated to semi-analytical solutions of Euler-Bernoulli beam equation that was used to describe the uniform flexible cantilever beam [5]. Repka [6] et al applied the Timoshenko beam model to the analysis of the flexoelectric effect for a cantilever beam under large deformations, and considered the geometric nonlinearity with von Kármán strains. Meanwhile, some methods, such as homotopy analysis method [7], rational elliptic balance method [8], enriched multiple scales method [9], improved homotopy analysis method [10][11], etc, have been gradually developed to solve nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Vibration Control of a Composite Cantilever Beam

Liu

Sun

2023

Preprint

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In this research, an adaptive control strategy adapted from Fuzzy Sliding Mode Control is established and applied in chaotic vibration control of a multiple-dimension nonlinear dynamic system of a laminated composite cantilever beam. The 3rd order shearing effect on the vibration of the beam is considered in the nonlinear dynamic model establishment, and the Hamilton principle as well as the Galerkin method is employed. It is discovered that a multi-dimensional nonlinear dynamic system of the cantilever beam needs to be considered for accurate vibration estimation. Therefore, the control strategy appropriate for the chaotic vibration control of a multiple-dimension system of the laminated composite beam is necessary, and then proves to be effective in chaotic vibration control in numerical simulation.

show abstract