Nonlinear primary and super-harmonic resonances of functionally graded carbon nanotube reinforced composite beams

Wu, Zhihua; Zhang, Yimin; Yao, Guo; Yang, Zhou

doi:10.1016/j.ijmecsci.2019.02.015

Cited by 43 publications

(5 citation statements)

References 55 publications

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“…In equations ( 5) and ( 6), 11 A , 11 B and 11 D are extension-extension, bending-extension and bending-bending coupling coefficients, respectively, which can be evaluated using the wellknown classical theory of FGM beams [13]. Their expressions are defined as follows:…”

Section: Linear Vibration Analysismentioning

confidence: 99%

Analysis of Geometrically Non-Linear Free Vibrations of Functional Graded Beams in a Thermal Environment

Khouddar¹,

Adri²,

Outassafte³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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The thermal non-linear vibrational behavior of functional graded beams is analyzed using Euler-Bernoulli beam theory and Hamilton's theorem, combined with spectral analysis. A set of non-linear equations is derived based on the von Kármán deformation-displacement relationship and the properties of the functional graded material are assumed to be temperature dependent and to follow a simple power distribution in the thickness direction. Numerical solutions of the non-linear dynamic equations of functional graded beams are obtained by an approximate method called the second formulation. In addition, numerical examples were performed to highlight the accuracy of the method used in this study, and the results are very consistent with those found in the literature. In the numerical examples, the influences played by thermal environmental conditions and volume fraction index are discussed in detail.

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Section: Linear Vibration Analysismentioning

confidence: 99%

Analysis of Geometrically Non-Linear Free Vibrations of Functional Graded Beams in a Thermal Environment

Khouddar¹,

Adri²,

Outassafte³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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show abstract

“…The analysis reveals that the IHB method has good convergence and accuracy with the ability to extract both stable and unstable solutions. Wu et al [32] derived nonlinear ordinary differential equations for functional gradient carbon nanotube reinforced composite beams and solved the vibrational response of the system subjected to transverse simple harmonic excitation by means of the IHB method in order to study its nonlinear primary and super-harmonic resonance responses. Kwangchol et al [33] modeled the nonlinear forced vibration of laminated beams by differential quadrature finite element method and IHB method, on the basis of which the role of internal resonance on the nonlinear frequency response of the structure was analyzed in detail.…”

Section: Introductionmentioning

confidence: 99%

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Wang,

Zhong,

Wang

2024

Preprint

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Combining the spectral geometry method and the incremental harmonic balance method (IHB), the nonlinear analytical model of functionally graded graphene platelet reinforced composite (FG-GPLRC) beams is developed in this paper. Nonlinear free and forced vibration characteristics are studied based on this model containing viscoelastic foundation and geometric nonlinear factors. Geometric nonlinear strain-displacement relationship and Lagrangian energy generalization for the FG-GPLRC beam structure are derived according to the Von-Kármán and Timoshenko theories. The IHB method is applied to track the nonlinear vibration response solution of the reduced-order model, which is constructed by introducing linear modal components into the overall nonlinear dynamic equation of the FG-GPLRC beam. Through comparison of the present solution with those from numerical method and literature, the correctness of the established nonlinear analytical model is evidenced. Further, the influence of material-, geometry-, foundation-related parameters and boundary constraints on the nonlinear frequency parameter and amplitude-frequency response of FG-GPLRC beams rested on viscoelastic foundation is analyzed, which can serve as a theoretical guide for designing and evaluating the dynamic environment adaptation of FG-GPLRC beams.

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“…The nonlinearity of structures can cause complex dynamic responses such as super-harmonic response (Permoon et al, 2018; Wu et al, 2019), subharmonic response (Rong et al, 2011), and soft and hard nonlinearity (Guo et al, 2022b; Han et al, 2021). It is worth noting that unstable closed detached response (CDR) branches may be introduced owing to the nonlinearity in the vibration control of the system (Habib et al, 2017; Zang et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration control of functionally graded material beam coupled with NiTiNOL–steel wire ropes

Zang

Zhang

2023

Journal of Vibration and Control

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This paper proposes a novel damping device, NiTiNOL–steel wire rope, which is a vibration absorber with linear hysteresis damping, nonlinear damping, and nonlinear stiffness. This study is the first to couple the NiTi–ST damping device with the functionally graded material beam model. The Runge–Kutta method and harmonic balance method are adopted to study the resonant response of the system from the numerical and analytical aspects, respectively. It proves that NiTi–ST provides effective vibration reduction for FGM beam structures. In addition, special attention is paid to the appearance of the closed detached response, which significantly affects the resonant peak value of the system. And the CDR phenomenon is eliminated by adjusting the parameters, and a good damping effect is achieved under large external excitation. Results confirm that NiTi–ST is a promising nonlinear damper that serves as a new method for the vibration suppression of continuum structures.

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Nonlinear primary and super-harmonic resonances of functionally graded carbon nanotube reinforced composite beams

Cited by 43 publications

References 55 publications

Analysis of Geometrically Non-Linear Free Vibrations of Functional Graded Beams in a Thermal Environment

Analysis of Geometrically Non-Linear Free Vibrations of Functional Graded Beams in a Thermal Environment

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Nonlinear vibration control of functionally graded material beam coupled with NiTiNOL–steel wire ropes

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