A solution method based on Lagrange multipliers and Legendre polynomial series for free vibration analysis of laminated plates sandwiched by two MFC layers

Baghaee, Mehdi; Farrokhabadi, Amin; Jafari-Talookolaei, Ramazan-Ali

doi:10.1016/j.jsv.2019.01.037

Cited by 19 publications

(3 citation statements)

References 35 publications

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“…For the Rayleigh-Ritz method, the key factor for the high performance of solutions is to choose an appropriate admissible displacement function. Various polynomials are used to represent the admissible displacement function (Chebyshev [25], Legendre [26], orthogonal [27], modified Fourier series [28], and Fourier-Bessel polynomials [29]). Huo et al [25] employed the Chebyshev polynomial and Fourier series to decompose the unified solution of the stress function to analyze the transverse vibration and buckling characteristics of the rectangular plate via the Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation

Qin,

Mei,

Wang

2024

Materials

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Based on the three-dimensional elasticity theory, the free vibration of functionally graded porous (FGP) sandwich rectangular plates is studied, and a unified solution for free vibration of the plates is proposed in this study. The arbitrary boundary conditions of FGP sandwich rectangular plates are simulated by using the Rayleigh–Ritz method combined with artificial spring theory. The calculation performances of the unified solution for FGP sandwich rectangular plates such as convergence speed and computational efficiency are compared extensively under different displacement functions. In addition, three kinds of elastic foundation (Winkler/Pasternak/Kerr foundations) and three porosity distributions are considered. Some benchmark results and accurate values for the free vibration of FGP sandwich rectangular plates resting on elastic foundations are given. Finally, the effects of diverse structural parameters, elastic foundations with different parameters, and boundary conditions on the free vibration of the FGP sandwich rectangular plates are analyzed.

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Section: Introductionmentioning

confidence: 99%

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation

Qin,

Mei,

Wang

2024

Materials

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“…On the basis of extended layerwise method, Xiao et al [42] derived the final governing equation for the thermo-electro-mechanical coupled effect of laminated piezoelectric plates with cracks. Furthermore, the piezoelectric macro fiber composites with high toughness which are critical in prediction of stresses, natural frequencies, critical loads and other mechanical area has gotten a lot of interest recently [43][44][45][46][47][48]. However, there have been relatively few works on the mechanical characteristics investigation of composite structures containing GSR actuators.…”

Section: Introductionmentioning

confidence: 99%

Electro-mechanical coupling model and interlaminar stress analysis of laminated plates containing GSR actuator

Ma,

Zhang,

Zhang

2023

Phys. Scr.

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Due to its remarkable physical features, graphene nanosheets (GPN) are one of the most appealing reinforcing materials for composites. For polyvinylidene fluoride (PVDF), GPN reinforced composites can dramatically increase its piezoelectric and mechanical characteristics. If the interlaminar shear deformation of laminated plates containing uniform graphene sheets reinforced (GSR) smart piezoelectric layer, which material properties vary widely from layer to layer and subjected to electromechanical loading cannot be accurately predicted, the interlaminar stresses may be very high, eventually leading to interlaminar failure. In light of this, an effective mechanoelectrical coupling model for the accurate prediction of interlaminar stress for composite plates contains GSR actuators is developed in present study. Meanwhile, the finite element formulation (FEF) can be substantially simplified due to the expression of transverse shear stress components becoming more succinct. Therefore, by using the suggested electro-mechanical coupling theory, a three-node FEF is easily constructed. The refinement of transverse shear stress prediction in the context of electromechanical coupling can be accomplished through the application of the Reissner mixed variation theory (RMVT). The performance of the recommended plate model will be evaluated using the results derived from three-dimensional (3D) elastic theory and the selected model. By employing the RMVT method, we improve predictions of transverse shear stresses while considering the electromechanical coupling effect. The results from our model are compared with alternative models and 3D elasticity theory, demonstrating its superiority in satisfying the continuity requirements of transverse shear stresses and exhibiting excellent agreement with exact solutions. This validates the accuracy and applicability of our proposed model. Further to that, the prediction of mechanical characteristics for laminated plates with GSR actuators were systematically studied from the thoroughly perspectives of electromechanical load, piezoelectric layer thickness, graphene volume fraction, and some other parameters.

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“…Static, buckling and dynamic analyses of laminated composite plates with MFC actuators have been extensively investigated [8][9][10][11][12][13][50][51][52][53][54]. In addition, piezoelectric materials were used in the smart structures for shape, vibration and buckling control [7,12,[55][56][57].…”

Section: Introductionmentioning

confidence: 99%

An Alternative Electro-Mechanical Finite Formulation for Functionally Graded Graphene-Reinforced Composite Beams with Macro-Fiber Composite Actuator

Fu¹,

Tang²,

Jin

et al. 2021

Materials

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With its extraordinary physical properties, graphene is regarded as one of the most attractive reinforcements to enhance the mechanical characteristics of composite materials. However, the existing models in the literature might meet severe challenges in the interlaminar-stress prediction of thick, functionally graded, graphene-reinforced-composite (FG-GRC)-laminated beams that have been integrated with piezoelectric macro-fiber-composite (MFC) actuators under electro-mechanical loadings. If the transverse shear deformations cannot be accurately described, then the mechanical performance of the FG-GRC-laminated beams with MFC actuators will be significantly impacted by the electro-mechanical coupling effect and the sudden change of the material characteristics at the interfaces. Therefore, a new electro-mechanical coupled-beam model with only four independent displacement variables is proposed in this paper. Employing the Hu–Washizu (HW) variational principle, the precision of the transverse shear stresses in regard to the electro-mechanical coupling effect can be improved. Moreover, the second-order derivatives of the in-plane displacement parameters have been removed from the transverse-shear-stress components, which can greatly simplify the finite-element implementation. Thus, based on the proposed electro-mechanical coupled model, a simple C0-type finite-element formulation is developed for the interlaminar shear-stress analysis of thick FG-GRC-laminated beams with MFC actuators. The 3D elasticity solutions and the results obtained from other models are used to assess the performance of the proposed finite-element formulation. Additionally, comprehensive parametric studies are performed on the influences of the graphene volume fraction, distribution pattern, electro-mechanical loading, boundary conditions, lamination scheme and geometrical parameters of the beams on the deformations and stresses of the FG-GRC-laminated beams with MFC actuators.

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A solution method based on Lagrange multipliers and Legendre polynomial series for free vibration analysis of laminated plates sandwiched by two MFC layers

Cited by 19 publications

References 35 publications

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation

Electro-mechanical coupling model and interlaminar stress analysis of laminated plates containing GSR actuator

An Alternative Electro-Mechanical Finite Formulation for Functionally Graded Graphene-Reinforced Composite Beams with Macro-Fiber Composite Actuator

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