Static and dynamic analyses of auxetic hybrid FRC/CNTRC laminated plates

Huang, Xiao; Yang, Jian; Azim, Iftikhar; Ren, Xin; Wang, Xing-er

doi:10.1515/ntrev-2020-0106

Cited by 11 publications

(3 citation statements)

References 65 publications

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“…This approach was applied successfully to solve various nonlinear boundary‐value problems of plates by many research teams in recent years. [ 37–43 ] To facilitate this two‐step perturbation method to solve nonlinear problems of porous sandwich plates, the motion Equation (8) is first re‐written in the dimensionless form as

L_{11} (W) - L_{12} (Ψ_{x}) - L_{13} (Ψ_{y}) + γ_{14} L_{14} (F) - L_{16} (M^{T}) + K_{1} W - K_{2} \nabla^{2} W = γ_{14} β^{2} L (W, F) + L_{17} (\ddot{W}) + γ_{80} (\frac{\partial {\ddot{Ψ}}_{x}}{\partial x} + β \frac{\partial {\ddot{Ψ}}_{y}}{\partial y}) + λ_{q}

L_{21} (F) + γ_{24} L_{22} (Ψ_{x}) + γ_{24} L_{23} (Ψ_{y}) - γ_{24} L_{24} (W) = - \frac{1}{2} γ_{24} β^{2} L (W, W)

L_{31} false(W false) + L_{32} false(Ψ_{x} false) - L_{33} false(Ψ_{y} false) + γ_{14} L_{34} false(F

…”

Section: Solution Methodologymentioning

confidence: 99%

“…This approach was applied successfully to solve various nonlinear boundary-value problems of plates by many research teams in recent years. [37][38][39][40][41][42][43] To facilitate this two-step perturbation method to solve nonlinear problems of porous sandwich plates, the motion Equation ( 8) is first re-written in the dimensionless form as…”

Section: Solution Methodologymentioning

confidence: 99%

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Modeling and Re‐Examination of Nonlinear Vibration and Nonlinear Bending of Sandwich Plates with Porous FG‐GPLRC Core

Shen

2023

Adv Eng Mater

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In this article, an inhomogeneous model is proposed to predict the material properties of porous GPL‐reinforced composite (GPLRC) and to predict the mechanical responses of a sandwich plate which consists of top and bottom metal face sheets and a porous GPLRC core. The GPLRC core is assumed to be multilayers, and each layer may have different values of porosity coefficient to achieve a piece‐wise functionally graded pattern. Young's moduli along with shear modulus of porous GPLRC core are predicted by a generic Halpin‐Tsai model in which the porosity is included. Thermo‐mechanical properties of both metal face sheets and porous GPLRC core are assumed to be temperature‐dependent. The governing equations of motion for porous sandwich plates are solved by applying a two‐step perturbation approach to obtain the analytical solutions for the two cases of nonlinear vibration and nonlinear bending of porous sandwich plates. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results reveal that, for most cases, the difference of natural frequencies between two models is over 30%, and the vibration frequency–amplitude curves and the bending load–deflection curves are underestimated by using the EIM.

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L_{11} (W) - L_{12} (Ψ_{x}) - L_{13} (Ψ_{y}) + γ_{14} L_{14} (F) - L_{16} (M^{T}) + K_{1} W - K_{2} \nabla^{2} W = γ_{14} β^{2} L (W, F) + L_{17} (\ddot{W}) + γ_{80} (\frac{\partial {\ddot{Ψ}}_{x}}{\partial x} + β \frac{\partial {\ddot{Ψ}}_{y}}{\partial y}) + λ_{q}

L_{21} (F) + γ_{24} L_{22} (Ψ_{x}) + γ_{24} L_{23} (Ψ_{y}) - γ_{24} L_{24} (W) = - \frac{1}{2} γ_{24} β^{2} L (W, W)

L_{31} false(W false) + L_{32} false(Ψ_{x} false) - L_{33} false(Ψ_{y} false) + γ_{14} L_{34} false(F

…”

Section: Solution Methodologymentioning

confidence: 99%

Section: Solution Methodologymentioning

confidence: 99%

Modeling and Re‐Examination of Nonlinear Vibration and Nonlinear Bending of Sandwich Plates with Porous FG‐GPLRC Core

Shen

2023

Adv Eng Mater

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“…Combined analytical numerical approach for auxetic structure under sudden load are studied (Huang et al, 2022). The static and dynamic performances of auxetic hybrid fibre reinforced composite and CNTRC have been analysed and the effects of the CNT, different foundation configurations and environmental conditions on the mechanical behaviours of hybrid laminated plate having NPR have been analysed (Huang et al, 2020a). The significant effects of temperatures on the dynamic response and foundation stiffness of NPR structure are also studied and analysed.…”

Section: Introductionmentioning

confidence: 99%

Chaotic vibration analysis of auxetic nanocomposite structures

Parhi

Roy

2022

Journal of Vibration and Control

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The present work deals with the study of nonlinear vibration behaviours of the carbon nanotube reinforced composite structures having negative Poisson’s ratio (CNTRC-NPR). Such types of flexible auxetic structures have many applications in various engineering fields. Based on classical laminated theory, auxetic structures can be designed by some special stacking sequence of layers in the laminated composites. A mathematical model is formulated for nonlinear vibration analysis of the clamped-clamped CNTRC-NPR beam under the time varying uniformly distributed transverse load. The present formulation is based on the Reddy’s third-order shear deformation theory and the governing equation of motion of such beam is derived by using the Hamilton’s principle. Based on the Galerkin’s method, the obtained governing partial differential equations are converted to an ordinary nonlinear second-order differential equation for the analysis of out plane vibration. The obtained vibrations of such auxetic structures are discussed using time series waveforms, phase portraits and Poincare maps, and the route of chaotic vibration of such structures is found and reported based on the bifurcation diagrams. The jump phenomena associated with the dynamics have also been characterized. Nonlinear vibrations of without and with auxetic nanocomposite structures have also been compared. It is found that the amplitude of transverse force of excitation is the controlling parameter of nonlinear dynamics of such CNTRC-NPR structures.

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