Nonlinear low-velocity impact response of functionally graded plate with nonlinear three-parameter elastic foundation in thermal field

Najafi, Farzin; Shojaeefard, Mohammad Hassan; Googarchin, Hamed Saeidi

doi:10.1016/j.compositesb.2016.09.070

Cited by 37 publications

(6 citation statements)

References 75 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%

See 1 more Smart Citation

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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“…The third term correlated with the variation of the strain energy can be obtained by inserting Equation ( 55) into ( 14) and then substituting it into Equation (35). This term is given as…”

Section: The Finite-element Formulationmentioning

confidence: 99%

“…While the authors highlighted the notable contribution of the carbon nanotubes distribution, the insignificance effects of the boundary conditions to the contact force response of the plates were underscored. Najafi et al [ 35 ] presented an analytical solution for the impact response of FG plates that rested on an elastic foundation. The material properties were assumed to be temperature dependent through the thickness of the plates and were calculated using Voigt [ 36 ] model.…”

Section: Introductionmentioning

confidence: 99%

Low‐Velocity Impact Response Analysis of Functionally Graded Piezoelectric Plates Using Finite‐Element Method and a Two‐Degrees‐of‐Freedom Spring‐Mass Model

2023

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The study focuses on the low‐velocity impact response of functionally graded piezoelectric plates. The effective material properties are determined using the rule of mixture and power law model. The kinematics of the plates is modeled by the first‐order shear deformation theory, and coupled governing equations of the plates are formulated using Hamilton's principle and Maxwell's law. A set of time‐dependent equations, extracted by applying the finite‐element method, is solved by the fourth‐order Runge–Kutta method. A linearized form of Hertz's contact law and a two‐degrees‐of‐freedom spring‐mass system are incorporated to find the contact force under the impact event. Numerical results are verified by comparing with the available literature data. The impact response of the plates constituted of different volume fractions and slenderness ratios in both simply supported and clamped boundary conditions are evaluated under different impact conditions. Based on the results of the present study, it is found that the volume fraction of the piezoelectric components, impact condition, in‐plane dimensions, and the plate slenderness ratio play significant roles in the impact behavior of the plates. Eventually, it is found that the applied electric voltage is not a notable factor in determining the impact response of the plates.

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“…Mantari et al (2011), , adopted the HSDT to study the static and dynamic behavior of laminated and sandwich plates using trigonometric shape functions. Najafi et al (2016) carried out the investigation for non-linear low-velocity impact on FG plate resting on elastic foundation in thermal environment using Reddy's HSDT in conjunction with von-Karman type non-linearity. Further, they extended their work for FGM beam and FG doubly curved panel resting on elastic foundation (Najafi et al, 2017a, b).…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of FG rotating plate using nonlinear-FEM

Parida

Mohanty

2019

MMMS

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Purpose The purpose of this paper is to investigate the linear and non-linear free vibration of a functionally graded material (FGM) rotating cantilever plate in the thermal environment. The study employs the development of a non-linear mathematical model using the higher order shear deformation theory in which the traction free condition is applied to derive the simplified displacement model with seven field variables instead of nine. Design/methodology/approach A mathematical model is developed based on the higher order shear deformation theory using von-Karman type non-linearity. The rotating plate domain has been discretized into C0 eight-noded quadratic serendipity elements with node wise 7 degrees of freedom. The material properties are considered temperature dependent and graded along the thickness direction obeying a simple power law distribution in terms of the volume fraction of constituents, based on Voigt’s micromechanical method. The governing equations are derived using Hamilton’s principle and are solved using the direct iterative method. Findings The importance of the present mathematical model developed for numerical analysis has been stated through the comparison studies. The results provide an insight into the vibration response of FGM rotating plate under thermal environment. The influence of various parameters like setting angle, volume fraction index, hub radius, rotation speed parameter, aspect ratio, side-thickness ratio and temperature gradient on linear and non-linear frequency parameters is discussed in detail. Originality/value A non-linear mathematical model is newly developed based on C0 continuity for the functionally graded rotating plate considering the 1D Fourier equation of heat conduction. The present findings can be utilized for the design of rotating plates made up of a FGM in the thermal environment under real-life situations.

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Nonlinear low-velocity impact response of functionally graded plate with nonlinear three-parameter elastic foundation in thermal field

Cited by 37 publications

References 75 publications

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

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

Low‐Velocity Impact Response Analysis of Functionally Graded Piezoelectric Plates Using Finite‐Element Method and a Two‐Degrees‐of‐Freedom Spring‐Mass Model

Vibration analysis of FG rotating plate using nonlinear-FEM

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