Studying nonlinear vibrations of composite conical panels with arbitrary-shaped cutout reinforced with graphene platelets based on higher-order shear deformation theory

Abstract

In this article, the vibrational behavior of conical panels in the nonlinear regime made of functionally graded graphene platelet–reinforced composite having a hole with various shapes is investigated in the context of higher-order shear deformation theory. To achieve this aim, a numerical approach is used based on the variational differential quadrature and finite element methods. The geometrical nonlinearity is captured using the von Karman hypothesis. Also, the modified Halpin–Tsai model and rule of mixture are applied to calculate the material properties of graphene platelet–reinforced composite for various functionally graded distribution patterns of graphene platelets. The governing equations are derived by a variational approach and represented in matrix-vector form for the computational purposes. Moreover, attributable to using higher-order shear deformation theory, a mixed formulation approach is presented to consider the continuity of first-order derivatives on the common boundaries of elements. In the numerical results, the nonlinear free vibration behaviors of functionally graded graphene platelet–reinforced composite conical panels including square/circular/elliptical hole and with crack are studied. The effects of boundary conditions, graphene platelet reinforcement, and other important parameters on the vibrational response of panels are comprehensively analyzed.

Nonlinear Free Vibration Analysis of Functionally Graded Porous Conical Shells Reinforced with Graphene Nanoplatelets

“…It is assumed all the internal pores are tiny and the total volume fraction of the pores is small. Unlike other models for evaluating the material properties [30] and [39], in which Young's modulus, shear modulus, and mass density need to be assumed, the present model is based on the following assumption about the volume fraction V P (z) of the internal pores: here, e 0 denotes the porosity coefficient. Young's elastic modulus E(z) and mass density ρ(z) for various porosity distributions can be expressed as [39].…”

“…In the literature above, the conical shells were regarded as the perfect structures without pores. However, internal pores may appear inside composite materials [30]. Thus, it is necessary to investigate the effect of internal pores on the dynamic behaviour of porous structures.…”

Selective layer-by-layer fillering and its effect on the dynamic response of laminated composite plates using higher-order theory

“…The Lagrangian first variation principle is used for FE formulation (Ansari et al, 2021) of LCPs under free vibration and is given by…”

“…The Kantorovich method (Fallah et al, 2013; Rostami et al, 2018), Ritz method (Xue and Wang, 2019), Hamilton’s principle (Thai et al, 2013b; Dastjerdi et al, 2020), finite integral transformation technique (Zhang et al, 2020), and discrete singular convolution technique (Civalek, 2014; Civalek and Baltacioglu, 2019; Civalek and Avcar, 2020; Mercan et al, 2016) specially used for the static and modal analysis of FG plates are reported. For non-linear modal analysis, Green–Lagrange formulation in HSDT is used (Ansari et al, 2021; Singh and Panda, 2017).…”

On the wave dispersion of a multi-scale hybrid nanocomposite microstructure via deep neural network technique

“…Therefore, artificial neural network (ANN) (Lingamdinne et al, 2023; Moradi et al, 2022) and PINN could be feasible procedures to obtain results in a short time span. The numerical solutions in structural mechanics have been used in nonlinear buckling (Al-Furjan et al, 2020a; Moayedi et al, 2020; Safarpour et al, 2020a, 2020b), wave propagation (Al-Furjan et al, 2021c; Ebrahimi et al, 2019b; Habibi et al, 2019b), and vibration (Sui et al, 2021; Dai et al, 2022) in different members including beams (Kharazan et al, 2021; Singh and Sharma, 2021; Ramírez-Neria et al, 2021; Shariati et al, 2020a, 2020b, 2020c), shells (Ansari et al, 2021; Habibi et al, 2019b, 2019c, 2021b), and plates (Shariyat and Khani Arani, 2022; Habibi et al, 2019a, 2021a; Huo et al, 2021). The nonlinear vibrations of shell structures with conical geometry made of composite materials and complicated cut-outs were investigated by Ansari et al (2021).…”