Nonlinear vibration of FG-CNTRC cylindrical panels with corrugated core using the FSDT

In this paper, a new design of cylindrical panels is proposed with two functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets and a corrugated core. The corrugated core layer is modelled by applying the homogeneous technique according to the firstorder shear deformation theory (FSDT). The nonlinear vibration behaviour of first-order shear deformable cylindrical panels with geometric nonlinearities is analysed in the present paper.
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Nonlinear vibration of FG-CNTRC cylindrical panels with corrugated core using the FSDT 82 99 Tuyển tập công trình Hội nghị Cơ học toàn quốc lần thứ XI, Hà Nội, 02-03/12/2022Nonlinear vibration of FG-CNTRC cylindrical panels with corrugated core using the FSDT Vu Minh Duc1,*, Tran Ngoc Hung1, Nguyen Thi Phuong2 1 Institute of Transport Technology, University of Transport Technology, Hanoi 100000, Vietnam 2 Faculty of Civil Engineering, University of Transport Technology, Hanoi 100000, Vietnam *Email: ducvm@utt.edu.vn Abstract. In this paper, a new design of cylindrical panels is proposed with two functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets and a corrugated core. The corrugated core layer is modelled by applying the homogeneous technique according to the first- order shear deformation theory (FSDT). The nonlinear vibration behaviour of first-order shear deformable cylindrical panels with geometric nonlinearities is analysed in the present paper. The stress function is considered and the Galerkin method is used to formulate the nonlinear motion equation system. Nonlinear dynamic responses of panels can be achieved by using the fourth-order Runge-Kutta method. Numerical investigations can show the very large effects of corrugated core, the volume fraction of carbon nanotube, and the type of carbon nanotube distribution on the nonlinear vibration behaviour of sandwich FG-CNTRC cylindrical panels. Keywords: Nonlinear vibration; First-order shear deformation theory; FG-CNTRC; Corrugated core;Galerkin method.1. Introduction The functionally graded material (FGM) is becoming an important material for the main structuressubjected to complex loading types in modern technologies of excellent thermo-mechanical properties.The linear and nonlinear vibration behaviour of many form of FGM plates and cylindrical panels wereanalysed by using different shell theories and different methods [1-3]. Zenkour [1] presented acomprehensive analysis of FGM plates in the problems of buckling and free vibration. The nonlinearvibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient was studiedby Liew et al. [2]. By using the higher-order shear deformation theory and the FGM smeared stiffenertechnique, Dong and Dung [3] investigated the nonlinear vibration analysis of stiffened FGM sandwichplates, cylindrical panels, and doubly curved shallow shells with four material models. Functionally graded carbon nanotube reinforced composite (FG-CNTRC) is a new kind ofnanocomposite material, where the carbon nanotubes (CNTs) are reinforced in an isotropic matrix andits volume fraction is continuously varied from one surface of the structure to another. Wang and Shen[4] investigated the nonlinear vibration of FG-CNTRC plates in thermal environments by using thehigher-order shear deformation theory and the two-step perturbation technique. Similarly, Yu and Shen[5] investigated the effects of positive and negative Poissons ratios on the nonlinear vibration of hybridFG-CNTRC/metal laminated plates. Free vibration analyses of FG-CNTRC plates were also mentionedby Zhu et al. [6] using the finite element method with the first-order shear deformation theory (FSDT).Wu and Li [7] considered the free vibration of FG-CNTRC plates with various boundary conditionsusing the three-dimensional elasticity theory. For FG-CNTRC cylindrical panels, Shen and Xiang [8]presented the nonlinear vibration of FG-CNTRC cylindrical panels resting on the elastic foundations inthermal environments. The stiffened FG-CNTRC cylindrical panels with FG-CNTRC stiffeners werementioned in the nonlinear vibration problems by Dong et al. [9]. For the corrugated structures, Liew etal. [10, 11] studied the nonlinear bending and vibration behaviours using the mesh-free method andmesh-free Galerkin method, respectively, by developing a homogeneous technique for first sheardeformable corrugations. 83100 Duc V.M. et al. A homogeneous technique for the corrugated core is applied for FSDT corrugated core andcombined appropriately with the FSDT of shells. The Galerkin procedure is applied to obtain thenonlinear motion equations of panels, and the dynamic responses can be archived by using the fourth-order Runge-Kutta method. Numerical examples show the large effects of corrugated core, CNT volumefraction, CNT distribution laws and geometrical parameters on the nonlinear vibration behaviours ofFG-CNTRC cylindrical panels.2. FG-CNTRC cylindrical panel with corrugated core and analytical solution Fig. 1. Geometrical properties of cylindrical panels, corrugated cores, and CNT distribution laws Consider the moderately thick cylindrical panels with FG-CNTRC face sheets and corrugatedcore with the geometrical properties presented in Fig. 1. The panel is subjected to the time-dependentharmonic pressure q Q sin Ωt (N/m2) uniformly distributed over the top surface. The corrugated core =is designed in trapezoidal or sinusoidal forms. Assuming that the panel is reinforced by CNTslongitudinal direction, while, the corrugations are also in the longitudinal direction of the panel. ThreeCNT distribution laws are presented in Fig. 1. 84 Nonlinear vibration of FG-CNTRC cylindrical panels with corrugated core … 101 The CNT volume fractions for the upper face sheet ( − h 2 ≤ z ≤ − hcore 2 ) are distributed throughthe following function ...