Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: internal resonances

2021 ◽  
Author(s):  
Chao Ye ◽  
Yan Qing Wang
Keyword(s):  
Forced Vibration ◽  
Metal Foam ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Internal Resonances ◽  
Graphene Platelet ◽  
Nonlinear Forced Vibration

Nonlinear Forced Vibration Analysis of FG-CNTRC Cylindrical Shells Under Thermal Loading Using a Numerical Strategy

2017 ◽  
Vol 09 (08) ◽  
pp. 1750108 ◽  
Author(s):  
Emad Hasrati ◽  
Reza Ansari ◽  
Jalal Torabi
Keyword(s):  
Frequency Response ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Governing Equations ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Numerical Strategy ◽  
Composite Cylindrical Shells

Employing an efficient numerical strategy, the nonlinear forced vibration analysis of composite cylindrical shells reinforced with single-walled carbon nanotubes (CNTs) is carried out. It is assumed that the distribution of CNTs along the thickness direction of the shell is uniform or functionally graded and the temperature dependency of the material properties is accounted. The governing equations are presented based on the first-order shear deformation theory along with von-Karman nonlinear strain-displacement relations. The vectorized form of energy functional is derived and directly discretized using numerical differential and integral operators. By the use of variational differential quadrature (VDQ) method, discretized nonlinear governing equations are obtained. Then, the time periodic differential operators are applied to perform the discretization procedure in time domain. Finally, the pseudo-arc length continuation method is employed to solve the nonlinear governing equations and trace the frequency response curve of the nanocomposite cylindrical shell. A comparison study is first presented to verify the efficiency and validity of the proposed numerical method. Comprehensive numerical results are then given to investigate the effects of the involved factors on the nonlinear forced vibration characteristics of the structure. The results show that the changes of fundamental vibrational mode shape have considerable effects on the frequency response curves of composite cylindrical shells reinforced with CNTs.

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation

2019 ◽  
Vol 55 (1-2) ◽  
pp. 53-68
Author(s):  
Farzad Ebrahimi ◽  
S Hamed S Hosseini
Keyword(s):  
Forced Vibration ◽  
Functionally Graded ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Electric Voltage ◽  
Modulation Equation ◽  
Flexoelectric Effect ◽  
Nonlinear Forced Vibration ◽  
Piezoelectric Structures ◽  
Porous Nanocomposite

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite is the objective of this study. The nanocomposite is exposed to electric voltage and external parametric excitation. First, a functionally graded porous core nanoplate is modeled and then two piezoelectric layers are glued with core. It is also rested on a visco-Pasternak foundation. Second, to derive governing equation of motion, two theories including Mindlin and Kirchhoff plate theories and Hamilton’s principle are utilized. In the next step, to obtain and solve ordinary differential equation, Galerkin technique and multiple time scales method are used, respectively. At the end, modulation equation of piezoelectric/functionally graded porous nanocomposite for both primary and secondary resonances is obtained and discussed. Emphasizing the effect of piezoelectric and flexoelectric, von Karman nonlinear deformation and parametric external excitation are simultaneously taken into account. It is found that electric voltage has no effect on the performance of piezoelectricity and flexoelectricity of the material on vibration behavior. The results of this study can be useful as benchmark for the next investigations in field of energy harvesting systems and piezoelectric structures.

Geometrically nonlinear dynamic analysis of functionally graded porous partially fluid-filled cylindrical shells subjected to exponential loads

2020 ◽  
pp. 107754632098246
Author(s):  
Majid Khayat ◽  
Abdolhossein Baghlani ◽  
Seyed Mehdi Dehghan ◽  
Mohammad Amir Najafgholipour
Keyword(s):  
Material Properties ◽  
Nonlinear Dynamic ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
Graphene Platelet ◽  
Graphene Platelets

This article investigates the influence of graphene platelet reinforcements and nonlinear elastic foundations on geometrically nonlinear dynamic response of a partially fluid-filled functionally graded porous cylindrical shell under exponential loading. Material properties are assumed to be varied continuously in the thickness in terms of porosity and graphene platelet reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin–Tsai equations are used to find the effective material properties of the graphene platelet–reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders’s theory. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. An incremental–iterative approach is used to solve the nonlinear equations of motion of partially fluid-filled cylindrical shells based on the Newmark direct integration and Newton–Raphson methods. The governing equations of liquid motion are derived using a finite strip formulation of incompressible inviscid potential flow. The effects of various parameters on dynamic responses are investigated. A detailed numerical study is carried out to bring out the effects of some influential parameters, such as fluid depth, porosity distribution, and graphene platelet dispersion parameters on nonlinear dynamic behavior of functionally graded porous nanocomposite partially fluid-filled cylindrical shells reinforced with graphene platelets.

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