Semi-exact solution for nonlinear dynamic analysis of nanobeams reinforced with functionally graded carbon nanotube located on a viscoelastic foundation

2019 ◽  
Vol 233 (18) ◽  
pp. 6626-6639
Author(s):  
Ahmad Fallah ◽  
MB Dehkordi ◽  
YT Beni
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Dynamic Response ◽  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Coefficient ◽  
Nonlinear Dynamic Analysis ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Viscoelastic Foundation

In this investigation, a transient nonlinear dynamic analysis of nanobeams reinforced with carbon nanotubes, which is located on a nonlinear viscoelastic foundation under the impulse loading, is investigated. The boundary conditions of the nanobeam are considered as clamped-clamped, and the carbon nanotube is distributed in different distribution along the thickness of nanobeam. First, using the Hamiltonian method and taking advantage of the couple stress theory and considering the Von Karman relationship between strain and displacement, the differential equation governing for Euler–Bernoulli nanobeam is obtained. Then, by using the semi-exact method and the Galerkin's method, the displacement derivatives are separated from the time derivatives and the equation derived is solved using Runge–Kutta's numerical method. In order to confirm the equation and its solution, a comparative study is performed that shows an appropriate fitting between the results. Finally, the influence of parameters such as nonlinear coefficient of foundation, applied force, size effect, and type of nanotube distribution on the nonlinear frequency to linear frequency ratio and transient nanobeam dynamic response is investigated. A study is also conducted on the effect of foundation damping coefficient and the inclusion of nonlinear effects on the transient dynamic response when the nanobeam is under impulse load and resonance conditions. The results show that the nonlinear vibrational frequency of the nanobeam with the FG-X carbon nanotube distribution is the highest, and the FG-O carbon nanotubes distribution is the least.

Nonlinear Dynamic Analysis of Functionally Graded Graphene Reinforced Composite Truncated Conical Shells

2019 ◽  
Vol 29 (11) ◽  
pp. 1950148 ◽  
Author(s):  
Aiwen Wang ◽  
Youqing Pang ◽  
Wei Zhang ◽  
Pengcheng Jiang
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Ritz Method ◽  
Nonlinear Dynamic Analysis ◽  
Shear Deformation Theory ◽  
Distribution Patterns ◽  
Equation Model ◽  
Functionally Graded ◽  
Conical Shells ◽  
Reinforced Composite

Functionally graded (FG) graphene reinforced composite (GRC) is a new class of advanced composite materials. In GRC, several layers of graphene platelets (GPLs) are randomly or uniformly dispersed in matrix. These GPLs have uniform arrangement, or are arranged with gradient, in the direction of thickness in accordance with three different graphene distribution rules. In this study, the nonlinear dynamic analysis of FG GRC truncated conical shells, subjected to a combined action of transverse excitation and axial force, is performed using the first shear deformation theory (FSDT). Estimation of equivalent Young’s modulus of the composites is calculated using a modified Halpin–Tsai model. In addition, a partial differential equation model is developed based on the Hamilton principle and nonlinear strain-displacement relationship. The Galerkin method and the fourth-order Runge–Kutta method are used to solve the equation. The dimensionless linear natural frequency of an FG GRC truncated conical shell is calculated by the Rayleigh–Ritz method and compared with available results in the literature to verify the accuracy of the present model. Simultaneously, significant effects of the different parameters, such as the total layer numbers, semi-vertex angles, GPLs weight fractions, distribution patterns and the length-to-thickness ratios, on the nonlinear dynamics including bifurcation and chaos of FG GRC truncated conical shells are investigated.

Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations

2016 ◽  
Vol 20 (2) ◽  
pp. 191-218 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Pham Hong Cong
Keyword(s):  
Dynamic Analysis ◽  
Material Properties ◽  
Nonlinear Dynamic ◽  
Thermal Environment ◽  
Nonlinear Dynamic Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Sandwich Plates ◽  
Elastic Foundations

Used the Reddy's higher-order shear deformation plate theory, the nonlinear dynamic analysis and vibration of imperfect functionally graded sandwich plates in thermal environment with piezoelectric actuators (PFGM) on elastic foundations subjected to a combination of electrical, damping loadings and temperature are investigated in this article. One of the salient features of this work is the consideration of temperature on the piezoelectric layer, and the material properties of the PFGM sandwich plates are assumed to be temperature-dependent. The governing equations are established based on the stress function, the Galerkin method, and the Runge–Kutta method. In the numerical results, the effects of geometrical parameters; material properties; imperfections; elastic foundations; electrical, thermal, and damping loads on the vibration and nonlinear dynamic response of the PFGM sandwich plates are discussed. The obtained natural frequencies are verified with the known results in the literature.

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