scholarly journals Nonlinear Vibration of Functionally Graded Graphene Nanoplatelets Polymer Nanocomposite Sandwich Beams

2020 ◽  
Vol 10 (16) ◽  
pp. 5669
Author(s):  
Mohammad Sadegh Nematollahi ◽  
Hossein Mohammadi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Nonlinear Vibration ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Laminated Composite ◽  
Weight Fraction ◽  
Distribution Patterns ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Beam Model ◽  
Sandwich Beams

We provide an analytical investigation of the nonlinear vibration behavior of thick sandwich nanocomposite beams reinforced by functionally graded (FG) graphene nanoplatelet (GPL) sheets, with a power-law-based distribution throughout the thickness. We assume the total amount of the reinforcement phase to remain constant in the beam, while defining a relationship between the GPL maximum weight fraction, the power-law parameter, and the thickness of the face sheets. The shear and rotation effects are here considered using a higher-order laminated beam model. The nonlinear partial differential equations (PDEs) of motion are derived from the Von Kármán strain-displacement relationships, here solved by applying an expansion of free vibration modes. The numerical results demonstrate the key role of the amplitudes on the vibration response of GPL-reinforced sandwich beams, whose nonlinear oscillation behavior is very important in the physical science, mechanical structures and other mathematical analyses. The sensitivity of the response to the total amount of GPLs is explored herein, along with the possible effects related to the power-law parameter, the structural geometry, and the environmental conditions. The results indicate that changing the nanofiller distribution patterns with the proposed model can remarkably increase or decrease the effective stiffness of laminated composite beams.

scholarly journals Elasticity Solutions for In-Plane Free Vibration of FG-GPLRC Circular Arches with Various End Conditions

2020 ◽  
Vol 10 (14) ◽  
pp. 4695
Author(s):  
Dongying Liu ◽  
Jing Sun ◽  
Linhua Lan
Keyword(s):  
Free Vibration ◽  
Weight Fraction ◽  
Distribution Patterns ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Scaled Model ◽  
Circular Arch ◽  
End Conditions ◽  
Elasticity Solutions ◽  
Graphene Platelets

In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details.

Large deflection geometrically nonlinear bending of sandwich beams with flexible core and nanocomposite face sheets reinforced by nonuniformly distributed graphene platelets

2019 ◽  
Vol 22 (3) ◽  
pp. 866-895 ◽  
Author(s):  
S Jedari Salami
Keyword(s):  
Sandwich Panel ◽  
Sandwich Beam ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Face Sheet ◽  
Sandwich Beams ◽  
Nonlinear Bending ◽  
Graphene Platelet ◽  
The Face ◽  
Graphene Platelets

This study investigates the nonlinear bending response of a novel class of sandwich beams with flexible core and face sheets reinforced with graphene platelets that are functionally graded distributed through the thickness. Nonlinear governing equations are established based on extended high-order sandwich panel theory and Von Kármán type of geometrical nonlinearity. In this theory, the face sheets follow the first-order shear deformation theory, and the two-dimensional elasticity is adopted for the core. These nonlinear differential equations are discretized into algebraic systems by means of the Ritz-based method from which the static bending solution can be achieved. The effective Young’s modulus of functionally graded graphene platelet-reinforced composite (GPLRC) face sheets is determined through the modified Halpin–Tsai micromechanics model, and associated Poisson’s ratio is evaluated by employing the rule of mixture. Comparison studies are provided for a sandwich beam with graphene-reinforced face sheets and conventional nanocomposite beam reinforced by graphene platelets due to lack of results for introduced sandwich beams. Besides, three-point bending test was carried out in order to assure the validity of nonlinear bending analysis of a sandwich beam based on extended high-order sandwich panel theory. Afterwards, parametric studies are given to examine the influences of graphene platelet distribution pattern, weight fraction, and core-to-face sheet thickness ratio together with the total number of layers on the linear and nonlinear bending performances of the sandwich beams. Numerical results demonstrate that distributing more graphene platelets near the upper and lower surface layers of the face sheets, named X-GPLRC, is capable to improve the bending strength and decrease the local deflection of the top face sheet, and this recovery effect becomes more significant as graphene platelet weight fraction increases. The results also reveal that the graphene platelet distribution pattern of the face sheets plays an important role to decrease the transverse shear stress of the core by dispersing more graphene platelets near surfaces of the face sheets (X-GPLRC). So, reducing the local deflection of the top face sheet tends to be much more safety of the soft core from any failure. Besides, sandwich beams with a lower weight fraction of graphene platelets in face sheets that are symmetrically distributed in such a way, called O-GPLRC, are also less sensitive to the nonlinear deformation.

scholarly journals Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

2016 ◽  
Vol 33 (1) ◽  
pp. 23-33 ◽  
Author(s):  
F. Ebrahimi ◽  
M. R. Barati
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Higher Order ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Beam Model ◽  
Thickness Direction ◽  
Power Law Distribution

AbstractThe present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

Nonlinear Vibration Analysis of Microscale Functionally Graded Timoshenko Beams using the Most General form of Strain Gradient Elasticity

2013 ◽  
Vol 30 (2) ◽  
pp. 161-172 ◽  
Author(s):  
R. Ansari ◽  
M. Faghih Shojaei ◽  
V. Mohammadi ◽  
R. Gholami ◽  
H. Rouhi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Functionally Graded ◽  
Small Scale ◽  
Length Scale ◽  
Beam Model ◽  
Strain Gradient Elasticity ◽  
Governing Equations

ABSTRACTBased on the Timoshenko beam model, the nonlinear vibration of microbeams made of functionally graded (FG) materials is investigated under different boundary conditions. To consider small scale effects, the model is developed based on the most general form of strain gradient elasticity. The nonlinear governing equations and boundary conditions are derived via Hamilton's principle and then discretized using the generalized differential quadrature technique. A pseudo-Galerkin approach is used to reduce the set of discretized governing equations into a time-varying set of ordinary differential equations of Duffing-type. The harmonic balance method in conjunction with the Newton-Raphson method is also applied so as to solve the problem in time domain. The effects of boundary conditions, length scale parameters, material gradient index and geometrical parameters are studied. It is found that the importance of the small length scale is affected by the type of boundary conditions and vibration mode. Also, it is revealed that the classical theory tends to underestimate the vibration amplitude and linear frequency of FG microbeams.

scholarly journals Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150597 ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Temperature Field ◽  
Symmetry Breaking ◽  
Power Law ◽  
Functionally Graded Material ◽  
Electrostatic Force ◽  
Functionally Graded ◽  
Beam Model ◽  
Uniform Temperature ◽  
Graded Material ◽  
Uniform Temperature Field

In this paper, we investigate the symmetric snap-through buckling and the asymmetric bifurcation behaviours of an initially curved functionally graded material (FGM) microbeam subject to the electrostatic force and uniform/non-uniform temperature field. The beam model is developed in the framework of Euler–Bernoulli beam theory, accounting for the through-thickness power law variation of the beam material and the physical neutral plane. Based on the Galerkin decomposition method, the beam model is simplified as a 2 d.f. reduced-order model, from which the necessary snap-through and symmetry breaking criteria are derived. The results of our work reveal the significant effects of the power law index on the snap-through and symmetry breaking criteria. Our results also reveal that the non-uniform temperature field can actuate the FGM microbeam and induce the snap-through and asymmetric bifurcation behaviours.

scholarly journals Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

2018 ◽  
Vol 38 (1) ◽  
pp. 122-142 ◽  
Author(s):  
Mohammad Arefi ◽  
Mahmoud Pourjamshidian ◽  
Ali Ghorbanpour Arani ◽  
Timon Rabczuk
Keyword(s):  
Nonlinear Vibration ◽  
Elasticity Theory ◽  
Strain Gradient ◽  
Scale Effects ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Numerical Results ◽  
Small Scale ◽  
Beam Model ◽  
Surface Stresses

This research deals with the nonlinear vibration of the functionally graded nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The flexoelectric functionally graded nano-beam is resting on nonlinear Pasternak foundation. Cubic nonlinearity is assumed for foundation. It is assumed that the material properties of the nano-beam change continuously along the thickness direction according to different patterns of material distribution. In order to include coupling of strain gradients and electrical polarizations in equation of motion, the nonlocal, nonclassical nano-beam model containing flexoelectric effect is employed. In addition, the effects of surface elasticity, di-electricity, and piezoelectricity as well as bulk flexoelectricity are accounted in constitutive relations. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory and the nonlocal strain gradient elasticity theory considering residual surface stresses. The differential quadrature method is used to calculate nonlinear natural frequency of flexoelectric functionally graded nano-beam as well as nonlinear vibrational mode shape. After validation of the present numerical results with those results available in literature, full numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface and bulk, residual surface stresses, nonlocal parameter, length scale effects (strain gradient parameter), cubic nonlinear Winkler and shear coefficients, power gradient index of functionally graded material, and geometric dimensions on the nonlinear vibration behaviors of flexoelectric functionally graded nano-beam. The numerical results indicate that, considering the flexoelectricity leads to the decrease of the bending stiffness of the flexoelectric functionally graded nano-beams.

Nonlinear Vibration of Sandwich Beams with Functionally Graded Negative Poisson’s Ratio Honeycomb Core

2019 ◽  
Vol 19 (03) ◽  
pp. 1950034 ◽  
Author(s):  
Chong Li ◽  
Hui-Shen Shen ◽  
Hai Wang
Keyword(s):  
Nonlinear Vibration ◽  
Poisson’S Ratio ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Sandwich Beams ◽  
Negative Poisson’S Ratio ◽  
Honeycomb Core ◽  
Negative Poisson's Ratio

This paper investigates the nonlinear flexural vibration of sandwich beams with functionally graded (FG) negative Poisson’s ratio (NPR) honeycomb core in thermal environments. The novel constructions of sandwich beams with three FG configurations of re-entrant honeycomb cores through the beam thickness direction are proposed. The temperature-dependent material properties of both face sheets and core of the sandwich beams are considered. 3D full-scale finite element analyses are conducted to investigate the nonlinear vibration, and the variation of effective Poisson’s ratio (EPR) of the sandwich beams in the large deflection region. Numerical simulations are carried out for the sandwich beam with FG-NPR honeycomb core in different thermal environmental conditions, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a basis for comparison. The effects of FG configurations, temperature changes, boundary conditions, and facesheet-to-core thickness ratios on the nonlinear vibration ratio curves and EPR–deflection curves of sandwich beams are discussed in detail.

scholarly journals Transverse Vibration of Axially Moving Functionally Graded Materials Based on Timoshenko Beam Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Suihan Sui ◽  
Ling Chen ◽  
Cheng Li ◽  
Xinpei Liu
Keyword(s):  
Power Law ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Vibration Modes ◽  
Graded Materials ◽  
Power Law Exponent ◽  
Axially Moving

The transverse free vibration of an axially moving beam made of functionally graded materials (FGM) is investigated using a Timoshenko beam theory. Natural frequencies, vibration modes, and critical speeds of such axially moving systems are determined and discussed in detail. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. Hamilton’s principle is employed to derive the governing equation and a complex mode approach is utilized to obtain the transverse dynamical behaviors including the vibration modes and natural frequencies. Effects of the axially moving speed and the power-law exponent on the dynamic responses are examined. Some numerical examples are presented to reveal the differences of natural frequencies for Timoshenko beam model and Euler beam model. Moreover, the critical speed is determined numerically to indicate its variation with respect to the power-law exponent, axial initial stress, and length to thickness ratio.

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