Free Vibrations of Functionally Graded Graphene-Reinforced Composite Blades with Varying Cross-Sections

2020 ◽  
pp. 2043006
Author(s):  
Jie Chen ◽  
Pai Cui ◽  
Qiu-Sheng Li
Keyword(s):  
Cross Sections ◽  
Mass Density ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Composite Blades

In this paper, free vibrations of functionally graded (FG) graphene-reinforced composite blades with varying cross-sections are investigated. Considering the cantilever boundary conditions, the dynamic model of a rotating blade is simplified as a varying cross-sections plate with pre-installed angle and pre-twisted angle. As a reinforcement, the graphene platelets (GPLs) are distributed either uniformly or gradiently on the plate along its thickness direction. The effective Young’s modulus is formulated by the modified Halpin–Tsai model. The rule of mixture is applied to calculate the effective Poisson’s ratio and mass density. The equations of motion are established by using the first-order shear deformation theory and von Karman geometric nonlinear theory. Based on the Rayleigh–Ritz method, the natural frequencies of the rotating FG blade reinforced with the GPLs are obtained. The accuracy of the present method is verified by comparing the obtained results with those of the finite element method and published literature. A comprehensive parametric study is conducted, with a particular focus on the effects of distribution pattern, weight fraction, and geometries size of the GPLs together with dimensional parameters of varying cross-sections blade on the dynamics of the FG blades reinforced with the GPLs.

Dynamic analysis of three-layer cylindrical shells with fractional viscoelastic core and functionally graded face layers

2020 ◽  
pp. 107754632096622
Author(s):  
Meisam Shakouri ◽  
Mohammad Reza Permoon ◽  
Abdolreza Askarian ◽  
Hassan Haddadpour
Keyword(s):  
Natural Frequency ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Core Layer ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Viscoelastic Core ◽  
Graded Layers

Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz method. The obtained results are validated with those in the literature, and finally, the effects of some geometrical and material parameters such as length-to-radius ratio, functionally graded properties, radius and thickness of viscoelastic layer on the natural frequency, and loss factor of the system are considered, and some conclusions are drawn.

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.

scholarly journals Third-order nonlocal elasticity in buckling and vibration of functionally graded nanoplates on Winkler-Pasternak media

2020 ◽  
Author(s):  
A. Cutolo ◽  
V. Mallardo ◽  
M. Fraldi ◽  
E. Ruocco
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Sensitivity Analyses ◽  
Third Order ◽  
Graded Material ◽  
Benchmark Solutions

Abstract The focus of the present work is to present an analytical approach for buckling and free vibrations analysis of thick functionally graded nanoplates embedded in a Winkler-Pasternak medium. The equations of motion are derived according to both the third-order shear deformation theory, proposed by Reddy, and the nonlocal elasticity Eringen's model. For the first time, the equations are solved analytically for plates with two simply supported opposite edges, the solutions also turning helpful as shape functions in the analysis of structures with more complex geometries and boundary conditions. Sensitivity analyses are finally performed to highlight the role of nonlocal parameters, aspect and side-to-thickness ratios, boundary conditions, and functionally graded material properties in the overall response of plates and cylindrical shells. It is felt that the proposed strategy could be usefully adopted as benchmark solutions in numerical routines as well as for predicting some unexpected behaviors, for instance, in terms of buckling load, in thick nanoplates on elastic foundations.

scholarly journals Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations

2019 ◽  
Vol 9 (8) ◽  
pp. 1580 ◽  
Author(s):  
Mohammad Arefi ◽  
Elyas Mohammad-Rezaei Bidgoli ◽  
Rossana Dimitri ◽  
Francesco Tornabene ◽  
J. N. Reddy
Keyword(s):  
Polymer Composite ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Graphene Nanoplatelets ◽  
Functionally Graded ◽  
Polar Coordinates ◽  
Geometrical Parameters ◽  
Size Dependent

This paper presents a free vibration analysis of functionally graded (FG) polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on a Pasternak foundation. The size-dependent governing equations of motion are derived by applying the Hamilton’s principle and the differential law consequent (but not equivalent) to Eringen’s strain-driven nonlocal integral elasticity model equipped with the special bi-exponential averaging kernel. The displacement field of the problem is here described in polar coordinates, according to the first order shear deformation theory. A large parametric investigation is performed, which includes different FG patterns, different boundary conditions, but also different geometrical parameters, number of layers, weight fractions, and Pasternak parameters.

scholarly journals Vibration characteristics of rotating functionally graded porous beams reinforced by graphene platelets

2021 ◽  
Vol 15 (4) ◽  
pp. 29-41
Author(s):  
Chu Thanh Binh ◽  
Tran Huu Quoc ◽  
Duong Thanh Huan ◽  
Ho Thi Hien
Keyword(s):  
Dispersion Model ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Beam Theory ◽  
Weight Fraction ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Rotating Speed ◽  
Porosity Coefficient ◽  
Graphene Platelets

This work aims to study the vibration characteristics of the rotating functionally graded porous beam reinforced by graphene platelets. The beam is mounted and rotated around a hub with a constant velocity. The material properties vary along the thickness direction with two types of porosity distributions and two dispersion patterns of graphene platelet. The equations of motion based on the Timoshenko beam theory are obtained and solved using the Chebyshev-Ritz method. The effects of the parameters such as hub radius, rotating speed, weight fraction, porosity distribution, porosity coefficient, and dispersion model are presented. The present method results are also compared with numerical results available in the literature.

Vibration of functionally graded carbon nanotube-reinforced composite plates under a moving load

2015 ◽  
Vol 22 (1) ◽  
pp. 37-55 ◽  
Author(s):  
Parviz Malekzadeh ◽  
Mojtaba Dehbozorgi ◽  
Seyyed Majid Monajjemzadeh
Keyword(s):  
Carbon Nanotube ◽  
Moving Load ◽  
Equations Of Motion ◽  
Micromechanical Model ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Integration Scheme ◽  
Aspect Ratios ◽  
Reinforced Composite

AbstractThe vibration behavior of functionally graded carbon nanotube (CNT)-reinforced composite (FG-CNTRC) plates under a moving load is investigated based on the first-order shear deformation theory of plates using the finite element method. An embedded single-walled CNT (SWCNT) in the polymer matrix and its surrounding interphase is replaced with an equivalent fiber to obtain the effective mechanical properties of the CNT/polymer composite plates using the Eshelby-Mori-Tanaka micromechanical model. The equations of motion of plate elements are derived by utilizing Hamilton’s principle. Newmark’s time integration scheme is employed to discretize the equations of motion in the temporal domain. The convergence of the method is numerically demonstrated and its accuracy is shown by performing comparison studies with existing solutions for the free vibration and static analysis of FG-CNTRC plates and also the exact solution of isotropic plates under a moving load. Then, the numerical results are presented to study the effects of various profiles of the CNT distribution, which includes both symmetric and asymmetric distributions, the velocity of the moving load, and thickness-to-length and aspect ratios together with boundary conditions on the dynamic characteristic of the FG-CNTRC plate under a moving load.

Buckling of functionally graded carbon nanotubes reinforced composite joined spherical-cylindrical-spherical thin-walled structure

2021 ◽  
pp. 095440622110057
Author(s):  
K Avramov ◽  
D Myrzaliyev ◽  
B Uspensky ◽  
N Sakhno ◽  
KK Seitkazenova
Keyword(s):  
Carbon Nanotubes ◽  
Axial Load ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Thin Walled ◽  
Functionally Graded Carbon Nanotubes

Functionally graded carbon nanotubes reinforced composite joined spherical-cylindrical-spherical thin-walled structure under the actions of axial and lateral distributed loads is considered. The static buckling of this structure is analyzed numerically. The Ritz method is used to derive the governing equations of the joined thin-walled structure buckling. Higher-order shear deformation theory is applied to describe the structure stress-strain state. The continuity conditions of the spherical-cylinder junction are derived. The displacements projections are chosen in the special form to satisfy these continuity conditions. The dependences of the buckling axial load on the CNTs distributions, CNTs volume fractions are analyzed numerically.

scholarly journals Buckling Behavior of FG-CNT Reinforced Composite Conical Shells Subjected to a Combined Loading

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 419 ◽  
Author(s):  
Abdullah H. Sofiyev ◽  
Francesco Tornabene ◽  
Rossana Dimitri ◽  
Nuri Kuruoglu
Keyword(s):  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Structural Response ◽  
Systematic Investigation ◽  
Functionally Graded ◽  
Combined Loading ◽  
Proportional Loading ◽  
Conical Shells ◽  
Reinforced Composite ◽  
Buckling Behavior

The buckling behavior of functionally graded carbon nanotube reinforced composite conical shells (FG-CNTRC-CSs) is here investigated by means of the first order shear deformation theory (FSDT), under a combined axial/lateral or axial/hydrostatic loading condition. Two types of CNTRC-CSs are considered herein, namely, a uniform distribution or a functionally graded (FG) distribution of reinforcement, with a linear variation of the mechanical properties throughout the thickness. The basic equations of the problem are here derived and solved in a closed form, using the Galerkin procedure, to determine the critical combined loading for the selected structure. First, we check for the reliability of the proposed formulation and the accuracy of results with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the proportional loading parameter, the type of distribution, and volume fraction of CNTs.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

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