Nonlinear stability of sandwich beams with carbon nanotube reinforced faces on elastic foundation under thermal loading

2018 ◽  
Vol 233 (5) ◽  
pp. 1701-1712 ◽  
Author(s):  
Yaser Kiani ◽  
Mostafa Mirzaei
Keyword(s):  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Material Properties ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Ritz Method ◽  
Numerical Results ◽  
Equilibrium Path ◽  
Sandwich Beams ◽  
Post Buckling

In this research, post-buckling response of sandwich beams with carbon nanotube reinforced face sheets subjected to uniform temperature rise loading and resting on a two-parameter elastic foundation is investigated. A single-layer theory formulation based on the first-order shear deformation beam theory is used. Material properties of the media are obtained according to a refined rule of mixtures approach which contains efficiency parameters. Suitable for the large deformations, von-Kármán strains are taken into consideration. The elastic foundation is modelled as the Pasternak model which takes into account the shear interaction of the springs. Material properties of the face sheets are considered to be position and temperature dependent. The governing equations of the system are obtained using the Ritz method for various combinations of clamped, simply supported and sliding supported edges. Post-buckling equilibrium path of the beam is obtained according to an iterative displacement control strategy. Numerical results of the present study are compared with the available data in the open literature. Then, the numerical results are provided to explore the effect of side-to-thickness ratio, volume fraction of carbon nanotube, distribution pattern of carbon nanotube, the ratio of face thickness-to-host thickness, boundary conditions and elastic foundation.

scholarly journals Independent coordinate coupling method for vibration analysis of a functionally graded carbon nanotube–reinforced plate with central hole

2019 ◽  
Vol 11 (8) ◽  
pp. 168781401987292 ◽  
Author(s):  
Yan Guo ◽  
Yanan Jiang ◽  
Bin Huang
Keyword(s):  
Carbon Nanotube ◽  
Volume Fraction ◽  
Ritz Method ◽  
Matching Condition ◽  
Functionally Graded ◽  
Central Hole ◽  
Lagrange’S Equation ◽  
Reinforced Plate ◽  
Distribution Type ◽  
Admissible Functions

In this article, the free vibration of a functionally graded carbon nanotube–reinforced plate with central hole is investigated by means of the independent coordinates-based Rayleigh–Ritz method. For the proposed method, the kinematic and potential energies are substituted into Lagrange’s equation in order to obtain the equation of motion. However, the total energies are computed by the difference of energies between the hole domain and the plate domain. By applying the displacement matching condition at the hole domain, two coordinate systems are coupled. For the Rayleigh–Ritz method, the mode shape functions of uniform beams are assumed as admissible functions. By this method, convergent results can be obtained with certain number of terms of admissible functions. The present results clearly reflect the effects of the carbon nanotube distribution type, carbon nanotube volume fraction, hole size, and boundary condition on the nondimensional natural frequencies. The provided results show that the present method is efficient in studying the vibration problems of functionally graded carbon nanotube–reinforced plate with central hole.

Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect

2017 ◽  
Vol 232 (12) ◽  
pp. 2244-2262 ◽  
Author(s):  
Suman Pal ◽  
Debabrata Das
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Coriolis Effect ◽  
Governing Equations

The present work investigates the free vibration behavior of double-tapered functionally graded beams rotating in thermal environment, using an improved mathematical model. The functional gradation for ceramic–metal compositions, following power-law, is considered to be symmetric with respect to the mid-plane, leading to metal-rich core and ceramic-rich outer surfaces of the beam. The temperature dependence of the material properties are considered using Touloukian model. The nonlinearity in strain–displacement relationships for both the axial and transverse shear strains are considered. Firstly, the governing equations for deformed beam configuration under time-independent centrifugal loading are obtained using minimum total potential energy principle, and the solution is obtained following Ritz method. Then the free vibration problem of the centrifugally deformed beam is formulated employing Lagrange’s principle and considering tangent stiffness of the deformed beam configuration. Coriolis effect is considered in the mathematical model, and the governing equations are transformed to the state-space for obtaining an eigenvalue problem. The results for the first two modes of both chord-wise and flap-wise vibrations are presented in nondimensional plane to show the effects of taperness parameter, root-offset parameter, volume fraction exponent, operating temperature, and functionally graded material composition. The results in comparative form are presented for both temperature-dependent and temperature-independent material properties.

Free Vibration and Buckling Analysis of Sandwich Beams with Functionally Graded Carbon Nanotube-Reinforced Composite Face Sheets

2015 ◽  
Vol 15 (07) ◽  
pp. 1540011 ◽  
Author(s):  
Helong Wu ◽  
Sritawat Kitipornchai ◽  
Jie Yang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Micromechanical Model ◽  
Sandwich Beam ◽  
Sheet Thickness ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Reinforced Composite

This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.

scholarly journals Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework

2017 ◽  
Vol 4 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Virendra Kumar Chaudhari ◽  
Niranjan L. Shegokar ◽  
Achchhe Lal
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Order Perturbation ◽  
Nonlinear Free Vibration ◽  
Reinforced Composite ◽  
Elastically Supported ◽  
Foundation Parameters

AbstractThis paper deals with the investigation of nonlinear free vibration behavior of elastically supported carbon nanotube reinforced composite (CNTRC) beam subjected to thermal loading with random system properties. Material properties of each constituent’s material, volume fraction exponent and foundation parameters are considered as uncorrelated Gaussian random input variables. The beam is supported by a Pasternak foundation with Winkler cubic nonlinearity. The higher order shear deformation theory (HSDT) with von-Karman non-linearity is used to formulate the governing equation using Hamilton principle. Convergence and validation study is carried out through the comparison with the available results in the literature for authenticity and accuracy of the present approach used in the analysis. First order perturbation technique (FOPT),Second order perturbation technique (SOPT) and Monte Carlo simulation (MCS) methods are employed to investigate the effect of geometric configuration, volume fraction exponent, foundation parameters, distribution of reinforcement and thermal loading on nonlinear vibration characteristics CNTRC beam.The present work signifies the accurate analysis of vibrational behaviour influences by different random variables. Results are presented in terms of mean, variance (COV) and probability density function (PDF) for various aforementioned parameters.

Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotube-reinforced face sheets resting on Pasternak elastic foundation

2017 ◽  
Vol 24 (11) ◽  
pp. 2327-2343 ◽  
Author(s):  
Rasool Moradi-Dastjerdi ◽  
Hamed Momeni-Khabisi
Keyword(s):  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Free And Forced Vibrations ◽  
Mesh Free ◽  
Pasternak Elastic Foundation

In this paper, free and forced vibrations, and also resonance and pulse phenomena in sandwich plates with an isotropic core and composite reinforced by wavy carbon nanotube (CNT) face sheets are studied based on a mesh-free method and first order shear deformation theory (FSDT). The sandwich plates are resting on Pasternak elastic foundation and subjected to periodic loads. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak’s elastic foundation coefficients, sandwich plate thickness, face sheets thickness, plate aspect ratio and time depended force are investigated on the free and forced vibrations, and resonance behavior of the sandwich plates with wavy CNT-reinforced face sheets.

Nonlinear buckling of orthogonal carbon nanotube-reinforced composite cylindrical shells under axial compression surrounded by elastic foundation in thermal environment

2019 ◽  
Vol 08 (04) ◽  
pp. 1950016 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Vu Minh Duc
Keyword(s):  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Axial Compression ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Geometrical Parameters ◽  
Postbuckling Behavior ◽  
Nonlinear Buckling ◽  
Reinforced Composite

Nonlinear buckling and postbuckling of orthogonal carbon nanotube-reinforced composite (Orthogonal CNTRC) cylindrical shells subjected to axial compression in thermal environments surrounded by elastic foundation are presented in this paper. Two layers of shell are reinforced by carbon nanotube (CNT) in two orthogonal directions (longitudinal and circumferential directions). Based on Donnell’s shell theory with von Karman’s nonlinearity and the Galerkin method, the governing equations are established to obtain the critical buckling loads and postbuckling load-deflection curves. The large effects of CNT volume fraction, temperature change, elastic foundation and geometrical parameters of cylindrical shells on the buckling load and postbuckling behavior of Orthogonal CNTRC cylindrical shells are obtained.

scholarly journals Thermo-Mechanical Post Buckling Analysis of Multiwall Carbon Nanotube-Reinforced Composite Laminated Beam under Elastic Foundation

2019 ◽  
Vol 6 (1) ◽  
pp. 212-228 ◽  
Author(s):  
Achchhe Lal ◽  
Kanif Markad
Keyword(s):  
Carbon Nanotube ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Buckling Analysis ◽  
Multiwall Carbon Nanotube ◽  
Laminated Beam ◽  
Reinforced Composite ◽  
Multi Walled Carbon Nanotube ◽  
Pasternak Elastic Foundation

AbstractIn present paper, buckling analysis is performed over laminated composite beam incorporating multi walled carbon nanotube (MWCNT) polymer matrix and then reinforced with E-glass fiber in an orthotropic manner under inplane varying thermal and mechanical loads by finite element method (FEM). Aim of the study is to develop a model which accurately perform the buckling deterministic analysis of multi-walled carbon nanotube reinforced composite laminated beam (MWCNTRCLB) with the evaluation of material property by applying Halpin–Tsai model. Combined Higher order shear deformation theory and Pasternak elastic foundation based on von Karman nonlinear kinematics and Winkler cubic nonlinearity respectively, are successfully implemented. Through minimum potential energy principle, generalized static analysis is performed using FEM, based on interactive MATLAB coding. The critical buckling load and critical buckling temperature is presented under the action of inplane variable mechanical and thermal load, with different boundary conditions, beam thickness ratio and MWCNT aspect ratio, variation with MWCNT volume fraction and coefficient of thermal expansion, with and without foundation for linear and nonlinear cases.

scholarly journals Forced Vibration Analysis of Composite Beams Reinforced by Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 571
Author(s):  
Ömer Civalek ◽  
Şeref D. Akbaş ◽  
Bekir Akgöz ◽  
Shahriar Dastjerdi
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Ritz Method ◽  
Time History ◽  
Composite Beams ◽  
Reinforced Composite ◽  
Forced Vibration Analysis

This paper presents forced vibration analysis of a simply supported beam made of carbon nanotube-reinforced composite material subjected to a harmonic point load at the midpoint of beam. The composite beam is made of a polymeric matrix and reinforced the single-walled carbon nanotubes with their various distributions. In the beam kinematics, the first-order shear deformation beam theory was used. The governing equations of problem were derived by using the Lagrange procedure. In the solution of the problem, the Ritz method was used, and algebraic polynomials were employed with the trivial functions for the Ritz method. In the solution of the forced vibration problem, the Newmark average acceleration method was applied in the time history. In the numerical examples, the effects of carbon nanotube volume fraction, aspect ratio, and dynamic parameters on the forced vibration response of carbon nanotube-reinforced composite beams are investigated. In addition, some comparison studies were performed, with special results of published papers to validate the using formulations.

scholarly journals Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

2016 ◽  
Vol 7 ◽  
pp. 511-523 ◽  
Author(s):  
Mostafa Mirzaei ◽  
Yaser Kiani
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Solution Method ◽  
Volume Fraction ◽  
Plate Theory ◽  
Ritz Method ◽  
Composite Plates ◽  
Functionally Graded ◽  
Plane Boundary

During the past five years, it has been shown that carbon nanotubes act as an exceptional reinforcement for composites. For this reason, a large number of investigations have been devoted to analysis of fundamental, structural behavior of solid structures made of carbon-nanotube-reinforced composites (CNTRC). The present research, as an extension of the available works on the vibration analysis of CNTRC structures, examines the free vibration characteristics of plates containing a cutout that are reinforced with uniform or nonuniform distribution of carbon nanotubes. The first-order shear deformation plate theory is used to estimate the kinematics of the plate. The solution method is based on the Ritz method with Chebyshev basis polynomials. Such a solution method is suitable for arbitrary in-plane and out-of-plane boundary conditions of the plate. It is shown that through a functionally graded distribution of carbon nanotubes across the thickness of the plate, the fundamental frequency of a rectangular plate with or without a cutout may be enhanced. Furthermore, the frequencies are highly dependent on the volume fraction of carbon nanotubes and may be increased upon using more carbon nanotubes as reinforcement.

scholarly journals Large deformation behavior of functionally graded porous curved beams in thermal environment

2021 ◽  
Author(s):  
S. F. Nikrad ◽  
A. Kanellopoulos ◽  
M. Bodaghi ◽  
Z. T. Chen ◽  
A. Pourasghar
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Bending Moment ◽  
Functionally Graded ◽  
Equilibrium Path ◽  
Curved Beams ◽  
Governing Equations

AbstractThe in-plane thermoelastic response of curved beams made of porous materials with different types of functionally graded (FG) porosity is studied in this research contribution. Nonlinear governing equations are derived based on the first-order shear deformation theory along with the nonlinear Green strains. The nonlinear governing equations are solved by the aid of the Rayleigh–Ritz method along with the Newton–Raphson method. The modified rule-of-mixture is employed to derive the material properties of imperfect FG porous curved beams. Comprehensive parametric studies are conducted to explore the effects of volume fraction and various dispersion patterns of porosities, temperature field, and arch geometry as well as boundary conditions on the nonlinear equilibrium path and stability behavior of the FG porous curved beams. Results reveal that dispersion and volume fraction of porosities have a significant effect on the thermal stability path, maximum stress, and bending moment at the crown of the curved beams. Moreover, the influence of porosity dispersion and structural geometry on the central radial and in-plane displacement of the curved beams is evaluated. Results show that various boundary conditions make a considerable difference in the central radial displacements of the curved beams with the same porosity dispersion. Due to the absence of similar results in the specialized literature, this paper is likely to provide pertinent results that are instrumental toward a reliable design of FG porous curved beams in thermal environment.

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