Free Vibration Behavior of Carbon Nanotube Reinforced Composite Conical Shell Panel Under Thermal Environment

2018 ◽  
Vol 24 (8) ◽  
pp. 5915-5918
Author(s):  
S. Yogesh Krishnan ◽  
A. K Caitanya ◽  
P Tripathy ◽  
V. R Kar
Keyword(s):  
Finite Element ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Material Properties ◽  
Conical Shell ◽  
Volume Fraction ◽  
Thickness Ratio ◽  
Frequency Responses ◽  
Reinforced Composite ◽  
Shell Panel

The free vibration of carbon nanotube reinforced composite conical shell panel is examined under temperature field. In this analysis, single-walled carbon nanotube and poly(m-phenylenevinylene-co-2,5-dioctoxy-pphenylenevinylene) are used as fibre and matrix materials, respectively. The material properties are considered as temperature-dependent. The effective material properties of carbon nanotube reinforced composite panel are evaluated through the extended rule-of-mixture. The finite element model is prepared using commercially available finite element tool ANSYS APDL. An eight node Serendipity shell element (SHELL281) is used to discretize the present conical model. The displacement field is framed in the first-order shear deformation theory with six degrees of freedom. The Block Lanczos eigenvalue extraction method is used to obtain the frequency responses. In order to obtain the appropriate mesh density for the said model, the convergence study is executed for various mesh sizes. The present results are compared and validated with the previously reported results. Finally, the influences of different parameters such as length-to-thickness ratio, volume fraction and temperature on the frequency responses of the carbon nanotube reinforced composite conical shell panel are demonstrated through numerical illustrations. The results reveal that the frequency parameters of conical shell panel enhance with the volume fraction and the length-to-thickness ratio, whereas reduce with the temperature value.

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.

Free vibration response of carbon nanotube reinforced pretwisted conical shell under thermal environment

2019 ◽  
Vol 234 (3) ◽  
pp. 770-783 ◽  
Author(s):  
Pabitra Maji ◽  
Mrutyunjay Rout ◽  
Amit Karmakar
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Conical Shell ◽  
Dynamic Equilibrium ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Mode Shapes

Finite element procedure is employed to analyze the free vibration characteristics of rotating functionally graded carbon nanotubes reinforced composite conical shell with pretwist under the thermal environment. In this paper, four types of carbon nanotube grading are considered, wherein the distribution of carbon nanotubes are made through the thickness direction of the conical shell. An eight-noded isoparametric shell element is used in the present formulation to model the panel based on the first-order shear deformation theory. For moderate rotational speeds, the generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion, neglecting the Coriolis effect. The finite element code is developed to investigate the effect of twist angle, temperature, aspect ratio, and rotational speed on natural frequencies. The mode shapes of a carbon nanotube reinforced functionally graded conical shell at different twist angles and rotational speeds are also presented.

An Edge-Based Smoothed Discrete Shear Gap Method for Static and Free Vibration Analyses of FG-CNTRC Plates

2019 ◽  
Vol 16 (04) ◽  
pp. 1850102 ◽  
Author(s):  
T. Nguyen-Quoc ◽  
S. Nguyen-Hoai ◽  
D. Mai-Duc
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
Correction Factors ◽  
Reinforced Composite ◽  
Strain Smoothing ◽  
Edge Based ◽  
Discrete Shear Gap

In this paper, an edge-based smoothed stabilized discrete shear gap method (ES-DSG) is integrated with the C0-type high-order shear deformation plate theory (C0-HSDT) for free vibration and static analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The material properties of FG-CNTRC are assumed to be graded through the thickness direction according to several distributions of the volume fraction of carbon nanotubes (CNTs). The stiffness formulation of the ES-DSG based on C0-HSDT is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements. This hence does not require shear correction factors. The accuracy and reliability of the proposed method are confirmed in several numerical examples.

Refined zigzag theory for vibration analysis of viscoelastic functionally graded carbon nanotube reinforced composite microplates integrated with piezoelectric layers

2016 ◽  
Vol 231 (13) ◽  
pp. 2464-2478 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
M Mosayyebi ◽  
F Kolahdouzan ◽  
R Kolahchi ◽  
M Jamali
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Sandwich Plate ◽  
Volume Fraction ◽  
Damping Ratio ◽  
Plate Boundary ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Zigzag Theory

Damped free vibration of carbon nanotube reinforced composite microplate bounded with piezoelectric sensor and actuator layers are investigated in this study. For the mathematical modeling of sandwich structure, the refined zigzag theory is applied. In addition, to present a realistic model, the material properties of system are supposed as viscoelastic based on Kelvin–Voigt model. Distributions of single-walled carbon nanotubes along the thickness direction of the viscoelastic carbon nanotube reinforced composite microplate are considered as four types of functionally graded distribution patterns. The viscoelastic functionally graded carbon nanotube reinforced composite microplate subjected to electromagnetic field is embedded in an orthotropic visco-Pasternak foundation. Hamilton’s principle is employed to establish the equations of motion. In order to calculate the frequency and damping ratio of sandwich plate, boundary condition of plate is assumed as simply-supported and an exact solution is used. The effects of some significant parameters such as damping coefficient of viscoelastic plates, volume fraction of carbon nanotubes, different types of functionally graded distributions of carbon nanotubes, magnetic field, and external voltage on the damped free vibration of system are investigated. Results clarify that considering viscoelastic property for system to achieve accurate results is essential. Furthermore, the effects of volume fraction and distribution type of carbon nanotubes are remarkable on the vibration of sandwich plate. In addition, electric and magnetic fields are considerable parameters to control the behavior of viscoelastic carbon nanotube reinforced composite microplate. It is hoped that the results of this study could be applied in design of nano/micromechanical sensor and actuator systems.

scholarly journals FREE VIBRATION OF TAPERED FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE BEAMS USING A HIERARCHICAL BEAM ELEMENT

2020 ◽  
Vol 57 (6A) ◽  
pp. 107
Author(s):  
Trinh Thi Hien
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Longitudinal Direction ◽  
Beam Element ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Published Data ◽  
Reinforced Composite

Free vibration of tapered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams is investigated. The beams with four types of carbon nanotube distribution in the thickness, namely the uniform (UD-CNT), X-type (FGX-CNT), A-type (FGA-CNT) and O-type (FGO-CNT), are assumed to be linearly tapered in longitudinal direction by three different taper cases. Based on the first-order shear deformation theory, equations of motion with variable coefficients are derived from Hamilton’s principle. Using hierarchical functions to interpolate the displacement field, a two-node beam element with nine degrees of freedom is formulated and employed to compute frequencies of the beams. The accuracy of the derived formulation is confirmed by comparing frequencies obtained in the present work with the published data. The effects of the total CNT volume fraction, CNT distribution type, taper cases, taper ratio, aspect ratio, boundary conditions, etc., on the vibration characteristics of the beams are examined and discussed.

Free vibration, bending and buckling of a FG-CNT reinforced composite beam

2017 ◽  
Vol 13 (4) ◽  
pp. 590-611 ◽  
Author(s):  
Puneet Kumar ◽  
J. Srinivas
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Volume Fraction ◽  
Virtual Work ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Content Type ◽  
Reinforced Composite ◽  
Reinforced Polymer

Purpose The purpose of this paper is to perform a numerical analysis on the static and dynamic behaviors of beams made up of functionally graded carbon nanotube (FG-CNT) reinforced polymer and hybrid laminated composite containing the layers of carbon reinforced polymer with CNT. Conventional fibers have higher density as compared to carbon nanotubes (CNTs), thus insertion of FG-CNT reinforced polymer layer in fiber reinforced composite (FRC) structures makes them sustainable candidate for weight critical applications. Design/methodology/approach In this context, stress and strain formulations of a multi-layer composite system is determined with the help of Timoshenko hypothesis and then the principle of virtual work is employed to derive the governing equations of motion. Herein, extended rule of mixture and conventional micromechanics relations are used to evaluate the material properties of carbon nanotube reinforced composite (CNTRC) layer and FRC layer, respectively. A generalized eigenvalue problem is formulated using finite element approach and is solved for single layer FG-CNTRC beam and multi-layer laminated hybrid composite beam by a user-interactive MATLAB code. Findings First, the natural frequencies of FG-CNTRC beam are computed and compared with previously available results as well as with Ritz approximation outcomes. Further, free vibration, bending, and buckling analysis is carried out for FG-CNTRC beam to interpret the effect of different CNT volume fraction, number of walls in nanotube, distribution profiles, boundary conditions, and beam-slenderness ratios. Originality/value A free vibration analysis of hybrid laminated composite beam with two different layer stacking sequence is performed to present the advantages of hybrid laminated beam over the conventional FRC beam.

Thermoelastic free vibration of rotating pretwisted sandwich conical shell panels with functionally graded carbon nanotube-reinforced composite face sheets using higher-order shear deformation theory

2021 ◽  
pp. 146442072199941
Author(s):  
Tripuresh Deb Singha ◽  
Tanmoy Bandyopadhyay ◽  
Amit Karmakar
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Shear Deformation ◽  
Conical Shell ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Reinforced Composite

This article presents a numerical investigation on the free vibration characteristics of rotating pretwisted sandwich conical shell panels with two functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets and a homogeneous core in uniform thermal environments. The carbon nanotubes are considered to be aligned with the span length and distributed either uniformly or functionally graded along the thickness of the sandwich conical shell panel. The material properties of FG-CNTRC face sheets and homogenous core are assumed to be temperature-dependent and computed employing micromechanics models. The shallow conical shell is modeled using finite element method within a framework of the higher-order shear deformation theory. Lagrange’s equation of motion is employed to derive the dynamic equilibrium equations of sandwich conical shell panels rotating at moderate rotational speeds wherein Coriolis effect is neglected. Computer codes are developed on the basis of present mathematical formulation to determine the natural frequencies of the sandwich conical panels. Convergence and comparison studies are performed to examine the consistency and accurateness of the present formulation. The numerical results are presented to analyze the effects of various parameters on the natural frequencies of the pretwisted FG-CNTRC sandwich conical shell panels under different thermal conditions.

scholarly journals Finite Element Model for Free Vibration Analyses of FG-CNT Reinforced Composite Beams using Refined Shear Deformation Theories

2021 ◽  
Vol 1206 (1) ◽  
pp. 012019
Author(s):  
Surojit Biswas ◽  
Priyankar Datta
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Distribution Type

Abstract The present article deals with the free vibration of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams employing various refined deformation theories and validates the accuracy and feasibility of these proposed theories. The theories involved are the first order shear deformation theory (FSDT) and other refined theories involving additional higher order terms. Carbon nanotubes (CNTs) are assumed to be oriented along the axis of the beam. Uniform and three types of different functionally graded (FG) distributions of CNTs through the thickness of the beam are considered. The rule of mixture is used to describe the effective material properties of the beams. The governing equations are derived using Hamilton’s principle and solved using the finite element method (FEM). A FEM code is compiled in MATLAB considering a C 0 finite element. The influences of different key parameters such as CNT volume fraction, distribution type of CNTs, boundary conditions and slenderness ratio on the natural frequencies of FG-CNTRC beams are investigated. It can be concluded that the above-mentioned parameters have significant influence on the free vibration of the beam and the accuracy of the proposed refined theories is good.

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