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.

Mechanical buckling analyses of sandwich annular plates with functionally graded carbon nanotube-reinforced composite face sheets resting on elastic foundation based on the higher-order shear deformation plate theory

2018 ◽  
Vol 22 (6) ◽  
pp. 1812-1837 ◽  
Author(s):  
J Torabi ◽  
R Ansari ◽  
E Hasrati
Keyword(s):  
Carbon Nanotube ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Annular Plates ◽  
Reinforced Composite ◽  
Composite Face

The main objective of this article is to analyze the buckling of sandwich annular plates with carbon nanotube-reinforced face sheets subjected to in-plane mechanical loading resting on the elastic foundation. It is assumed that the sandwich plate is composed of the homogeneous core layer and two functionally graded carbon nanotube-reinforced composite face sheets. The effective material properties of the functionally graded carbon nanotube-reinforced composite face sheets are estimated using the modified rule of mixture method. The higher-order shear deformation theory along with the variational differential quadrature method is employed to derive the governing equations. To this end, the quadratic form of energy functional of the structure is derived based on higher-order shear deformation theory which is directly discretized using numerical differential and integral operators. The validity of the proposed numerical approach is first shown and the effects of various parameters are then investigated on the buckling of sandwich annular plates. It was found that the elastic foundation coefficients, type of distribution of carbon nanotubes, inner-to-outer radius ratio and core-to-face sheet thickness ratio play important roles in the stability of the structure. Furthermore, the numerical results of the higher- and first-order shear deformation theories are compared.

Thermoelastic flexural analysis of FG-CNT doubly curved shell panel

2018 ◽  
Vol 90 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Kulmani Mehar ◽  
Subrata Kumar Panda
Keyword(s):  
Carbon Nanotube ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Order Model ◽  
Content Type ◽  
Reinforced Composite ◽  
Shell Panel ◽  
Doubly Curved

Purpose The purpose of this paper is to develop a general mathematical model for the evaluation of the theoretical flexural responses of the functionally graded carbon nanotube-reinforced composite doubly curved shell panel using higher-order shear deformation theory with thermal load. It is well-known that functionally graded materials are a multidimensional problem, and the present numerical model is also capable of solving the flexural behaviour of different shell panel made up of carbon nanotube-reinforced composite with adequate accuracy in the absence of experimentation. Design/methodology/approach In this current paper, the responses of the single-walled carbon nanotube-reinforced composite panel is computed numerically using the proposed generalised higher-order mathematical model through a homemade computer code developed in MATLAB. The desired flexural responses are computed numerically using the variational method. Findings The validity and the convergence behaviour of the present higher-order model indicate the necessity for the analysis of multidimensional structure under the combined loading condition. The effect of various design parameters on the flexural behaviour of functionally graded carbon nanotube doubly curved shell panel are examined to highlight the applicability of the presently proposed higher-order model under thermal environment. Originality/value In this paper, for the first time, the static behaviour of functionally graded carbon nanotube-reinforced composite doubly curved shell panel is analysed using higher-order shear deformation theory. The properties of carbon nanotube and the matrix material are considered to be temperature dependent. The present model is so general that it is capable of solving various geometries from single curve to doubly curved panel, including the flat panel.

A New Shear Deformation Theory for Free Vibration of Functionally Graded Beams

2013 ◽  
Vol 455 ◽  
pp. 198-201 ◽  
Author(s):  
Song Xiang
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Present Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A n-order shear deformation theory is used to study the free vibration of functionally graded beams. Present theory satisfies the zero transverse shear stress boundary conditions on the top and the bottom surface of the beam. The natural frequencies computed by present theory are compared with previous published results which demonstrate the accuracy of present theory.

A Trigonometric Shear Deformation Theory for Free Vibration Analysis of Functionally Graded Plates

2014 ◽  
Vol 680 ◽  
pp. 284-287
Author(s):  
Jiang Wu ◽  
Song Xiang
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Functionally Graded Plate ◽  
Simply Supported

A trigonometric shear deformation theory is presented to analyze the free vibration of functionally graded plate. The Navier-type analytical method is used to solve the governing differential equations. The natural frequencies of simply supported functionally graded plates are calculated and compared with the available results.

The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

2019 ◽  
Vol 50 (9-11) ◽  
pp. 267-290
Author(s):  
Ali Bakhsheshy ◽  
Hossein Mahbadi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Scale Parameter ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
The Third

This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness of the microplate. Gradient of the material is assumed to obey from the power law in terms of the volume fraction of the constituents. Assuming the uniform and nonuniform temperature distributions, the effect of thermal environment on dynamic behavior of the microplate is discussed in detail. Applying the Ritz method, the displacement field is expanded by admissible functions which satisfy the essential boundary conditions, and Hamilton principle is employed to determine the natural frequencies of the microplate. Developed model has been applied to determine the natural frequencies in problems of thin/thick, one-directional/bi-directional functionally graded, and homogeneous/nonhomogeneous microplates. Effects of parameters such as the thermal environment, power law indexes [Formula: see text] and length scale parameter on free vibration of these problems are studied in detail. The results show that higher values of length scale parameter and temperature rise decrease the natural frequency of the bi-directional functionally graded microplate. According to results obtained by classical and third-order shear deformation theories, the third-order shear deformation theory is proposed for vibration analysis of microplates with thickness-to-length ratio less than five.

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