scholarly journals Natural frequencies analysis of functionally graded circular cylindrical shells

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Nabeel T. Alshabatat ◽  
Mohammad Zannon
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Third Order ◽  
The Third ◽  
Circular Cylindrical Shells

In the present work, a study on natural frequencies of functionally graded materials (FGM) circular cylindrical shells is presented. TheFGM is considered to be a mixture of two materials. The volumetric fractions are considered to vary in the radial direction (i.e., through the thickness) in compliance with a conventional power-law distribution. The equivalent material properties are estimated based on the Voigt model. The analysis of the FGM cylindrical shells is performed using the third-order shear deformation shell theory and the principle of virtual displacements. Moreover, the third-order shear deformation shell theory coupled with Carrera’s unified formulation is applied for the derivation of the governing equations associated with the free vibration of circular cylindrical shells. The accuracy of this method is examined by comparing the obtained numerical results with other previously published results. Additionally, parametric studies are performed for FGM cylindrical shells with several boundary conditions in order to show the effect of several design variables on the natural frequencies such as the power-law exponent, the circumferential wave number, the length to radius ratio and the thickness to radius ratio.

Nonlinear stability analysis of stiffened functionally graded material sandwich cylindrical shells with general Sigmoid law and power law in thermal environment using third-order shear deformation theory

2017 ◽  
Vol 21 (3) ◽  
pp. 938-972 ◽  
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga ◽  
Pham Minh Vuong
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Nonlinear Stability ◽  
Functionally Graded Material ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Thermal Loads ◽  
Third Order ◽  
Graded Material

This paper investigates analytically nonlinear buckling and postbuckling of functionally graded sandwich circular thick cylindrical shells filled inside by Pasternak two-parameter elastic foundations under thermal loads and axial compression loads. Shells are reinforced by closely spaced functionally graded material (FGM) rings and stringers. The temperature field is taken into account. Two general Sigmoid law and general power law, with four models of stiffened FGM sandwich cylindrical shell, are proposed. Using the Reddy’s third-order shear deformation shell theory (TSDT), stress function, and Lekhnitsky’s smeared stiffeners technique, the governing equations are derived. The closed form to determine critical axial load and postbuckling load-deflection curves are obtained by the Galerkin method. The effects of the face sheet thickness to total thickness ratio, stiffener, foundation, material, and dimensional parameters on critical thermal loads, critical mechanical loads and postbuckling behavior of shells are analyzed. In addition, this paper shows that for thin shells we can use the classical shell theory to investigate stability behavior of shell, but for thicker shells the use of TSDT for analyzing nonlinear stability of shell is necessary and suitable.

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.

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

scholarly journals Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zakaria Ibnorachid ◽  
Lhoucine Boutahar ◽  
Khalid EL Bikri ◽  
Rhali Benamar
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement

In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

Sign in / Sign up

Export Citation Format

Share Document