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.

Effect of carbon nanotube-reinforced magneto-electro-elastic facings on the pyrocoupled nonlinear deflection of viscoelastic sandwich skew plates in thermal environment

2021 ◽  
pp. 146442072110440
Author(s):  
Vinyas Mahesh
Keyword(s):  
Carbon Nanotube ◽  
Complex Modulus ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Energy Principle ◽  
Design Engineers ◽  
Total Potential ◽  
Viscoelastic Core

This work presents a finite-element-based numerical formulation to evaluate the nonlinear deflections of magneto-electro-elastic sandwich skew plates with a viscoelastic core and functionally graded carbon nanotube-reinforced magneto-electro-elastic face sheets. Meanwhile, the proposed formulation accommodates the geometrical skewness as well. The magneto-electro-elastic sandwich skew plate is operated in the thermal environment and subjected to various multiphysics loads, including electric and magnetic loads. The viscoelastic core is modelled via the complex modulus approach. Two different forms of viscoelastic cores, such as Dyad 606 and EC 2216, are considered in this study. Also, different thickness configurations of core and facing arrangements are taken into account. The plate kinematics is presumed through higher-order shear deformation theory, and von Karman's nonlinear strain displacement relations are incorporated. The global equations of motion are arrived at through the total potential energy principle and solved via the direct iterative method. Special attention is paid to assessing the influence of pyroeffects, coupling fields and electromagnetic boundary conditions on the nonlinear deflections of magneto-electro-elastic sandwich plates working in the thermal environment and subjected to electromagnetic loads, which is the first of its kind. Also, parametric studies dealing with the skew angles, carbon nanotube distributions and volume fractions, thickness ratio, and aspect ratio have been discussed. The results of this work are believed to be unique and serve as a guide for the design engineers towards developing sophisticated smart structures for various engineering applications.

Geometrically nonlinear dynamic analysis of functionally graded porous partially fluid-filled cylindrical shells subjected to exponential loads

2020 ◽  
pp. 107754632098246
Author(s):  
Majid Khayat ◽  
Abdolhossein Baghlani ◽  
Seyed Mehdi Dehghan ◽  
Mohammad Amir Najafgholipour
Keyword(s):  
Material Properties ◽  
Nonlinear Dynamic ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
Graphene Platelet ◽  
Graphene Platelets

This article investigates the influence of graphene platelet reinforcements and nonlinear elastic foundations on geometrically nonlinear dynamic response of a partially fluid-filled functionally graded porous cylindrical shell under exponential loading. Material properties are assumed to be varied continuously in the thickness in terms of porosity and graphene platelet reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin–Tsai equations are used to find the effective material properties of the graphene platelet–reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders’s theory. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. An incremental–iterative approach is used to solve the nonlinear equations of motion of partially fluid-filled cylindrical shells based on the Newmark direct integration and Newton–Raphson methods. The governing equations of liquid motion are derived using a finite strip formulation of incompressible inviscid potential flow. The effects of various parameters on dynamic responses are investigated. A detailed numerical study is carried out to bring out the effects of some influential parameters, such as fluid depth, porosity distribution, and graphene platelet dispersion parameters on nonlinear dynamic behavior of functionally graded porous nanocomposite partially fluid-filled cylindrical shells reinforced with graphene platelets.

Influence of Symmetrical Boundary Conditions on Free Vibration of Functionally Graded Cylindrical Shells With Ring Support

2009 ◽  
Author(s):  
M. R. Isvandzibaei ◽  
M. M. Najafizadeh ◽  
P. Khazaeinejad
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Third Order ◽  
Graded Materials ◽  
Ring Support

In the present work, the free vibration of thin cylindrical shells with ring support made of functionally graded materials under various symmetrical boundary conditions is presented. Temperature and position dependent material properties are varied linearly through the thickness of the shell. The functionally graded cylindrical shell has ring support which is arbitrarily placed along the shell and imposed a zero lateral deflection. The third order shear deformation theory is employed to formulate the problem. The governing equations of motion are derived using the Hamilton’s principle. Results are presented on the frequency characteristics and influence of the boundary conditions and the locations of the ring support on the natural frequencies. The present analysis is validated by comparing the results with those available in the literature.

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.

scholarly journals Vibration analysis of a sandwich cylindrical shell in hygrothermal environment

2021 ◽  
Vol 10 (1) ◽  
pp. 414-430
Author(s):  
Chunwei Zhang ◽  
Qiao Jin ◽  
Yansheng Song ◽  
Jingli Wang ◽  
Li Sun ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Single Layer ◽  
Functionally Graded ◽  
Sandwich Shell ◽  
Continuous Change ◽  
Multilayered Structures ◽  
Cylindrical Sandwich Shell ◽  
Vibrational Behavior

Abstract The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

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.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

Natural frequency, damping and forced responses of sandwich plates with viscoelastic core and graphene nanoplatelets reinforced face sheets

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1165-1177 ◽  
Author(s):  
Ali Mohseni ◽  
Meisam Shakouri
Keyword(s):  
Sandwich Plate ◽  
Effective Properties ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Graphene Nanoplatelets ◽  
Complex Eigenvalue ◽  
Viscoelastic Core ◽  
Forced Vibration Analysis ◽  
Forced Responses

The free and forced vibration analysis of a sandwich plate with the viscoelastic core and face layers reinforced functionally with multilayered graphene nanoplatelets is presented. Different graphene nanoplatelet distributions are considered through the thickness, and the effective properties of the graphene reinforced nanocomposite are obtained by the rule of mixture. The equations of motion are extracted using Hamilton’s principle and assuming the classical thin plate theory for face layers and the first-order shear deformation theory for the thick viscoelastic core. Assuming the simply-supported boundary condition for all edges, the displacement components are proposed by Fourier series and the complex eigenvalue problem is solved to obtain the natural frequencies as well as the loss factors. The results are validated with available investigations, and effects of some important parameters on the free and forced responses of the sandwich plate are studied.

Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers

2020 ◽  
pp. 2150016
Author(s):  
Mohsen Rahmani ◽  
Sajjad Dehghanpour
Keyword(s):  
Thermal Stresses ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Type I ◽  
Sandwich Beams ◽  
Temperature Dependent ◽  
The Core ◽  
Graded Layers ◽  
Lagrange Strain

By using a high order sandwich beams theory which is modified by considering the transverse flexibility of the core, free vibration characteristics of two models of sandwich beams are studied in this paper. In type-I, functionally graded layers coat a homogeneous core, and in type-II, an FG core is covered by homogeneous face sheets. To increase the accuracy of the model of the FGM properties, even and uneven porosity distributions are applied, and all materials are considered temperature-dependent. Nonlinear Lagrange strain and thermal stresses of the face sheets and in-plane strain of the core are considered. To obtain the governing equations of motion, Hamilton’s principle is used and a Galerkin method is used to solve them for simply supported and clamped boundary conditions. To verify the results of this study, they are compared with the results of literatures. Also, the effect of variation of temperature, some geometrical parameters and porosities on the frequency are studied.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

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