Nonlinear vibrations of fluid-filled functionally graded cylindrical shell considering a time-dependent lateral load and static preload

2015 ◽  
Vol 230 (1) ◽  
pp. 102-119 ◽  
Author(s):  
Frederico Martins Alves da Silva ◽  
Roger Otávio Pires Montes ◽  
Paulo Batista Gonçalves ◽  
Zenón José Guzmán Nuñez Del Prado
Keyword(s):  
Cylindrical Shell ◽  
Shell Thickness ◽  
Nonlinear Vibrations ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Time Dependent ◽  
Nonlinear Frequency ◽  
Power Law Distribution

In the recent years, functionally gradient materials (FGMs) have gained considerable attention with possible applications in several engineering fields, especially in a high-temperature or hazardous environment. In this work, the nonlinear vibrations of a simply supported fluid-filled functionally graded cylindrical shell subjected to a lateral time-dependent load and axial static preload are analyzed. To model the shell, the Donnell nonlinear shell theory is used. The fluid is assumed to be incompressible, nonviscous, and irrotational. A new function to describe the variation in the volume fraction of the constituent material through the shell thickness is proposed, extending the concept of sandwich structures to a functionally graded material. Material properties are graded along the shell thickness according to the proposed volume fraction power law distribution. A consistent reduced order model derived from a perturbation technique is used to describe the displacements of the shell and, the Galerkin method is applied to derive a set of coupled nonlinear ordinary differential equations of motion. Results show the influence of the variation of the two constituent materials along the shell thickness, internal fluid, static preload, and shell geometry on the natural frequencies, nonlinear frequency–amplitude relation, resonance curves, and bifurcation scenario of the FG cylindrical shell.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

On the Dynamic Response of Imperfection Sensitive Higher Order Functionally Graded Plates with Random System Parameters

2019 ◽  
Vol 11 (03) ◽  
pp. 1950025 ◽  
Author(s):  
Mohammed Shakir ◽  
Mohammad Talha
Keyword(s):  
Volume Fraction ◽  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Integration Scheme ◽  
Power Law Distribution ◽  
Random System ◽  
System Parameters

This paper presents the influence of various random system parameters on dynamics response of imperfection sensitive higher order shear deformable functionally graded material (FGM) plates. Young’s moduli, Poisson’s ratio and volume fraction index are considered as random system parameters. The material properties of the FGM plates are assumed to vary along the thickness direction using simple power-law distribution in terms of the volume fraction of the constituents. The plate kinematics is based on Reddy’s higher order shear deformation theory. Finite element method (FEM) is employed in conjunction with first-order perturbation technique (FOPT) and Newmark integration scheme to explore the influence of different system parameters, like volume fraction indices, aspect ratio, material uncertainties, and imperfection amplitude on the dynamic responses of the FGM plates.

Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates

2017 ◽  
Vol 21 (3) ◽  
pp. 895-916 ◽  
Author(s):  
Sid Ahmed Belalia
Keyword(s):  
Mechanical Properties ◽  
Functionally Graded Material ◽  
Large Amplitude ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Nonlinear Frequency ◽  
Graded Material

In this paper, the geometrically nonlinear formulation based on von Karman’s assumptions is employed to study the large amplitude free vibrations of functionally graded materials sandwich plates. The functionally graded material sandwich plate is made up of two layers of power-law functionally graded material face sheet and one layer of ceramic homogeneous core. A hierarchical finite element is employed to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia. The equations of motion for the nonlinear vibration of the functionally graded material sandwich plates are obtained using Lagrange’s equations. Employing the harmonic balance method, the equations of motion are converted from time domain to frequency domain and then solved iteratively using the linearized updated mode method. Results for linear and nonlinear frequency parameters of the simply supported functionally graded material sandwich plates are computed and compared with the published values, and an excellent agreement was found. The influence of the mechanical properties of the functionally graded material, thickness ratio of FGM layers, and volume fraction exponent on the backbone curves and on the nonlinear frequency parameters are investigated. The effects of the material properties of two different types of ceramics on the large amplitude vibration behaviors of the functionally graded material sandwich plates is also presented and discussed for the first time.

Nonlinear Dynamics of Functionally Graded Material Plates Under Dynamic Liquid Load and with Longitudinal Speed

2017 ◽  
Vol 09 (04) ◽  
pp. 1750054 ◽  
Author(s):  
Yan Qing Wang ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Functionally Graded Material ◽  
Internal Resonance ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Modal Interaction ◽  
Liquid Load ◽  
Graded Material

This paper investigates the dynamics of functionally graded material (FGM) plates under dynamic liquid load and with longitudinal speed. The liquid is assumed to be ideal so that it is incompressible, inviscid and irrotational. Based on the D’Alembert’s principle, the mathematical model of the system is developed by taking into account geometrical and material nonlinearities as well as velocity potential and Bernoulli’s equation. The Galerkin method is employed to discretize the partial differential governing equation to a series of ordinary differential ones, which are then analyzed via the use of the method of harmonic balance. Analytical results are compared with numerical ones to validate the present method. The stability of the steady-state response is examined by means of the perturbation technique. Linear analysis of the system shows the possible appearance of internal resonance, and nonlinear frequency-response curves demonstrate strong hardening-spring property of the system. A modal interaction behavior through 1:1 internal resonance is detected; the behavior can happen in a wide domain of constituent volume fraction, which is a unique phenomenon in moving FGM plates compared with their metallic counterparts. Furthermore, results show the modal interaction can be easily evoked in the moving FGM plate under dynamic liquid load, even while the plate is subjected to minimal exciting force or large damping. In addition, influence of the plate location on nonlinear dynamics of the system is examined; results show the dynamic response of the plate will change considerably when the plate is near the container wall.

scholarly journals Dynamic stability of functionally graded plate under in-plane compression

2005 ◽  
Vol 2005 (4) ◽  
pp. 411-424 ◽  
Author(s):  
Andrzej Tylikowski
Keyword(s):  
Asymptotic Stability ◽  
Power Law ◽  
Volume Fraction ◽  
Direct Method ◽  
Functionally Graded ◽  
Time Dependent ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Plane State ◽  
The Stability

Functionally graded materials have gained considerable attention in the high-temperature applications. A study of parametric vibrations of functionally graded plates subjected to in-plane time-dependent forces is presented. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. Material properties are graded in the thickness direction of the plate according to volume fraction power law distribution. An oscillating temperature causes generation of in-plane time-dependent forces destabilizing the plane state of the plate equilibrium. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov's direct method. Effects of power law exponent on the stability domains are studied.

Supersonic Flutter of Functionally Graded Plates in a Thermal Environment

2006 ◽  
Author(s):  
H. M. Navazi ◽  
H. Haddadpour
Keyword(s):  
Differential Equations ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Time Integration ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Numerical Time Integration ◽  
Flutter Margin

In this paper, an analytical investigation intended to determine the flutter margin of supersonic functionally graded panels is carried out. For this purpose, piston theory aerodynamics has been employed to model quasi-steady aerodynamic loading. The material properties of the plate are assumed to be graded continuously across the panel thickness. The variation of temperature-dependent thermoelastic properties follows a simple power-law distribution in terms of the volume fraction of the constituent materials. The effects of compressive in-plane loads and static pressure differential are studied. Both uniform and through the thickness nonlinear temperature distributions are also considered. Hamilton’s principle is used to determine the coupled partial differential equations of motion. Using Galerkin’s method, the derived equations are transformed into a set of coupled ordinary differential equations, and then solved by numerical time integration. Some examples comparing the flutter margin of FG panels with that of plates made of pure metals and pure ceramics are presented. The results of the present study are compared with those of the previous works, where finite element method was used. It is shown that the use of functionally graded materials can yield an increase or decrease of the aeroelastic stability in the supersonic flow for different regions.

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 Weight optimisation of functionally graded beams using modified differential evolution

2019 ◽  
Vol 13 (2) ◽  
pp. 48-63 ◽  
Author(s):  
Pham Hoang Anh ◽  
Tran Thuy Duong
Keyword(s):  
Differential Evolution ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Parameter Distribution ◽  
Power Law Distribution ◽  
De Algorithm ◽  
Fgm Beam

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.

scholarly journals Mechanical Properties of Al 25 wt.% Cu Functionally Graded Material

2019 ◽  
Vol 26 (1) ◽  
pp. 327-337 ◽  
Author(s):  
Aref Mehditabar ◽  
Gholam H. Rahimi ◽  
Seyed Ebrahim Vahdat
Keyword(s):  
Cylindrical Shell ◽  
Wear Rate ◽  
Rate Coefficient ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Functionally Graded ◽  
Compressive Test ◽  
High Entropy ◽  
Graded Material ◽  
Maximum Volume Fraction

AbstractThe present work refers to describe the effects of Al2Cu variations on various properties of thick-walled functionally graded (FG) cylindrical shell. Al-25 wt.% Cu hypo-eutectic alloy ingot is melted and centrifugally casted to obtain high entropy FG composite. A series of microstructure examinations such as FESEM and EDX analysis were carried out to determine the distributions of constituent phases and elements. It is revealed that the maximum volume fraction of Al2Cu particle is reached near the inner surface with 35.7 Vol.% and then reduces gradually to 32.5 Vol.% at the outer surface of FG cylindrical shell. The effects of the variations Al2Cu along radial direction of FG tube are discussed through Vickers hardness, wear rate, coefficient of thermal expansion and compressive test measurements. The experimental results show that the wear and hardness are varied in graded manner which the highest wear resistance with wear rate of 9.1×10−5g/mm2 and hardness with 153HV are found towards Al2Cu enriched zone or inner periphery. Moreover, the studied FG cylindrical shell shows drop 2.5% in yield stress and 4.5% in elastic modulus from intermediate to inner layers due to Al2Cu particles clustering in metal matrix.

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