Nonlinear Dynamics of Functionally Graded Cylindrical Shells With Internal Fluid

2015 ◽  
Author(s):  
Frederico M. A. Silva ◽  
Roger Otávio P. Montes ◽  
Paulo B. Gonçalves ◽  
Zenón J. G. N. del Prado
Keyword(s):  
Cylindrical Shell ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Axial Loading ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Internal Fluid ◽  
Graded Material ◽  
Low Dimensional ◽  
The Galerkin Method

This work analyzes the nonlinear vibrations of a simply supported functionally graded cylindrical shell considering the effects of an internal fluid and static preloading. The cylindrical shell is subjected to a time dependent axial loading. The fluid is considered to be incompressible, non-viscous and irrotational and its effect on the shell wall is obtained using the potential flow theory. The shell is modeled by Donnell nonlinear shallow shell theory. The axial and circumferential displacement fields are described in terms of lateral displacement, thus generating a low-dimensional model, while the lateral displacement field is determined by a perturbation procedure which provides a general expression for the nonlinear vibration modes. These modal expansions satisfy the boundary and symmetry conditions of the problem. The discretized equations of motion are obtained by applying the Galerkin method. Various numerical techniques are employed to obtain the resonance curves and time responses of the cylindrical shell, showing the influence of the geometry, the internal fluid, static preloading and functionally graded material law on the shell dynamics and stability.

Buckling Analysis for a Ring-Stiffened FGM Cylindrical Shell Under Hydrostatic Pressure and Thermal Loads

2014 ◽  
Vol 30 (4) ◽  
pp. 403-410 ◽  
Author(s):  
H.-L. Dai ◽  
L.-L. Qi ◽  
H.-Y. Zheng
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Thermal Loads ◽  
Temperature Dependent ◽  
Stiffened Cylindrical Shell ◽  
Buckling Behavior ◽  
Graded Material ◽  
The Galerkin Method

AbstractThis paper studies the buckling analysis for a ring-stiffened cylindrical shell consisted of functionally graded material (FGM) subjected to hydrostatic pressure and thermal loads. Material properties of the ring-stiffened FGM cylindrical shell are assumed to be temperature-dependent, and vary smoothly through the thickness direction of the structure according to a volume exponent. Based on the Donnell assumptions, buckling loads of the ring-stiffened FGM cylindrical shell are presented by utilizing the Galerkin method. Numerical results reveal that thermal loads, volume exponent and geometric parameters have significant effects on the buckling behavior of the ring-stiffened cylindrical shell.

Nonlinear Vibrations of Partially Fluid-Filled Cylindrical Shells

2010 ◽  
Author(s):  
Paulo B. Gonc¸alves ◽  
Frederico M. A. da Silva ◽  
Zeno´n J. G. N. del Prado
Keyword(s):  
Nonlinear Vibration ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Hydrodynamic Pressure ◽  
Vibration Modes ◽  
Internal Fluid ◽  
Irrotational Motion ◽  
Low Dimensional ◽  
The Galerkin Method ◽  
Modal Solution

The present work investigates the nonlinear dynamic behavior and instabilities of partially fluid-filled cylindrical shell subjected to lateral pressure. Donnell shallow shell theory is employed to model the shell. The fluid is modeled as non-viscous and incompressible and its irrotational motion is described by a velocity potential which satisfies the Laplace equation. A discrete low-dimensional model for the nonlinear vibration analysis of thin cylindrical shells is derived to study the shell vibrations. First, a general expression for the nonlinear vibration modes that satisfy all the relevant boundary, continuity and symmetry conditions is derived using a perturbation procedure validated in previous studies and then the Galerkin method is used to discretize the equations of motion. The same modal solution is used to derive the hydrodynamic pressure on the shell wall. The influence played by the height of the internal fluid on the natural frequencies, nonlinear shell response and bifurcations is examined.

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 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.

Free Vibration and Elastic Critical Load of Functionally Graded Material Thin Cylindrical Shells Under Internal Pressure

2018 ◽  
Vol 18 (11) ◽  
pp. 1850138 ◽  
Author(s):  
Yueyang Han ◽  
Xiang Zhu ◽  
Tianyun Li ◽  
Yunyan Yu ◽  
Xiaofang Hu
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Internal Pressure ◽  
Critical Load ◽  
Natural Frequency ◽  
Functionally Graded Material ◽  
Present Method ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Graded Material

An analytical approach for predicting the free vibration and elastic critical load of functionally graded material (FGM) thin cylindrical shells filled with internal pressured fluid is presented in this study. The vibration of the FGM cylindrical shell is described by the Flügge shell theory, where the internal static pressure is considered as the prestress term in the shell equations. The motion of the internal fluid is described by the acoustic wave equation. The natural frequencies of the FGM cylindrical shell under different internal pressures are obtained with the wave propagation method. The relationship between the internal pressure and the natural frequency of the cylindrical shell is analyzed. Then the linear extrapolation method is employed to obtain the elastic critical load of the FGM cylindrical shell from the condition that the increasing pressure has resulted in zero natural frequency. The accuracy of the present method is verified by comparison with the published results. The effects of gradient index, boundary conditions and structural parameters on the elastic critical load of the FGM cylindrical shell are discussed. Compared with the experimental and numerical analyses based on the external pressure, the present method is simple and easy to carry out.

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.

Research on Vibration and Sound Radiation from Submarine Functionally Graded Material Nonpressure Cylindrical Shell

2013 ◽  
Vol 690-693 ◽  
pp. 3046-3049
Author(s):  
Yan Bing Zhang ◽  
Chun Yu Ren ◽  
Xi Zhu
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Radiation ◽  
Radiation Power ◽  
Sound Radiation ◽  
Functionally Graded ◽  
Underwater Sound ◽  
Graded Materials ◽  
Graded Material ◽  
Vibration And Sound Radiation ◽  
Sound Radiation Power

In this paper, we establish the finite element (FEM) and boundary element (BEM) models of a submarine section, and study the underwater sound radiation field of three different non-pressure shells made of steel, steel with anechoic tile, and the functionally graded materials (FGM) separately using a method combining of FEM and BEM . Research shows that the combination of FEM and BEM can address the acoustic radiation calculation problem of FGM, and in comparison with steel and anechoic tile laying submarine section, the weight of FGM non-pressure shell reduces 1600kg, and the sound radiation power decreases 4db and 2.5db respectively, thus having better performance in vibration and noise reduction.

Effects of piezoelectric rings on electro-elasto-dynamic behaviour of functionally graded cylindrical shell

2016 ◽  
Vol 28 (2) ◽  
pp. 272-289 ◽  
Author(s):  
Mohammadreza Saviz
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Virtual Work ◽  
Electrical Potential ◽  
Axial Direction ◽  
Functionally Graded ◽  
Radial Coordinate ◽  
Graded Material

A layer-wise finite element approach is adopted to analyse the hollow cylindrical shell made of functionally graded material with piezoelectric rings as sensor/actuator, under dynamic load. The mechanical properties of the substrate are regulated by volume fraction as a function of radial coordinate. The thickness of functionally graded material shell and piezo-rings is divided into mathematical sub-layers and then the general layer-wise laminate theory is formulated through introducing piecewise continuous approximations across the thickness, accounting for any discontinuity in derivatives of the displacement at the interface between the ring and cylinder. The virtual work statement including structural and electrical potential energies yields the three-dimensional governing equations which are reduced to two-dimensional differential equations, using layer-wise method. For axisymmetric case, the resulted equations are solved with one-dimensional finite element method in the axial direction. By assembling stiffness and mass matrices, the required stress and displacement continuities at each interface and between the two adjacent elements are forced. The results for free vibration and static loading are applied to study the convergence and verified by comparing them to solutions of similar existing problems. The induced deformation by piezoelectric actuators as well as the effect of rings on functionally graded material shell is investigated.

Sign in / Sign up

Export Citation Format

Share Document