Circumferential waves in pre-stressed functionally graded cylindrical curved plates

AbstractInitial stress (pre-stress) in functionally graded material (FGM) structures is often inevitable because of the limitation of available manufacturing technology. On the basis of the “mechanics of incremental deformations”, the circumferential wave characteristics in FGM cylindrical curved plates under uniform initial stresses in the radial and axial directions are investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. Through numerical examples, the convergence of the polynomial method is discussed. The influences of the initial stresses on the circumferential Lamb-like and the circumferential SH waves are investigated, respectively. Numerical results show that they are quite distinct. Moreover, the influences of the initial stress in the axial direction are very different from those in the radial direction, both on the dispersion curves and on the displacement and stress distributions.

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Viscoelastic Circumferential SH Wave in Graded Hollow Cylinders

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.543-547.7 ◽

2014 ◽

Vol 543-547 ◽

pp. 7-11

Author(s):

X.D. Yang ◽

J.G. Yu

Keyword(s):

Wave Propagation ◽

Nondestructive Evaluation ◽

Functionally Graded Material ◽

Functionally Graded ◽

Polynomial Method ◽

Sh Wave ◽

Graded Material ◽

Viscoelastic Theory ◽

Hollow Cylinders ◽

Dispersion And Attenuation

In this article, circumferential SH wave propagation in functionally graded material (FGM) hollow cylinders is investigated. Based on the Kelvin-Voigt viscoelastic theory, the controlling differential equations in terms of displacements are deduced. By the Legendre polynomial method, the asymptotic solutions are obtained. Through the numerical results, the influences of gradient profile and the influences of the radius to thickness ratio on dispersion and attenuation are illustrated. The work is crucial for guided ultrasonic nondestructive evaluation for graded hollow cylinders.

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Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative

Materials ◽

10.3390/ma13183953 ◽

2020 ◽

Vol 13 (18) ◽

pp. 3953 ◽

Cited By ~ 5

Author(s):

Ahmed E. Abouelregal ◽

Hijaz Ahmad ◽

Shao-Wen Yao

Keyword(s):

Axial Direction ◽

Functionally Graded ◽

Piezoelectric Medium ◽

Piezoelectric Response ◽

Modified Model ◽

The Laplace Transform ◽

Graded Material ◽

Limited Length ◽

Functionally Graded Piezoelectric ◽

Generalized Heat Conduction

The current work deals with the study of a thermo-piezoelectric modified model in the context of generalized heat conduction with a memory-dependent derivative. The investigations of the limited-length piezoelectric functionally graded (FGPM) rod have been considered based on the presented model. It is assumed that the specific heat and density are constant for simplicity while the other physical properties of the FGPM rod are assumed to vary exponentially through the length. The FGPM rod is subject to a moving heat source along the axial direction and is fixed to zero voltage at both ends. Using the Laplace transform, the governing partial differential equations have been converted to the space-domain, and then solved analytically to obtain the distributions of the field quantities. Numerical computations are shown graphically to verify the effect of memory presence, graded material properties, time-delay, Kernel function, and the thermo-piezoelectric response on the physical fields.

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Modeling of vibration for functionally graded beams

Open Mathematics ◽

10.1515/math-2016-0057 ◽

2016 ◽

Vol 14 (1) ◽

pp. 661-672 ◽

Cited By ~ 2

Author(s):

Gülsemay Yiğit ◽

Ali Şahin ◽

Mustafa Bayram

Keyword(s):

Initial Conditions ◽

Adomian Decomposition Method ◽

Expansion Method ◽

Variable Coefficients ◽

Functionally Graded ◽

Fourier Series Expansion ◽

Bernoulli Beam ◽

Adomian Decomposition ◽

Graded Material ◽

Euler Bernoulli Beam

AbstractIn this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

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

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x16651154 ◽

2016 ◽

Vol 28 (2) ◽

pp. 272-289 ◽

Cited By ~ 1

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.

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Evaluation of Response Variability of Functionally Graded Material Beam with Varying Sectional Area due to Spatial Randomness in Elastic Modulus along Axial Direction

Journal of the Computational Structural Engineering Institute of Korea ◽

10.7734/coseik.2014.27.3.199 ◽

2014 ◽

Vol 27 (3) ◽

pp. 199-206

Author(s):

Hyuk Chun Noh

Keyword(s):

Elastic Modulus ◽

Functionally Graded Material ◽

Axial Direction ◽

Response Variability ◽

Functionally Graded ◽

Sectional Area ◽

Graded Material ◽

Spatial Randomness

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On modal analysis of axially functionally graded material beam under hygrothermal effect

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406219888234 ◽

2019 ◽

Vol 234 (5) ◽

pp. 1085-1101 ◽

Cited By ~ 6

Author(s):

Pankaj Sharma ◽

Rahul Singh ◽

Muzamal Hussain

Keyword(s):

Modal Analysis ◽

Functionally Graded Material ◽

Volume Fraction ◽

Axial Direction ◽

Functionally Graded ◽

Element Analysis ◽

Hygrothermal Effect ◽

Graded Material ◽

Eigen Frequencies ◽

Axially Functionally Graded Material

This investigation focuses on the modal analysis of an axially functionally graded material beam under hygrothermal effect. The material constants of the beam are supposed to be graded smoothly along the axial direction under both power law and sigmoid law distribution. A finite element analysis with COMSOL Multiphysics® (version 5.2) package is used to find the Eigen frequencies of the beam. The accuracy of the technique is authenticated by relating the results with the prior investigation for reduced case. The effects of moisture changes, temperature, and volume fraction index, length-to-thickness ratio on the Eigen frequencies are investigated in detail. It is believed that the present investigation may be useful in the design of highly efficient environmental sensors for structural health monitoring perspective.

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Natural Vibration of Functionally Graded Cylindrical Shells With Infinite and Finite Lengths

Journal of Vibration and Acoustics ◽

10.1115/1.4004900 ◽

2011 ◽

Vol 134 (1) ◽

Cited By ~ 3

Author(s):

Zhiyuan Cao ◽

Shougao Tang

Keyword(s):

Functionally Graded Material ◽

Mode Shape ◽

Natural Vibration ◽

Separation Of Variables ◽

Cylindrical Shells ◽

Analytic Solutions ◽

Variable Coefficients ◽

Functionally Graded ◽

Graded Material ◽

Membrane Bending

Upon the basic theory of functionally graded material cylindrical shell, the original 3-D foundational equations with variable coefficients are transformed into anisotropic and membrane-bending coupling 2-D equations with constant coefficients. The separation-of-variables mode shape functions in axial and circumferential directions for cylindrical shells with infinite and finite lengths are proposed for analytic solutions, which satisfy the basic differential equations, of natural vibration. The general approach presented in the paper for the solutions of natural frequency and mode shape of functionally graded cylindrical shells can be applied to cylindrical shells with any kind of functionally graded material, different length, and boundary conditions.

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Extension of Boley’s method to functionally graded beams

Acta Mechanica ◽

10.1007/s00707-020-02850-0 ◽

2020 ◽

Author(s):

J. Gahleitner ◽

J. Schoeftner

Keyword(s):

Finite Element ◽

Stress Function ◽

Poisson Ratio ◽

Axial Direction ◽

Functionally Graded ◽

Thickness Direction ◽

Functionally Graded Beam ◽

Element Analysis ◽

Perfect Agreement ◽

Graded Material

AbstractThe objective of this contribution is the computation of the Airy stress function for functionally graded beam-type structures subjected to transverse and shear loads. For simplification, the material parameters are kept constant in the axial direction and vary only in the thickness direction. The proposed method can be easily extended to material varying in the axial and thickness direction. In the first part an iterative procedure is applied for the determination of the stress function by means of Boley’s method. This method was successfully applied by Boley for two-dimensional (2D) isotropic plates under plane stress conditions in order to compute the stress distribution and the displacement field. In the second part, a shear loaded cantilever made of isotropic, functionally graded material is studied in order to verify our theory with finite element results. It is assumed that the Young’s modulus varies exponentially in the transverse direction and the Poisson ratio is constant. Stresses and displacements are analytically determined by applying our derived theory. Results are compared to a 2D finite element analysis performed with the commercial software ABAQUS. It is found that the analytical and numerical results are in perfect agreement.

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