scholarly journals Vibrations of Three-Layered Cylindrical Shells with FGM Middle Layer Resting on Winkler and Pasternak Foundations

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Abdul Ghafar Shah ◽  
Aalia Ali ◽  
Muhmmad Nawaz Naeem ◽  
Shahid Hussain Arshad
Keyword(s):  
Cylindrical Shell ◽  
Wave Propagation ◽  
Functionally Graded Material ◽  
Middle Layer ◽  
Functionally Graded ◽  
Numerical Results ◽  
Thickness Direction ◽  
Dynamical Equations ◽  
Elastic Foundations ◽  
Graded Material

Vibrations of a cylindrical shell composed of three layers of different materials resting on elastic foundations are studied out. This configuration is formed by three layers of material in thickness direction where the inner and outer layers are of isotropic materials and the middle is of functionally graded material. Love shell dynamical equations are considered to describe the vibration problem. The expressions for moduli of the Winkler and Pasternak foundations are combined with the shell dynamical equations. The wave propagation approach is used to solve the present shell problem. A number of comparisons of numerical results are performed to check the validity and accuracy of the present approach.

Viscoelastic Circumferential SH Wave in Graded Hollow Cylinders

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.

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.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

2012 ◽  
Vol 12 (02) ◽  
pp. 311-335 ◽  
Author(s):  
X. Q. HE ◽  
L. LI ◽  
S. KITIPORNCHAI ◽  
C. M. WANG ◽  
H. P. ZHU
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Optimum Combination ◽  
Thickness Direction ◽  
Power Law Distribution ◽  
Deployable Structures ◽  
Graded Material ◽  
Two Parameter

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

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.

scholarly journals An application of isogeometric analysis for active control the solid functionally graded material plates with actuator patches using piezoelectric material

2020 ◽  
Vol 2 (SI2) ◽  
pp. First
Author(s):  
Khuong Duy Nguyen ◽  
Nguyen Manh Tien ◽  
Nguyen Xuan Hung ◽  
Vu Cong Hoa
Keyword(s):  
Piezoelectric Material ◽  
Active Control ◽  
Functionally Graded Material ◽  
Isogeometric Analysis ◽  
Piezoelectric Materials ◽  
Middle Layer ◽  
Basic Function ◽  
Functionally Graded ◽  
Three Dimensional Model ◽  
Graded Material

This paper applies isogeometric analysis (IGA) to simulate active control of the functionally graded material (FGM) plates by using piezoelectric material patches. This control helps to reduce the deflection of the plate under the effect of static load, which makes the structure more resistant to loading. IGA is built on the non-uniform rational basis spline (NURBS) basic function with many advantages such as: describing geometry exactly by approximating by higher order function and directly using this function to approach procedure. Furthermore, NURBS geometry has mesh flexibility and high continuity between elements, making the problem highly accurate. Three-dimensional model for plate-like structure consists of upper and lower layers made of piezoelectric materials, the middle layer is FGM. The obtained results will be verified with the published results to prove the efficiency of the proposed method for this problem. Through the obtained results, it is shown that IGA is used effectively for the active control problem by piezoelectric patches to reduce the displacement of FGM plates. The efficiency shown when using a small number of degrees of freedom but still ensuring the solution has accurate results when compared with the reference solution.

Sign in / Sign up

Export Citation Format

Share Document