Guided waves in a functionally graded 1-D hexagonal quasi-crystal plate with piezoelectric effect

2021 ◽  
pp. 1045389X2110639
Author(s):  
Bo Zhang ◽  
Jiangong Yu ◽  
Hongmei Zhou ◽  
Xiaoming Zhang ◽  
Lahoucine Elmaimouni
Keyword(s):  
Significant Influence ◽  
Guided Waves ◽  
Coupling Effect ◽  
Functionally Graded ◽  
Crystal Plate ◽  
Polynomial Method ◽  
Coupling Coefficients ◽  
Governing Equations ◽  
Phonon Modes ◽  
Sh Waves

For the purpose of design and optimization for piezoelectric quasi-crystal transducers, guided waves in a functionally graded 1-D hexagonal piezoelectric quasi-crystal plate are investigated. In this paper, a model combined with the Bak’s and elastohydrodynamic models is utilized to derive governing equations of wave motion, and real, pure imaginary, and complex roots of governing equations are calculated by using the modified Legendre polynomial method. Subsequently, dispersion curves and displacements of phonon and phason modes are illustrated. Then, guided waves in functionally graded 1-D hexagonal piezoelectric quasi-crystal plates with different quasi-periodic directions are studied. And the phonon-phason coupling effect on Lamb and SH waves are analyzed. Accordingly, some interesting results are obtained: The phonon-phason coupling just affects Lamb waves in the x- and z-direction quasi-crystal plates, and SH waves in the y-direction quasi-crystal plate. Besides, frequencies of propagative phason modes decrease as phonon-phason coupling coefficients Ri increase. Furthermore, a variation in the polarization has a more significant influence on phonon modes, and a variation in the quasi-periodic direction has a more significant influence on phason modes.

Guided Wave Propagation in Functionally Graded One-Dimensional Hexagonal Quasi-Crystal Plates

2020 ◽  
Vol 36 (6) ◽  
pp. 773-788
Author(s):  
B. Zhang ◽  
J.G. Yu ◽  
X.M. Zhang
Keyword(s):  
Coupling Effect ◽  
Guided Wave ◽  
Functionally Graded ◽  
Polynomial Method ◽  
Coupling Coefficients ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Sh Waves ◽  
One Dimensional ◽  
Non Destructive

ABSTRACTDue to the high brittleness, cracks, holes, and other defects that are easily generated in quasi-crystal structures can affect safe applications in serious cases. For guided wave non-destructive testing, the propagation of Lamb and SH waves in functionally graded one-dimensional hexagonal quasi-crystal plates are investigated. Governing equations of wave motion in the context of Bak’s model are deduced and solved by the Legendre orthogonal polynomial method. Dispersion curves, phonon and phason displacement, and stress distributions are illustrated. The convergence of the present method applied to functionally graded quasi-crystal plates is verified. Moreover, the influences of the phonon-phason coupling effect and graded fields on wave characteristics are analyzed. Some new results are obtained: angular frequencies of phason modes always decrease as phonon-phason coupling coefficients, Ri, increase; and phonon and phason displacements of Lamb and SH waves at high frequencies are mainly distributed in the region that contains more quasi-crystal material with a smaller elasticity modulus and less rigidity. The obtained results establish the theoretical foundation of guided wave non-destructive testing for functionally graded quasi-crystal plates.

Axial guided wave characteristics in functionally graded one-dimensional hexagonal piezoelectric quasi-crystal cylinders

2021 ◽  
pp. 108128652110134
Author(s):  
B. Zhang ◽  
X.H. Wang ◽  
L. Elmaimouni ◽  
J.G. Yu ◽  
X.M. Zhang
Keyword(s):  
Coupling Effect ◽  
Energy Conversion Efficiency ◽  
Guided Wave ◽  
Functionally Graded ◽  
Phonon Modes ◽  
One Dimensional ◽  
Longitudinal Modes ◽  
Wave Characteristics ◽  
Piezoelectric Effects ◽  
Hollow Cylinders

In one-dimensional hexagonal piezoelectric quasi-crystals, there exist the phonon–phason, electro–phonon, and electro–phason couplings. Therefore, the phonon–phason coupling and piezoelectric effects on axial guided wave characteristics in one-dimensional hexagonal functionally graded piezoelectric quasi-crystal (FGPQC) cylinders are investigated by utilizing the Legendre polynomial series method. The dispersion curves and cut-off frequencies are illustrated. Wave characteristics in three hollow cylinders with different quasi-periodic directions are comparatively studied. Some new wave phenomena are revealed: the phonon–phason coupling and piezoelectric effects on the longitudinal and torsional phonon modes ( N = 0) vary as the quasi-periodic direction changes; the phonon–phason coupling effect on flexural–torsional modes in the r-, z-FGPQC hollow cylinders, and on flexural–longitudinal modes in ϑ-FGPQC hollow cylinders increases as N increases. The corresponding results obtained in this work lay the theoretical foundation for the design and manufacture of piezoelectric transducers with high resolution and energy-conversion efficiency.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes

2021 ◽  
pp. 107754632110004
Author(s):  
Hassan Afshari ◽  
Hossein Amirabadi
Keyword(s):  
Carbon Nanotubes ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Conical Shells ◽  
First Order ◽  
Effective Mechanical Properties ◽  
Comprehensive Study

In this article, a comprehensive study is conducted on the free vibration analysis of rotating truncated conical shells reinforced with functionally graded agglomerated carbon nanotubes The shell is modeled based on the first-order shear deformation theory, and effective mechanical properties are calculated based on the Eshelby–Mori–Tanaka scheme along with the rule of mixture. By considering centrifugal and Coriolis accelerations and initial hoop tension, the set of governing equations is derived using Hamilton’s principle and is solved numerically using the differential quadrature method Convergence and accuracy of the presented model are confirmed and the effects of different parameters on the forward and backward frequencies of the rotating carbon nanotube-reinforced truncated conical shells are investigated.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation

2017 ◽  
Vol 21 (8) ◽  
pp. 2700-2734 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
MH Zamani
Keyword(s):  
Young’S Modulus ◽  
Silica Aerogel ◽  
Young's Modulus ◽  
Nonlocal Parameter ◽  
Core Layer ◽  
Functionally Graded ◽  
Electric Field Effect ◽  
Governing Equations ◽  
Model Foundation ◽  
Mechanical Bending

In the present research electro-mechanical bending behavior of sandwich nanoplate with functionally graded porous core and piezoelectric face sheets is carried out. Vlasov’s model foundation is utilized to model the silica Aerogel foundation. Two functions are considered for nonuniform variation of material properties of the core layer along the thickness direction such as Young’s modulus, shear modulus, and density. The governing equations are deduced from Hamilton’s principle based on sinusoidal shear and normal deformation theory. In order to solve seven governing equations, an iterative technique is accomplished. After all, deflection and stresses are verified with corresponding literatures. Eventually, the numerical results reveal that applied voltage, plate aspect ratio, thickness ratio, nonlocal parameter, porosity index, Young’s modulus, and height of silica Aerogel foundation have substantial effects on the electro-mechanical bending response of functionally graded porous sandwich nanoplate.

Thermal Effects on the Vibration of Functionally Graded Deep Beams with Porosity

2017 ◽  
Vol 09 (05) ◽  
pp. 1750076 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Thermal Effects ◽  
Functionally Graded ◽  
Deep Beam ◽  
Material Distribution ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Deep Beams

The purpose of this study is to investigate the thermal effects on the free vibration of functionally graded (FG) porous deep beams. Mechanical properties of the FG deep beam are temperature-dependent and vary across the height direction with different porosity models. The governing equations problem is obtained by using the Hamilton’s principle. In the solution of the problem, plane piecewise solid continua model and finite element method are used. The effects of porosity parameters, material distribution, porosity models and temperature rising on the vibration characteristics are presented and discussed with porosity effects for FG deep beams.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

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