Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders

2009 ◽  
Vol 25 (4) ◽  
pp. 555-563 ◽  
Author(s):  
H. M. Wang ◽  
C. B. Liu ◽  
H. J. Ding
Keyword(s):  
Exact Solution ◽  
Torsional Vibration ◽  
Transient Behavior ◽  
Functionally Graded ◽  
Hollow Cylinders

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.

Torsional vibration of functionally graded carbon nanotube reinforced conical shells

2018 ◽  
Vol 25 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Yaser Kiani
Keyword(s):  
Torsional Vibration ◽  
Conical Shell ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Coupled Equations ◽  
Parametric Studies ◽  
Torsional Frequency ◽  
Generalized Differential

AbstractThe present study deals with the free torsional vibration of a composite conical shell made of a polymeric matrix reinforced with carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the conical shell may be uniform or functionally graded. Five different cases of functionally graded reinforcements are considered. First-order shear deformable shell theory compatible with the Donnell kinematic assumptions is used to establish the motion equations of the shell. These equations are two coupled equations which should be treated as an eigenvalue problem. The generalized differential quadrature method is used to obtain a numerical solution for the torsional frequency parameters and the associated mode shapes of the shell. After validating the results of this study for the cases of isotropic homogeneous cone and annular plates, parametric studies are carried out to analyze the influences of geometrical characteristics of the shell, volume fraction of CNTs, and grading profile of the CNTs. It is shown that volume fraction of CNTs is an important factor with regard to torsional frequencies of the shell; however, grading profile does not change the torsional frequencies significantly.

scholarly journals Exact Solution for the Torsional Vibration of an Elastic Pile in a Radially Inhomogeneous Saturated Soil

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xibin Li ◽  
Zhiqing Zhang ◽  
Jianchao Sheng
Keyword(s):  
Exact Solution ◽  
Torsional Vibration ◽  
Saturated Soil ◽  
Exponential Form ◽  
Soil System ◽  
Time Harmonic ◽  
Radial Inhomogeneity ◽  
Inner Region ◽  
Radially Inhomogeneous ◽  
Mathematical Derivation

An exact solution is proposed to study the time-harmonic torsional vibration of an elastic pile embedded in a radially inhomogeneous saturated soil. The radially inhomogeneous saturated soil is composed of inner disturbed and outer semi-infinite undisturbed concentric annular regions, with the shear modulus of the inner region changing in an exponential form along the radial direction. The governing equation of each region of the saturated soil is solved through rigorous mathematical derivation and the soil torsional impedance is derived with an exact and explicit expression. Making use of the boundary and continuity conditions of the pile-soil system, the torsional complex stiffness at the pile top is obtained in an exact closed form in the frequency domain. Selected numerical results are presented to investigate the influence of the radial inhomogeneity of the surrounding soil on the vibration characteristics of the pile-soil system.

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.

scholarly journals Bifurcation of pressurized functionally graded elastomeric hollow cylinders

2017 ◽  
Vol 109 ◽  
pp. 259-276 ◽  
Author(s):  
Weiqiu Chen ◽  
Dongying Liu ◽  
Sritawat Kitipornchai ◽  
Jie Yang
Keyword(s):  
Functionally Graded ◽  
Hollow Cylinders
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