3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid

Chen, Weiqiu; Bian, Zuguang; Lv, ChengSi; Ding, Hu

doi:10.1016/j.ijsolstr.2003.09.036

Cited by 178 publications

(76 citation statements)

References 46 publications

(46 reference statements)

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“…While the vibrational behaviour of a thick walled cylinder is of considerable engineering importance, all of the previously discussed papers are mainly focused on cylindrical shells using the classical equations of thin shell theories, except Chen et al 7 who investigated a thick hollow cylinder using equations of piezoelasticity based on laminate model as opposed to classical shell theories. Classical or thin-shell theories are based on the simplifying assumptions of Kirchhof-Love's hypothesis.…”

Section: -7mentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

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A two-dimensional functionally heterogeneous thick hollow cylinder with a finite length is considered and its natural modes and frequencies are determined. Since mode shapes of a thick cylinder are three-dimensional, even with axisymmetric conditions, three-dimensional theory of elasticity implemented for problem formulation. The axisymmetric conditions are assumed for the cylinder. The material properties of the two-dimensional functionally graded material (2D-FGM) cylinder are varied in the radial and axial directions with power law functions. Effects of volume fraction distribution on the different types of anti-symmetric mode shape configuration and vibrational behaviour of a simply supported cylinder are analyzed. Three-dimensional equations of motion are used and the eigen value problem is developed based on direct variational method. The study shows that the 2D-FGM cylinder exhibit interesting vibrational characteristics and mode shapes when the constituent volume fractions are varied.

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Section: -7mentioning

confidence: 99%

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Asgari¹

2017

IJAV

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“…In the direction of wave propagation, material constants of two materials with radial polarization are listed in Table 1 [25]. The gradient field used here is .…”

Section: Fgpm Spherically Curved Platesmentioning

confidence: 99%

Wave propagation in functionally graded piezoelectric spherically curved plates

Yu¹,

Wu²,

Hongli³

et al. 2007

Physica Status Solidi (b)

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Based on linear three-dimensional piezoelasticity, a Legendre orthogonal polynomial series expansion approach is used for determining the characteristics of guided waves in continuous functionally graded piezoelectric materials (FGPM) as spherically curved plates. The displacement components and electric potential, expanded in a series of Legendre polynomials, are introduced into the governing equations along with position-dependent material constants so that the solution of the wave equation is reduced to an eigenvalue problem. Our results from a homogeneous anisotropic spherically curved plate are compared with those published earlier to confirm the accuracy and range of applicability of this polynomial approach. Guided-wave dispersion curves for FGPM and the corresponding FGM spherically curved plates are calculated and the effect of piezoelectricity is shown. The mechanical displacement distribution and electric potential distribution are also illustrated. Finally, the influence of the ratio of radius to thickness on the dispersion curves is discussed.

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“…The state space method (SSM) satisfies all of the fundamental equations (Ying and Wang, 2009;, and has been widely used for static and dynamic analyses of FGM cylindrical shells. Chen et al (2004) studied the free vibration of an FGM cylinder filled with fluid. Hasheminejad and Rajabi (2008) performed an exact analysis for 3D scattering of a time-harmonic plane-progressive sound wave obliquely incident upon an arbitrarily thick bilaminated circular hollow cylinder of infinite extent.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells

Liang

Kou

Liu

et al. 2015

J. Zhejiang Univ. Sci. A

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Abstract:A good understanding of the mechanical behavior of functionally graded material (FGM) cylindrical shells is necessary for designers and researchers. However, the 3D transient response of FGM cylindrical shells under various boundary conditions has not yet been analyzed. In this paper, the problem is addressed by proposing an approach integrating the state space method, differential quadrature method, and Durbin's numerical inversion method of Laplace transform. The laminate model is used to obtain the transient solution in the radial direction. At the edges, four kinds of boundary conditions are considered: Clamped-Clamped, Clamped-Simply supported, Clamped-Free, and Simply supported-Simply supported. The results of the proposed method and finite element (FE) method agree with each other excellently. Convergence studies show that the proposed method has a fast convergence rate. The natural frequencies obtained by the proposed method, experiment, and other theoretical methods are in close agreement with each other. The effects of the load frequency and duration, length/outer radius ratio, and the (outer radius−inner radius)/outer radius ratio on the transient response of FGM shells are investigated. Two laws of variation of material properties along the radial direction are considered: the first has material properties varying according to an exponential law along the radial direction, while the second has material properties varying according to a power law. The effect of a functionally graded index on the transient response of FGM shells is investigated in both cases. The results obtained in this paper can serve as benchmark data for further research.

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3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid

Cited by 178 publications

References 46 publications

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Free Vibration Analysis of Functionally Heterogeneous Hollow Cylinder Based on Three Dimensional Elasticity Theory

Wave propagation in functionally graded piezoelectric spherically curved plates

A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells

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