On free vibration of a functionally graded piezoelectric rectangular plate

Chen, W. Q.; Ding, Hu

doi:10.1007/bf01177452

Cited by 123 publications

(45 citation statements)

References 14 publications

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“…The electromechanical behavior of functionally graded piezoelectric shells was examined in [15] by using a high-order theory. The free vibration problem of functionally graded piezoelectric rectangular plate was analyzed in [16] using a laminated approximation based on a three-dimensional theory. In addition, exact treatments for functionally graded piezoelectric materials have been carried out.…”

Section: Introductionmentioning

confidence: 99%

The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply

Ootao

Tanigawa

2005

Arch Appl Mech

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This paper is concerned with the theoretical treatment of the transient piezothermoelastic problem involving a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply in the width direction. The thermal, thermoelastic and piezoelectric constants of the strip are assumed to vary exponentially in the thickness direction. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the exact solution for a simply supported strip under the state of plane strain. Some numerical results for the temperature change, the displacement, the stress and electric potential distributions are presented in figures and table. Furthermore, the influence of the nonhomogeneity of the material and that of the electric boundary conditions are investigated.

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Section: Introductionmentioning

confidence: 99%

The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply

Ootao

Tanigawa

2005

Arch Appl Mech

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“…To the best of the authors' knowledge, these are the only works on wave propagation in FGPM plates. In addition, some recent works consider the free vibration of functionally graded piezoceramic spheres [39] and in rectangular plates [40]. Thus, several issues remain to be investigated, such as the propagation of SV-P waves in FGM and FGPM, the effect of anisotropy and inhomogeneity, the response of FGPM layer for electrical pulse excitation, and so forth.…”

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confidence: 99%

Wave propagation analysis in inhomogeneous piezo-composite layer by the thin-layer method

Chakraborty

Gopalakrishnan

Kausel

2005

Int. J. Numer. Meth. Engng

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SUMMARYThe thin-layer method (TLM) is used to study the propagation of waves in inhomogeneous piezocomposite layered media caused by mechanical loading and electrical excitation. The element is formulated in the time-wavenumber domain, which drastically reduces the cost of computation compared to the finite element (FE) method. Fourier series are used for the spatial representation of the unknown variables. The material properties are allowed to vary in the depthwise direction only. Both linear and exponential variations of elastic and electrical properties are considered. Several numerical examples are presented, which bring out the characteristics of wave propagation in anisotropic and inhomogeneous layered media. The element is useful for modelling ultrasonic transducers (UT) and one such example is given to show the effect of electric actuation in a composite material and the difference in the responses elicited for various ply-angles. Further, an ultrasonic transducer composed of functionally graded piezoelectric materials (FGPM) is modelled and the effect of gradation on mechanical response is demonstrated. The effect of anisotropy and inhomogeneity is shown in the normal modes for both displacement and electric potential. The element is further utilized to estimate the piezoelectric properties from the measured response using non-linear optimization, a strategy that is referred to as the pulse propagation technique (PPT).

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“…The obtained solution is exact in that the electric potential, displacements, and stresses exactly satisfy the governing motion equations of anisotropic piezoelasticity, the traction boundary conditions on the top and bottom planes, the end conditions, and the interlaminar continuity conditions on the interfaces between the layers. Unlike the sub-layer based methods [25][26][27][28], the present study considers FGP layers as the transversely nonhomogeneous piezoelectric material with continuous variation of electro-mechanical properties along the thickness direction. In deriving the present exact formulation, it is also assumed that all material properties are variable along the thickness direction of the laminates.…”

Section: Introductionmentioning

confidence: 99%

“…The rare exact 3D solutions can be found in the literature for the accurate dynamic analysis of FGP laminates. The available limited studies [25][26][27][28] which consider dynamic problems of FGP devices are based on this unjust assumption that the FGP layer consists of a number of homogeneous sub-layers. The preparation of input material data in these methods not only is very time consuming but also their solution accuracy depends strongly on the number of sub-layers.…”

Section: Introductionmentioning

confidence: 99%

“…Liu and Tani [26] used this sub-layer structure scheme to study the wave propagation in FGP plates. Chen and Ding [27] analyzed the free vibration of FGP rectangular plates using the aforementioned method. Based on the 3D theory of piezoelectricity, the method called state-space based DQM was employed by Li and Shi [28] to study the free vibration of an FGP beam under di erent boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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A three-dimensional Peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending

Lezgy-Nazargah

2016

Scientia Iranica

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Abstract. The available three-dimensional (3D) solutions reported for the analysis of Functionally Graded Piezoelectric (FGP) laminates are based on this simplifying assumption that the FGP layer consists of a number of homogeneous sub-layers. The accuracy of these formulations not only is dependent on the number of sub-layers, but also leads to inaccurate results in the prediction of higher natural frequencies of the FGP laminates. In the present paper, a 3D Peano series solution is developed for the cylindrical bending vibration of the FGP laminates. This novel formulation exactly satis es the equations of motion, the charge equation, and the boundary and interface conditions of the continuously nonhomogeneous piezoelectric layers. The obtained solution is exact because no a priori assumption for the displacement components and the electric potential along the thickness direction of FGP layers is introduced. The in uences of the di erent functionally gradient material properties and di erent electric boundary conditions on the natural frequencies and mode shapes of the FGP laminate have also been studied through examples. The present solution and its obtained numerical results can be employed to assess the accuracy of di erent FGP laminated beam/plate theories. It can also be used for FGP vibration behavior comprehension purposes.

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On free vibration of a functionally graded piezoelectric rectangular plate

Cited by 123 publications

References 14 publications

The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply

The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply

Wave propagation analysis in inhomogeneous piezo-composite layer by the thin-layer method

A three-dimensional Peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending

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