An asymptotic theory for dynamic response of laminated piezoelectric shells

Wu, Chih Ping; Lo, Jyh-Yeuan

doi:10.1007/s00707-005-0306-3

Cited by 21 publications

(8 citation statements)

References 23 publications

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“…The review articles by Gopinathan et al [1] and Wang and Yang [2] give many references to work prior to 2000. In recent years many investigations concern the derivation of plate and shell equations, but only a few references are given here [3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Modelling of thin piezoelectric layers on plates

2008

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The derivation of plate equations for a plate consisting of two layers, one anisotropic elastic and one piezoelectric, is considered. Power series expansions in the thickness coordinate for the displacement components and the electric potential lead to recursion relations among the expansion functions. Using these in the boundary and interface conditions, a set of equations is obtained for some of the lowest-order expansion functions. This set is reduced to six equations corresponding to the symmetric (in-plane) and antisymmetric (bending) motions of the elastic layer. These equations are given to linear (for the symmetric equations) or quadratic (for the antisymmetric equations) order in the thickness. It is noted that it is, in principle, possible to go to any order, and that it is believed that the corresponding equations are asymptotically correct. A few numerical results for guided waves along the plate and a 1D actuator case illustrate the accuracy.

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Section: Introductionmentioning

confidence: 99%

Modelling of thin piezoelectric layers on plates

2008

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“…Bisegna and Caruso (2001) present a classification and critical comparison among higher-order piezoelectric plate models based on power series expansions prior to 2001. Also many investigations in recent years concern the modelling of layered piezoelectric structures based on power series expansions of some small parameter; a few references are given here (Lim and Lau, 2005;Pouget, 2002, 2006;Kapuria, 2004;Kapuria and Achary, 2005;Lim et al, 2006;Wu and Lo, 2006). The finite element method is developed for such problems in, e.g., Kögl and Bucalem (2005), Vasques and Rodrigues (2005), Robbins and Chopra (2006).…”

Section: Introductionmentioning

confidence: 99%

Modelling of finite piezoelectric patches: Comparing an approximate power series expansion theory with exact theory

Mauritsson

2009

International Journal of Solids and Structures

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a b s t r a c tPlate equations for a plate consisting of one elastic layer and one piezoelectric layer with an applied electric voltage have previously been derived by use of power series expansions of the field variables in the thickness coordinate. These plate equations are here evaluated by the consideration of a time harmonic 2D vibration problem with finite layers. The boundary conditions at the sides of the layers then have to be considered. Numerical comparisons of the displacement field are made with solutions from two other theories; a solution with equivalent boundary conditions for a thin piezoelectric layer applied on an elastic plate and an exact solution based on Fourier series expansions. The two approximate theories are shown to be equally good and they both yield accurate results for low frequencies and thin plates.

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“…This is because 3D results provide a standard for assessing 2D theoretical methodologies and numerical models, and a reference for making the kinetic and kinematic assumptions a priori when an advanced 2D theory is to be developed. Some comprehensive literature surveys with regard to the 2D and 3D elasticity and piezoelectricity analyses of multilayered hybrid FRC and piezoelectric beams, plates and shells were carried out by Noor and Burton, 1,2 Noor et al, 3 Carrera, 4-6 Carrera and Ciu®reda, 7 Carrera and Brischetto, 8 Saravanos and Heyliger 9 and Wu et al 10 Wu et al 10 classi¯ed the exact 3D analytical approaches for the coupled analysis of multilayered hybrid FRC and piezoelectric plates/shells into four di®erent ones, namely the Pagano, 11-14 state space, [15][16][17][18] series expansion, [19][20][21] and perturbation [22][23][24][25][26][27] methods. Among these, it is apparent that the Pagano method, based on the principle of virtual displacement (PVD), is both simple and the most widely applied for these structures.…”

Section: Introductionmentioning

confidence: 99%

Quasi-3D Stability and Vibration Analyses of Sandwich Piezoelectric Plates with an Embedded CNT-Reinforced Composite Core

2016

Int. J. Str. Stab. Dyn.

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Quasi-three-dimensional (3D) stability and free vibration analyses of bi-axially loaded, simplysupported, sandwich piezoelectric plates with an embedded either a functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) core or a multilayered¯ber-reinforced composite (FRC) one are presented. Three di®erent distributions of carbon nanotubes (CNTs) through the thickness of the CNTRC core, i.e. uniformly distributed and FG V-, rhombus-and X-type variations, are considered, and the e®ective material properties of the CNTRC core are estimated using the rule of mixtures. The Pagano method, which is conventionally used for the analysis of multilayered FRC plates, is modi¯ed to be feasible for the study of sandwich hybrid CNTRC and piezoelectric ones, in which Reissner mixed variational theorem, the successive approximation and transfer matrix methods, and the transformed real-valued solutions of the system equations are used. The modi¯ed Pagano solutions for the stability and free vibration of multilayered hybrid FRC and piezoelectric plates are in excellent agreement with the exact 3D ones available in the literature, and those for sandwich hybrid CNTRC and piezoelectric plates may be used as the benchmark solutions to assess the ones obtained by using various 2D theories and numerical models.

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An asymptotic theory for dynamic response of laminated piezoelectric shells

Cited by 21 publications

References 23 publications

Modelling of thin piezoelectric layers on plates

Modelling of thin piezoelectric layers on plates

Modelling of finite piezoelectric patches: Comparing an approximate power series expansion theory with exact theory

Quasi-3D Stability and Vibration Analyses of Sandwich Piezoelectric Plates with an Embedded CNT-Reinforced Composite Core

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