Exact electroelastic analysis of piezoelectric laminae via state space approach

Lee, Jong; Long, Jiang

doi:10.1016/0020-7683(95)00083-6

Cited by 172 publications

(64 citation statements)

References 13 publications

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“…The transfer matrix method is especially suitable for multilayered media, as it ensures the continuity conditions on the interface without the need of layer-by-layer consideration. Its successful application in piezoelectric laminates can be seen in [14]. However, the basic matrix equation there is required to be reduced to a set of ordinary differential equations with the thickness coordinate as the only spatial variable.…”

Section: Discussionmentioning

confidence: 99%

Three-dimensional analysis of an antiparallel piezoelectric bimorph

Lim

Soh

2000

Acta Mechanica

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Summary. Three-dimensional electromechanical responses of a piezoelectric bimorph are studied. The bimorph is antiparallel in the sense that it consists of two identical, plate-like piezoelectric elements with opposite poling directions. Both the top and bottom surfaces of the bimorph are fully covered with negligibly thin conductive electrodes. By introducing a small parameter and using the transfer matrix method it is shown that a three-dimensional solution of the problem can be readily constructed, provided the solution to a set of two-dimensional equations very similar to those in the classic plate theory is obtainable. The three-dimensional solution satisfies all the field equations as well as the boundary conditions on the major surfaces and at the interface between the two piezoelectric plates. In many special cases, the electric edge condition can be fulfilled point by point, and thus the solution is exact in SaintVenant's sense. The formulation and new analytical results for a strip-shaped cantilever bimorph under the action of applied voltage and end moment are presented.

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Section: Discussionmentioning

confidence: 99%

Three-dimensional analysis of an antiparallel piezoelectric bimorph

Lim

Soh

2000

Acta Mechanica

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“…(13). The next two sections will show how to apply these two state equations in analyzing functionally graded piezoceramic hollow spheres.…”

Section: Two State Equationsmentioning

confidence: 98%

“…Recently, piezoelectric materials have become an important subject of research in solid mechanics. 3D state space formulations have been derived to analyze piezoelectric laminates in Cartesian and cylindrical coordinates, [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings

Chen¹,

Ye³

et al. 2002

Archive of Applied Mechanics (Ingenieur Archiv)

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The problem of a piezoceramic hollow sphere is investigated analytically based on the 3D equations of piezoelasticity. The functionally graded property of the material along the radial direction can be taken arbitrarily in the paper. Displacement and stress functions are introduced, and two independent state equations with variable coefficients are derived. By employing the laminate model, the two state equations are transformed into ones with constant variables from which the state variable solution is easily obtained. Two linear relationships between the state variables at the inner and outer spherical surfaces are established. Numerical calculations are performed for different boundary conditions imposed on the spherical surfaces.

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“…In the literature, many papers have been devoted to the static analysis of rectangular piezoelectric plates, [3,6,7,9,15,[19][20][21][22]26]. Except for the work of Vel and Batra [26] who employ Eshelby-Stroh formalism and consider various types of boundary condition, all the above mentioned contributions address simply supported type boundary conditions only.…”

Section: Introductionmentioning

confidence: 98%

Elastic/piezoelectric solids with electro-mechanical singular surfaces

Shodja

Kamali

2006

Comput Mech

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When a tensor-valued function σ (x) is continuous in regions 0 and 1 , but has a finite jump across the interface 01 between 0 and 1 , then 01 is referred to as singular surface relative to the field σ (x). In this paper, it is intended to give a general treatment of three-dimensional static and free vibration analysis of bodies composed of multi-phase elastic and/or piezoelectric bodies with electro-mechanical singular surfaces. The geometry of the medium, boundary conditions, and the geometry of the singular surfaces may be arbitrary. The displacement field and the electric potential in each region are expressed in terms of functions composed of 3-D series and special 3-D functions. The composite functions are selected in such a way that they satisfy exactly: (1) the continuity of the displacement and the electric potential across the singular surfaces; and (2) the homogeneous and inhomogeneous kinematical boundary conditions. This methodology leads to remarkable accuracies in computation of the field quantities, including the quantities, which are discontinuous across the singular surfaces. Taking advantage of any symmetry that may be present in the problem, will substantially increase the convergence rate. For illustrations several examples are examined. Comparisons

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Exact electroelastic analysis of piezoelectric laminae via state space approach

Cited by 172 publications

References 13 publications

Three-dimensional analysis of an antiparallel piezoelectric bimorph

Three-dimensional analysis of an antiparallel piezoelectric bimorph

3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings

Elastic/piezoelectric solids with electro-mechanical singular surfaces

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