By Jiashi Yang
This quantity is meant to supply researchers and graduate scholars with the elemental facets of the continuum modeling of electroelastic interactions in solids. A concise therapy of linear, nonlinear, static and dynamic theories and difficulties is gifted. The emphasis on formula and realizing of difficulties precious in machine purposes instead of resolution innovations of mathematical difficulties. the math utilized in this ebook is minimal.
This quantity is appropriate for a one-semester graduate path on electroelasticity. it may possibly even be used as a reference for graduate scholars and researchers in mechanics and acoustics.
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Extra resources for An Introduction to the Theory of Piezoelectricity
3-7) under translations, rotations, and scale changes, respectively. They can be verified by direct differentiation. 3-11) are in divergence-free form and are called conservation laws. They can be transformed to path-independent integrals by the divergence theorem. 3-1. 3-4). 3-2. 3-3. Study the conservation laws for linear, static piezoelectricity . 4. 2-1) has been used. Therefore, 43 where is the kinetic energy density, and is the quasistatic Poynting vector. 4-2) may be considered as a generalized version of Poynting’s theorem in electromagnetics.
8-5), the constitutive relations of ceramics poled in the direction take the following form: and The equations of motion and charge are Sometimes a piezoelectric device is heterogeneous with ceramics poled in different directions in different parts. In this case it is not possible to orient the axis along different poling directions unless a few local 53 coordinate systems are introduced. Therefore, material matrices of ceramics poled along other axes are useful. 8-5) by rotating rows and columns properly.
5-8), yields Similarly, for the electric field E, we introduce an anti-symmetric tensor by Then the curl-free condition on E takes the following form: In summary, the equations for this formulation are Note that in this formulation the internal energy U is used, which is positive definite. 6. CURVILINEAR COORDINATES Cylindrical and spherical shapes are often used in piezoelectric devices. To analyze these devices, it is usually convenient to use cylindrical or spherical coordinates. 2 Spherical Coordinates The spherical coordinates are defined by In spherical coordinates we have the strain-displacement relation 48 The electric field-potential relation is The equations of motion are The electrostatic charge equation is 7.
An Introduction to the Theory of Piezoelectricity by Jiashi Yang