# An Introduction to the Theory of Piezoelectricity: 9 by Jiashi Yang

By Jiashi Yang

This quantity is meant to supply researchers and graduate scholars with the fundamental 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 is on formula and figuring out of difficulties valuable in equipment functions instead of resolution suggestions of mathematical difficulties. the math utilized in this booklet is minimum. This quantity is appropriate for a one-semester graduate path on electroelasticity. it might even be used as a reference for graduate scholars and researchers in mechanics and acoustics.

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**Additional resources for An Introduction to the Theory of Piezoelectricity: 9 (Advances in Mechanics and Mathematics)**

**Example text**

Integrity bases for constructing a scalar function of a symmetric tensor and a vector for all crystal classes are known [7]. 6. INITIAL-BOUNDARY-VALUE PROBLEM Since the curl-free equation is automatically satisfied. The angular momentum equation is satisfied because is symmetric. The present mass density appears in the equation of conservation of mass only, and therefore can be calculated from the equation after the deformation and the electric field have been found. The energy equation is satisfied by the forms of the constitutive relations.

3-1. 3-4). 3-2. 3-3. Study the conservation laws for linear, static piezoelectricity [13]. 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. 2-9) have been used. 4-5) is called the energy integral which states that the energy at time t is the energy at time plus the work done to the body from to t. 4-6). 4-5) to it. The initial energy and the external work for the difference are zero.

A mechanical traction acts on the interface. 6-1. A material interface. We want to derive interface jump or continuity conditions. Construct a pillbox on the interface as shown. 6-8) can be written in the material form as where For mechanical boundary conditions S is partitioned into and on which motion (or displacement) and traction are prescribed, respectively. -6) and the following boundary conditions: where and are the prescribed boundary motion and potential, is the surface traction per unit undeformed area, and is the surface free charge per unit undeformed area.