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 on formula and realizing of difficulties priceless in equipment functions instead of resolution ideas of mathematical difficulties. the math utilized in this publication is minimal.
This quantity is appropriate for a one-semester graduate path on electroelasticity. it will probably even be used as a reference for graduate scholars and researchers in mechanics and acoustics.
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Additional info for An Introduction to the Theory of Piezoelectricity
In this case, circuit equation(s) will need to be considered. 2-4) allows the superposition of solutions. Suppose the solutions under two different sets of loads of and are combined load of and respectively. 2-4) is This is called the principle of superposition and can be shown as and 38 The principle of superposition can be generalized to include boundary loads. 4 Compatibility Since the six strain components are derived from three displacement components, it is natural to expect some relations among the strain components whether they are linear or nonlinear.
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. For dynamic problems, initial conditions need to be added.
We neglect powers of and higher than the first as well as their products in all expressions. The linear terms themselves are also dropped in comparison with any finite quantity such the Kronecker delta or 1. 1-1), which implies that, to the first order of approximation, the displacement and potential gradients calculated from the material and spatial coordinates are numerically equal. Therefore, within the linear theory, there is no need to distinguish capital and lowercase indices. Only lowercase indices will be used in the linear theory.
An Introduction to the Theory of Piezoelectricity by Jiashi Yang