Download e-book for iPad: An Introduction to the Theory of Piezoelectricity by Jiashi Yang
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 knowing of difficulties worthy in machine purposes instead of answer innovations of mathematical difficulties. the math utilized in this ebook is minimal.
This quantity is acceptable for a one-semester graduate direction on electroelasticity. it might probably 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
2-1. For linear piezoelectricity we use x as the independent spatial coordinates. Let the unit outward normal of S be n. 2-1. A piezoelectric body and partitions of its surface. For boundary conditions we consider the following partitions of S: where is the part of S on which the mechanical displacement is prescribed, and is the part of S where the traction vector is prescribed. represents the part of S which is electroded where the electric potential is no more than a function of time, and is the unelectroded part.
3-6) makes stationary. 3-2) should be considered as constraints among the independent variables. These constraints, along with the boundary data in Equations can be removed by the method of Lagrange multipliers. 3-10) makes stationary. 3-7) has all of the fields as independent variables. Its stationary condition yields all the equations and boundary conditions. Variational principles like this are called mixed or generalized variational principles. 3-7) under translations, rotations, and scale changes, respectively.
The compatibility conditions are necessary conditions for the six strain components derived from three displacement components. They are also sufficient in the sense that for six strain components satisfying these compatibility conditions, there exist three displacement components from which the six strain components are derivable. 2-14) is true over a simplyconnected domain only. For a multiply-connected domain, some additional conditions are needed. The compatibility conditions are useful when solving a problem using stress components rather than displacement components as the primary unknowns.
An Introduction to the Theory of Piezoelectricity by Jiashi Yang