An Introduction to the Theory of Piezoelectricity (Advances by Jiashi Yang
By Jiashi Yang
This booklet is predicated on lecture notes for a graduate direction that has been provided at college of Nebraska-Lincoln off and on due to the fact 1998. The direction is meant to supply 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 is on formula and realizing of difficulties valuable in machine functions instead of resolution concepts of mathematical difficulties. the math utilized in the e-book is minimum. The booklet is appropriate for a one-semester graduate path on electroelasticity. it might probably even be used as a reference for researchers. i need to take this chance to thank UNL for a Maude Hammond Fling school examine Fellowship in 2003 for the practise of the 1st draft of this booklet. I additionally desire to thank Ms. Deborah Derrick of the varsity of Engineering and expertise at UNL for enhancing counsel with the ebook, and Professor David Y. Gao of Virginia Polytechnic Institute and kingdom college for recommending this booklet to Kluwer for book within the sequence of Advances in Mechanics and arithmetic. JSY Lincoln, Nebraska 2004 Preface Electroelastic fabrics convey electromechanical coupling. They adventure mechanical deformations while positioned in an electrical box, and develop into electrically polarized less than mechanical rather a lot. Strictly talking, piezoelectricity refers to linear electromechanical couplings merely.
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Extra info for An Introduction to the Theory of Piezoelectricity (Advances in Mechanics and Mathematics)
1-1. 1-15). 2. 1 Displacement-Potential Formulation In summary, the linear theory of piezoelectricity consists of the equations of motion and charge constitutive relations and the strain-displacement and electric field-potential relations where u is the mechanical displacement vector, T is the stress tensor, S is the strain tensor, E is the electric field, D is the electric displacement, is the electric potential, is the known reference mass density (or in the previous chapter), is the body free charge density, and f is the body force per unit mass.
8. TOTAL STRESS FORMULATION A more compact formulation will result if we introduce the following total energy density: Then the constitutive relations take the following form: where we have introduced a total stress tensor in material form. 7-1) becomes The following expressions will be useful in Chapter 6. 29 Chapter 2 LINEAR PIEZOELECTRICITY FOR INFINITESIMAL FIELDS In this chapter we specialize the nonlinear equations in Chapter 1 to the case of infinitesimal deformations and fields, which results in the linear theory of piezoelectricity.
We consider small amplitude motions of an electroelastic body around its reference state due to small mechanical and electrical loads. , electric potential gradient It is also assumed that the is infinitesimal. 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.