Download An introduction to the theory of piezoelectricity by Jiashi Yang PDF

By Jiashi Yang

ISBN-10: 1441936394

ISBN-13: 9781441936394

This quantity is meant to supply researchers and graduate scholars with the fundamental elements of the continuum modeling of electroelastic interactions in solids. A concise remedy of linear, nonlinear, static and dynamic theories and difficulties is gifted. The emphasis is on formula and knowing of difficulties worthy in gadget functions instead of resolution options of mathematical difficulties. the maths utilized in this ebook is minimum. 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 info for An introduction to the theory of piezoelectricity

Sample text

For dynamic problems, initial conditions need to be added. 7. 7-1. 7-6). 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.

For ceramics poled in the direction, we have For ceramics poled in the 9. direction, we obtain QUARTZ AND LANGASITE Quartz is probably the most widely used piezoelectric crystal. It belongs to crystal class 32 (or Langasite and some of its isomorphs (langanite and langatate) are emerging piezoelectric crystals which have stronger piezoelectric coupling than quartz and also belong to crystal class 32.

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.

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