Elastic Dielectrics

Abstract

Chapter 7 is concerned with the continuum theory of elastic dielectrics. In Section 7.2 we list basic equations. The uniqueness theorem for the linear theory is presented in Section 7.3. Piezoelectric material moduli and their symmetry regulations for all thirty-two crystal classes are discussed in Section 7.4. In Section 7.5 we start to give solutions for various problems such as the thickness vibrations of piezoelectric plates (Section 7.5), the extensional vibrations of piezoelectric rods (Section 7.6), surface waves (Section 7.7), the radially symmetric vibrations of thin ceramic rings (Section 7.8), the spherically symmetric vibrations of ceramic shells (Section 7.9), and the piezoeleetrically generated electric field (Section 7.10). These problems are useful for both experimental research and technological applicaton.¹ In contrast to these solutions in the linear theory, nonlinear solutions are rare and deserve special attention, especially since the recent development of piezoelectric polymers (Sessler [1981]). These problems are concerned with the behavior of incompressible dielectric solids under “controllable surface” loads. Thus, for example, homogeneous deformations of a slab under a uniform electric field, such as simple shear, are discussed in Section 7.11. Cylindrically symmetric deformations of a thick tube under a radial field are covered in Section 7.12.