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

By Jiashi Yang

This quantity is meant to supply researchers and graduate scholars with the fundamental features 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 figuring out of difficulties priceless in machine functions instead of answer concepts of mathematical difficulties. the maths utilized in this e-book is minimum. This quantity is acceptable for a one-semester graduate path on electroelasticity. it might probably even be used as a reference for graduate scholars and researchers in mechanics and acoustics.

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1. LINEARIZATION In this section we reduce the nonlinear electroelastic equations in the previous chapter to the linear theory of piezoelectricity for infinitesimal deformation and fields. 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.

1-15). 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.

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. The material time derivative of an infinitesimal field variable f(y,t) is simply the partial derivative with respect to t: 32 For the finite strain tensor In the linear theory, the infinitesimal strain tensor will be denoted by The material electric field becomes Similarly, Since the various stress tensors are either approximately zero (quadratic in the infinitesimal gradients) or about the same, we will use to denote the stress tensor that is linear in the infinitesimal gradients.

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