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 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 on formula and realizing of difficulties worthy in gadget purposes instead of answer thoughts of mathematical difficulties. the maths utilized in this publication is minimal.

Audience

This quantity is appropriate for a one-semester graduate path on electroelasticity. it may even be used as a reference for graduate scholars and researchers in mechanics and acoustics.

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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.

5. 1 Four-Vector Formulation Let us define the four-space coordinate system [14] 45 and the four-vector where subscripts p, q, r, s will be assumed to run 1 to 4. Also define the second-rank four-tensor and the fourth-rank four-tensor and all other components of where Then and Therefore, yields the homogeneous equation of motion and the charge equation. 2 Vector Potential Formulation Consider the case when there is no body charge. Since the divergence of D vanishes, we can introduce a vector potential by 46 which satisfies the divergence-free condition on D.

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. They can be verified by direct differentiation. 3-11) are in divergence-free form and are called conservation laws.

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