By Jiashi Yang
This quantity is meant to supply researchers and graduate scholars with the elemental facets 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 figuring out of difficulties worthy in gadget functions instead of resolution ideas of mathematical difficulties. the maths utilized in this booklet is minimal.
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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Extra resources for An Introduction to the Theory of Piezoelectricity
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. They can be transformed to path-independent integrals by the divergence theorem.
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.
Show that 4. 1-49) has been used. Use the divergence theorem 19 which implies that where and (a scalar) defined by are the reference or material electric displacement and body free change per unit undeformed volume. From Equation which implies that where defined by is the reference electric field. From the total mass of the material body is a constant, which is the mass in the reference state where is the mass density in the reference state. 1-56) have been used. Hence 21 In summary, the balance laws in material form are CONSTITUTIVE RELATIONS 5.
An Introduction to the Theory of Piezoelectricity by Jiashi Yang