Page 241 - Mechanics of Microelectromechanical Systems
P. 241
228 Chapter 4
where {D} is the dielectric displacement vector and is the electrical
permittivity matrix (the subscript indicates that the matrix is determined
under constant-stress conditions). The vector {D} is defined as:
and the symmetric permittivity matrix is:
When premultiplying Eq. (4.99) by the vector the following
equation is obtained, which contains only specific energy (energy per unit
volume) terms:
where is the mechanical energy and is formulated as:
and is the piezoelectric energy defined as:
The following equation can be obtained from Eq. (4.107) through left-
multiplication by
where the electric energy is:
