Dynamics of Structures with Thin Piezoelectric Layers
The subject of this thesis is dynamics of structures with thin piezoelectric layers. Piezoelectric materials are used in sensor and actuators and common applications for these are vibration damping, ultrasonic transducers, buzzards and more.
In one part of the thesis power series expansions are used to obtain approximate plate equations or approximate boundary conditions. This is done by expanding the displacements and the electric potential in power series in the thickness coordinate. These expansions are then plugged into the equations of motion, where all but the lowest order expansion functions can be eliminated. The boundary conditions then give either the approximate plate equations, or the approximate boundary conditions.
Approximate plate equations are obtained for two different cases. In the first case they are developed for an elastic, isotropic, homogeneous plate. The obtained plate equations are then compared with, e.g., Mindlin's plate theory. In the second case the approximate plate equations are obtained for a piezoelectric and an elastic plate bonded together.
Another part of the thesis deals with the calculation of eigenfrequencies for a solid 3D piezoelectric cylinder. The modes for an infinite plate are derived in a cylindrical coordinate system. These are then used to obtain the eigenmodes and eigenfrequencies of a circular cylinder with finite radius.
In the last part the optimal placement of piezoelectric actuators on an elastic plate is discussed. The optimal locations are found by investigating the transfer function for the plate, with the actuators applied. These locations are the points where the piezoelectric actuators will have most impact on the underlying elastic structure.