Modal Based Correction Methods for the Placement of Piezoceramic Modules

Conventional Finite-Element programs are able to compute the vibration response of mechanical structures. Increasingly also so-called multi-field problems can be solved. For piezoelectric actuators and sensors, electrical degrees of freedom apart from the mechanical ones have to be considered too. The pure actuator effect can also be modelled using the coefficients of thermal expansion. But regarding the optimal placement of flat piezoceramic modules, which couple in the mechanical part through the d31-effect, it proves to be advantageous to consider them after doing the computational complex modal analysis. In this paper, this modal coupling approach is described in detail. It introduces an additional modelling error, because the effect of the stiffness and mass of the modules is not considered in the construction process of the functional space, from which modal shapes are derived. But due to the comparatively small contribution to the global mass and stiffness of such flat devices, this additional error can generally be accepted. Furthermore this error can be reduced to an arbitrarily small amount, if the number of retained eigenmodes is increased and the gain in computational speed is significant. For the calculations, self-written triangle elements with full electro-mechanical coupling have been used, being coded completely in MATLAB. Finally the optimization procedure for the placement of the piezoceramic modules including their mass and stiffness is demonstrated for a test structure.