Resonant Piezoelectric Shunt Damping of Structures

Excessive resonance vibrations of large civil engineering structures are e
ectively mitigated by the resonant mechanical absorber, while the damping of medium to small sized structures may be mitigated more eÿciently by the electromechanical absorber. The latter is often designed as a pair of electrically shunted piezoceramic patches glued directly to the vibrating structure. Mechanical energy is hereby con-verted into electrical energy which is led in to the shunt consisting of an inductance tuned to secure a maximum energy dissipation in an electric resistance.
The present thesis concerns numerical modeling of piezoelectric absorbers bonded to general plate-like structures and the derivation of a precise shunt tuning proce-dure, which is practical in terms of numerical and experimental implementation. The thesis is organized in three parts, respectively, covering the development of a numerical model, the derivation of optimum shunt tuning and the experimental im-plementation, wherein a beam and a plate example are used throughout the thesis to validate the numerical models and proposed tuning methods.
In the first part, a numerical model describing general plate-like structures with pairs of co-located piezoceramic patches is developed. As the piezoceramic patch bonded to a plate surface mainly influences the plate vibration through the moments generated by the in-plane patch deformations, a plane stress-reduction of the full piezoceramic properties is introduced. Subsequently, the electrode equipotentiality and electric wiring of the piezoceramic patches are modeled and a governing vibra-tion problem is obtained. The same vibration problem is governing in a commercial finite element program and two eigenvalue problems associated with the short and open circuit (SC and OC) piezoelectric absorbers are then considered to determine the e
ective electromechanical coupling of the considered beam and plate examples.
In the second part, a modal representation of the mechanical displacements in the governing vibration problem is introduced, whereby the mechanical equations uncouple. However, because of the piezoelectric shunt the electric domain couples the modal equations. An approximation of the contribution from the non-resonant vibration modes is therefore introduced by an additional term to the inherent piezo-electric capacitance. This additional correction term is determined from the solution to the SC and OC eigenvalue problems, while a third eigenvalue problem may be evaluated to determine a specific non-resonant inertia e
ect. This method is im-plemented in the developed numerical model and in a commercial finite element program, whereby single- and multi-mode tuning of multiple piezoelectric absorbers are demonstrated for the considered beam and plate examples.
In the final part, the proposed shunt tuning procedure is shown suitable for exper-imental implementation, where it requires the acquisition of two absorber response in the SC and OC limits. Good correlation between the numerical and experimental results and shunt tuning is demonstrated for the beam and plate examples and it is shown that the omission of the non-resonant modes contribution leads to detuning of the absorbers and reductions in the attainable damping.