A Theoretical Analysis of an ‘Electromechanical’ Beam Tuned Mass Damper

An equivalent lumped-parameter model of a beam-like piezoelectric TMD (tune mass damper) under short-circuited conditions is analyzed. This enabled the calculation of the optimal viscous damping required by a TMD according to the classical theory for a given application. This hypothetical optimally damped, electrically uncoupled system, is then used as a benchmark to calculate the optimal R-L-C parameters in the actual (electrically coupled) TMD using optimisation tools in MATLAB. Four different R-L-C circuit configurations are investigated. The frequency response functions (receptances) of the host structure with the attached electromechanical TMD are compared with those from the benchmark system which is designed using classical mechanical vibration theory. The analysis is performed by the analytical modal analysis method (AMAM) and verified by the dynamic stiffness method. The results show that, for all four circuit configurations, correct tuning of the R-L-C parameters is capable of producing a response that very closely replicates the benchmark response. Of the four circuit configurations considered, the most convenient and economical is the one where the bimorphs were connected in parallel with each other across a capacitor that was in turn connected in parallel with a resistor-inductor series combination. MATLAB optimisation program developed for the simulations is presented as Annex-A of the book.