Improved Analytical Modelling of Smart Piezoelectric Beams and its Experimental Verification

Analytical models can contribute a lot to a better understanding of the structural behaviour of smart structures. In the paper an enhanced analytical model of a cantilever beam is presented. The beam is attached with piezoelectric patches that are used as sensors and actuators in a collocated and a non-collocated manner. In the analysis of the bending vibrations, an Euler-Bernoulli model is combined with a model of the longitudinal vibrations. The mechanical coupling between actuators and collocated sensors is modelled analytically and included in the transfer function as feedthrough. Additionally the model incorporates the effective electromechanical coupling and considers the modelling error due to model truncation. The analytical frequency response functions (FRFs) are verified and compared with experimental data in the frequency range up to 5 kHz including the first 10 bending modes and the first longitudinal mode. The observed differences between the simulated and the measured eigenfrequencies are less than 0.5% except for the first bending and longitudinal mode. The average amplitude modelling error is about 1dB for collocated and about 2dB for non-collocated patch combinations in the frequency range up to 3 kHz