“…The above sections address the elastic vibration and obtain the driving rules through a model-based analysis. Alternatively, these can also be handled by the model-free method (Chen et al., 2011; Wang et al., 2014a, 2014b; Wang et al., 2011a, 2014b). Assuming that Wup l and Wvp l represent the tangential and radial deflections induced by the l th harmonic excitation of the p th piezoelectric patch.…”