NONLINEAR BEHAVIOR OF CANTILEVER-BASED PIEZOELECTRIC ENERGY SCAVENGERS UNDER LARGE EXCITATIONS I. Paprotny 1* , E. Halvorsen 3 , Q. Xu 1,2 , W.W. Chan 1 , R.M. White 1 and P.K. Wright 2 1 Berkeley Sensor & Actuator Center (BSAC), University of California, Berkeley, USA 2 Department of Mechanical Engineering, University of California, Berkeley, USA 3 Department of Micro and Nano Systems Technology, Vestfold University College, Norway *Presenting Author: igorpapa@eecs.berkeley.edu Abstract: A common way to model piezoelectric cantilever based energy scavengers is to model the system as a simple single degree-of-freedom (1DOF) damped harmonic resonator, reducing the coupled multiple degree-of- freedom system to one-dimensional motion of an equivalent mass. In this work, we investigated nonlinear behavior of cantilever-based piezoelectric energy scavengers in cases when the proof mass center is located off axis and some distance from the cantilever tip. This was done by developing a three degree-of-freedom (3DOF) circuit- based model of the scavenger. As hypothesized, the model exhibited a softening type nonlinear behavior, resulting in a 1-3 % frequency shift. Our results are comparable, albeit smaller in magnitude, than the experimental data obtained from our Piezoelectromagnetic (PEM) AC energy scavenger. These results indicate that the geometric nonlinearities account for some of the nonlinear behavior observed in the PEM AC energy scavenger. Keywords: Energy Scavenging, Piezoelectromagnetic, Nonlinear, Piezoelectric, Smart Grid INTRODUCTION The most common geometry for piezoelectric energy scavengers is a rectangular cantilever covered with piezoelectric material, with a proof-mass attached to its tip [1]. During alternating excitations of the proof mass, the strain in the piezoelectric layer converts the mechanical energy stored in the resonating spring- mass system to electric power. The common way to model piezoelectric cantilever based energy scavengers is to model the system as a simple single degree-of-freedom (1DOF) damped harmonic resonator, reducing the coupled multiple degree-of- freedom system to one-dimensional motion of an equivalent mass. However, in cases where the excitations of the proof-mass are large, and/or where the mass-center is offset from the neutral bending axis of the cantilever, a significant portion of the mechanical energy is used for rotating the mass, which may exuberate the effect of higher order interactions between the individual degrees of freedom. Such effects are often truncated in a 1DOF model. This work was motivated by experimental results obtained from our Piezoelectromagnetic (PEM) AC energy scavengers [2], where we observed a 4-6 % change in the resonant frequency with increasing excitations. PEM AC scavengers use piezoelectric conversion from a mechanically resonating system excited by a magnet interacting with the current in a nearby conductor as the means for providing power for wireless Smart Grid sensing applications. We postulated that in our PEM AC scavenger, purely mechanical nonlinear effects cause the change in the resonant frequency of the scavenger as a function of the varying load. Such a shift is especially problematic for narrow-band scavengers, such as the PEM AC scavengers [2], and a model that fully describes this phenomenon is highly desirable in order to remedy this effect. Apart from intrinsic mechanical effects, nonlinear behavior of the energy scavengers can be among other caused by nonlinearity in the piezoelectric coupling [3], the design of nonlinear springs, or switchable power conditioning circuits. Purposefully nonlinear energy scavengers have been shown to generate higher power output under large bandwidth excitations. In narrow-band applications, such as AC energy scavenging, an accurate model of the nonlinear behavior may ultimately enable us to use the PEM AC energy scavenger as a current sensor, enabling compact and truly self-powered current sensing applications for the Smart Grid. PEM AC ENERGY SCAVENGING Piezoelectromagnetic (PEM) AC energy scavengers use a strong permanent magnet to couple a resonating mechanical mass-spring system (e.g., cantilever) to a current-carrying conductor, and then use piezoelectric transduction to convert the mechanical energy from the resonating circuit to electric power [2]. Fig. 1 shows a mesoscale PEM AC scavenger, consisting of a piezoelectric bi-morph cantilever (a) with magnets attached at its tip (b), placed in the vicinity of a single current-carrying conductor (c). Physical stoppers in the form of nonlinear springs (d) prevent excessive excitation in the case of overcurrent conditions. The magnetic circuit of this scavenger has been optimized to maximize the coupling to a single current-carrying conductor. to appear in PowerMEMS 2011