This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Sensors and Actuators A 211 (214) Contents lists available at ScienceDirect Sensors and Actuators A: Physical j ourna l h o mepage: A bistable buckled beam based approach for vibrational energy harvesting B. Andò a,, S. Baglio a, A.R. Bulsara b, V. Marletta a a D.I.E.E.I., University of Catania, Catania, Italy b Space and Naval Warfare Systems Center Pacific, Code 71, San Diego, CA , USA a r t i c l e i n f o Article history: Received 2 August 213 Received in revised form 15 November 213 Accepted 17 December 213 Available online 6 March 214 Keywords: Nonlinear energy harvesting Bistable systems Snap through buckling Wideband vibrations Piezoelectric materials a b s t r a c t This paper presents a low cost solution for vibrational energy harvesting based on a bistable clampedclamped polyethylene terephthalate (PET) beam and two piezoelectric transducers. Beam switching (between two stable steady states) is activated by environmental vibrations. The mechanical-to-electrical energy conversion is performed by two piezoelectric transducers laterally installed to experience beam impacts each time the device switches from one stable state to the other one. The main advantage of our approach lies in the wide frequency bandwidth of the device; in turn, this leads to improved efficiency at very low cost. 214 Elsevier B.V. All rights reserved. 1. Introduction Many efforts have, recently, been devoted to the development of autonomous solutions aimed at powering electronic devices by exploiting the energy scavenged from their operating environment. This interest stems from the fact that electronic devices, typically, utilize batteries whose limited lifespan (which necessitates their periodic replacement) can be a problem, especially when the devices are embedded into complex structures including (even) the human body. Moreover, energy saving policies increasingly drive the development of new strategies to harvest energy from unconventional sources. Different solutions for power harvesting from assorted energy sources have been addressed by researchers worldwide. Examples are solar energy conversion [1], thermoelectric power generation [2], the (less well known) radio-frequency (RF) power conversion [3], and power stemming from environmental mechanical vibrations [4]. Among these, environmental mechanical vibrations represent one of the most ubiquitously available sources that can, potentially, deliver a useful amount of energy [5]. Ambient Selected Paper based on the paper presented at The 17th International Conference on Solid-State Sensors, Actuators and Microsystems, June 16 2, 213, Barcelona, Spain. Corresponding author. Tel.: addresses: bruno.ando@dieei.unict.it (B. Andò), salvatore.baglio@dieei.unict.it (S. Baglio), bulsara@spawar.navy.mil (A.R. Bulsara), vincenzo.marletta@dieei.unict.it (V. Marletta). mechanical vibrations come in a large variety of forms such as induced oscillations, seismic noise, vehicle motion, acoustic noise, multitone vibrating systems, and, more generally, noisy environments. Sometimes, the energy to be collected may be confined in a very specific region of the frequency spectrum, as in the case of rotating machines [6]; in practice, though, energy is often distributed over a wide spectrum of frequencies. Traditional solutions for energy harvesters are typically based on linear resonant mechanical structures, e.g. cantilever beams with inertial masses, and often exploit a piezoelectric, electromagnetic or electrostatic conversion mechanism [7,8]. Such devices are really efficient when stimulated very close to their resonance frequency. Different solutions, for increasing the operating frequency range of vibration energy harvesters, have been proposed in the literature; these solutions present different disadvantages, e.g. complexity, a decrease in the power generated, the need for extra systems and energy, low efficiency, difficulty in implementation, etc. [9]. In practice, though, the need for harvesters able to scavenge energy more efficiently from wideband vibrational sources drives the development of different harvesting solutions exploiting nonlinear mechanisms [1]. Recently, it has been demonstrated that nonlinear bistable systems, under the proper conditions, can provide better performance, compared to linear resonant oscillators, in terms of the amount of energy extracted from wide spectrum vibrations [11 13]. Nonlinear bistable systems are usually realized by a suitable design of the device topology, e.g. the clamped-clamped cantilever beam with pre-compression along the Y-axis, as shown /$ see front matter 214 Elsevier B.V. All rights reserved.

3 154 B. Andò et al. / Sensors and Actuators A 211 (214) Fig. 1. Working principle of the Double Piezo NonLinear Harvester (DP-NLH). in Fig. 1. The clamped clamped beam exhibits a bistable behavior in response to stress applied perpendicular to its surface. When an external mechanical force, stemming from external vibrations is applied to the bistable beam, it snaps between its stable equilibrium states analogous to a credit card fixed and squeezed by fingers at both its ends. Recently, methodologies to implement nonlinear vibrational energy harvesters, based on the use of low cost technologies and bistable devices have been proposed [1 13]. In particular, in [1] an approach based on a piezoelectric beam converter, coupled to permanent magnets which create a bistable system switching between two stable states, has been proposed. A solution in the micro-scale, exploiting a novel approach involving purely mechanical fully compliant bistable MEMS devices for vibration energy harvesting, has been proposed in [11]. In [12], the use of rapid prototyping techniques for the realization of a nonlinear energy harvester exploiting the benefits of bistable dynamics and assuring a suitable behavior at low frequencies has been addressed. The mechanical-to-electrical energy conversion was performed by a screen printed piezoelectric layer electrically connected using InterDigiTed electrodes (IDT) realized by the inkjet printing of a silver based solution on a flexible polyethylene terephthalate (PET) substrate. A low cost solution for energy harvesting from vibrations based on a bistable clamped-clamped PET beam and two piezoelectric transducers exploiting the benefits of a STB (Snap through Buckling) configuration was presented in [13]. In the Double Piezo- NonLinear Harvester (DP-NLH), the beam switching was activated by environmental vibrations while the mechanical-to-electrical energy conversion was performed by two piezoelectric transducers. The latter convert mechanical energy, collected each time the device switches from one stable state to the other, into electrical energy. In all the above solutions it has been demonstrated that, under proper conditions, a nonlinear bistable configuration significantly improves energy harvesting from wide-spectrum vibrations. A review of research on vibration energy harvesting via bistable systems has been, recently, published [14]. Relative to the work described in [12], in this paper a deep investigation into the device behavior is carried out. In particular, after a more detailed description of the buckled beam based nonlinear harvester, the investigation of the mechanical behavior of the device is presented, together with the analytical representation of the potential energy function underpinning the switching mechanism and experimental validation of the proposed model. For the electrical characterization of the DP-NLH performance, results obtained by a complete experimental survey are shown, including an evaluation of the power produced. It has been demonstrated that the amount of power generated by the DP-NLH harvester is suitable for real applications, e.g. powering wireless sensor nodes. Finally, a case of study where the DP-NLH was connected to a standard electronic circuit for energy harvesting is presented. The advantages of the DP-NLH stem, mainly, from the intrinsic nonlinear nature of the conversion methodology. In practice, the bistable dynamics implemented by the buckled beam allow for rapid switching (between the two stable states of the bistable configuration) and large displacements, both of which are crucial to enhancing the efficiency of the power conversion process. Moreover, compared to traditional (linear) vibrational harvesters, the bistable dynamics yields an enhanced device behavior in terms of an extension of the frequency band where the device is able to scavenge energy from mechanical vibrations [1]. We reiterate that linear harvesters offer the most efficient energy harvesting alternative when they are tuned to (i.e. resonant with) a particular (in this case, vibrational) frequency in their operating environment. The low cost of the device, which is intrinsic in the proposed conversion mechanism, is a further advantage. In the following, a detailed description of the device is presented, together with a characterization of its mechanical behavior and its (experimental) performance as an energy harvester. The paper is organized as follows. Section 2 is dedicated to the mechanical characterization of the buckled beam while Section 3 is devoted to the DP-NLH device and its electrical characterization. A case of study in which the DP-NLH device is connected to a standard electronic circuit for energy harvesting is discussed in Section 4. Concluding remarks are given in Section The buckled beam structure and its mechanical characterization A schematization of the DP-NLH harvester is shown in Fig. 1. It consists of a pre-compressed flexible PET beam in a clampedclamped configuration, with only two allowed (i.e. stable) steady states. The PET beam dimensions are 1 cm 1 cm while its thickness is 1 m. Under externally induced vibration, the device can switch between its stable states; the switching mechanism is underpinned by a nonlinear (bistable) potential energy function. Two low cost piezoelectric diaphragms are used to convert the beam impacts (in each steady state) into electric charges. The DP-NLH energy harvester, presented here, is able to convert low frequency mechanical vibrations into electrical energy; in particular, this device has been demonstrated to be able to provide enough energy to supply low power electronic devices. As demonstrated in [15], in order to observe the bistability, the following condition between the beam thickness and the separation (arising from the beam pre-compression along the Y-axis) between the stable states must be fulfilled: Q = X/2 > 2.31 t

4 B. Andò et al. / Sensors and Actuators A 211 (214) RMS Acceleration [m/s 2 ] frequency [Hz] Fig. 3. Dynamic mechanical characterization of the DP-NLH device in case of a beam pre-compression of 3 mm and a proof mass of 1 g [TRANSDUCERS 213]. Fig. 2. Side view of a bistable PET beam in its two stable states. The upper and lower equilibrium positions are separated by a distance X which increases as the pre-compression Y increases. In order to achieve switching events between these stable states, a force F having amplitude larger than a threshold (imposed by the energy barrier inherent in the bistability) must be applied in the out-of-plane direction of the beam. In the framework of energy harvesting, the force F is generated by external vibrations. For application purposes, structures able to snap between their stable states under the effect of low intensity and low frequency vibrations, are particularly important The dynamic mechanical characterization of the STB device Several measurements have been performed in order to investigate the mechanical behavior of the bistable beam. The experiments have been performed on a STB beam, 1 cm long 1 cm wide. A real view of the bistable PET beam with an added proof mass together with the setup adopted to apply the pre-compression, in its two stable states, is shown in Fig. 2. Preliminary investigations have aimed to measure the deflection along the X-axis (distance between the two stable states) as a function of a fixed pre-compression along the Y-axis [13]. To measure the stable state positions of the PET beam a laser system (Baumer OADM 12U643/S35A) was used. Experimental results are shown in Table 1. It is clear that the beam pre-compression affects the impact force against the piezoelectric devices and, hence, the energy harvested [12,13]. For the current architecture, an important role is played by the proof mass added to the beam. For the laboratory prototype, a proof mass of 1 g and a precompression of 3 mm have been fixed. In practice, the proof mass Table 1 Distance between the two stable states X of a PET beam 1 cm 1 cm, for precompressions of 1, 3 and 5 mm. Pre-compression Y [mm] Distance X [mm] affects the impact force, the acceleration required for the beam switching, and the device bandwidth. Although the device is aimed towards the proof of concept of the bistable methodology proposed for energy harvesting from environmental vibrations, as discussed in Section 3.1, the above choices yield a sufficient amount of energy to power compatible some small electronics applications, e.g. powering wireless sensor nodes [4]. Moreover, experimental results confirm that the acceleration values are compatible with standard sources (e.g. kitchen blender casing, external windows next to a busy street, vehicles, etc.) of vibrations, which have been previously characterized [4]. Given our (earlier) comments about the bandwidth of the device, the frequency behavior of the device merits a deep analysis. In order to assess the dynamic behavior of the device, and to confirm the advantages emanating from the bistable mechanism (i.e. boosting the harvester performance in a wide frequency band), several repeated cycles of mechanical stimulation have been applied by a dedicated experimental setup underpinned by a standard shaker. The analog accelerometer Freescale Semiconductor MMA726Q has been used to perform an independent measurement of the input stimulus. The experiment was aimed at estimating the minimum acceleration (related to the amplitude and frequency of the signal driving the shaker) able to make the beam switch between its stable states. The shaker was driven by periodic sinusoidal signals with increasing frequency in the range 4 15 Hz. Signals from a reference accelerometer were acquired on a Lecroy 65A WaveRunner digital oscilloscope with a sampling frequency f s = 2 khz. The investigations have been performed for different values of the precompression and the proof mass. As an example, the results obtained in the case of a beam precompression of 3 mm and a proof mass of 1 g are given in Fig. 3 which shows the minimum Root-Mean-Square (RMS) accelerations (supra-threshold) allowing switching events for different frequencies of the sinusoidal stimulus applied to the shaker. In practice, the envisaged broadband operation of the proposed bistable architecture emerges via the possibility of inducing switching events by slightly supra-threshold acceleration values for the entire frequency range of interest. Moreover, the working frequency range and the values of acceleration obtained are compatible with standard mechanical sources in real applications (e.g. car engine compartments, vehicles, and handheld tools) [4]. The observed response of the bistable beam in the working frequency range of interest confirms the suitability of the STB approach in boosting the device performance especially when the

5 156 B. Andò et al. / Sensors and Actuators A 211 (214) frequency of the mechanical source is unknown or unpredictable, as long as it is in a well-defined range. The switching dynamics occur very fast, with each switching event ending in one of the two stable states; these define the maximum allowed transition amplitude. As already mentioned, features such as speed and large buckling boost the device performance in terms of mechanical-to-electrical energy conversion Modeling the beam mechanical behavior The STB harvester can be modeled as a classical second order mass-damper-spring system, with an additive nonlinear term stemming from the bistable potential energy function. The dynamical behavior is underpinned by the nonlinear differential equation: mẍ + dẋ (x) = F(t) (1) where m is the mass of the cantilever beam, d the damping coefficient, ẍ, ẋ and x are, respectively, the acceleration, the velocity and the displacement of the cantilever beam, F(t) is the stochastic source modeling the external input mechanical vibrations. (x) is the restoring force which is linked to the potential energy function U(x) via (x) = U(x) (2) x A quartic potential energy function was adopted, by us, to describe the nonlinear mechanism [16] U(x) = 1 4 ax4 1 2 bx2 (3) By considering the form (3) of the potential, the following form of Eq. (1) can be obtained mẍ + dẋ + ax 3 b x = F(t) (4) In this paper we consider, only, the switching mechanism, i.e., we seek (dynamical) information related to the energy barrier that the external stimulus has to overcome to produce switching between the two stable states; we neglect intra-well motion. The first step towards fitting Eq. (4) to the observed behavior was the reconstruction of the reaction force (x) through experimental data. In particular, the pre-compressed beam was stressed by a controlled force applied orthogonally to the beam center (along the X-axis). The applied force was independently measured by the Fig. 4. Experimental setup for the estimation of the potential form U(x) (see Eq. (2)). load cell (Transducer Techniques GSO-1) embedded in the experimental setup customized for this particular experiment (Fig. 4). As a consequence of the applied stress, a beam deflection is experienced until the beam switches to the opposite stable state. Fig. 5 shows the measured beam reaction force along the X-axis as a function of the displacement along the same axis in case of a beam 1 cm 1 cm with pre-compression 3 mm. Reaction force along X-axis [mn] Observed Predicted Elastic Potential Energy U(x) [N*mm] Displacement along X-axis from stable states [mm] (a) Displacement x of the central mass along X-axis from initial position [mm] (b) Fig. 5. (a) The measured beam reaction force along the X-axis as a function of the displacement along the same axis. Comparison between the observed behavior and the predicted behavior by Eq. (2) in case of pre-compression Y = 3 mm. (b) The estimated potential U(x) by Eq. (3) in case of pre-compression 3 mm.

6 B. Andò et al. / Sensors and Actuators A 211 (214) f=4hz, a = 3.51 m/s 2 RMS f=5hz, a = 4.98 m/s 2 RMS f=8hz, a = m/s 2 RMS f=1hz, a = m/s 2 RMS Power [µw] Fig. 6. Real view of the lab-scale prototype [TRANSDUCERS 213]. In order to fit the observed behavior by Eq. (4), a Nelder Mead optimization algorithm [17] was implemented through a dedicated Matlab script exploiting the following minimization index: ) 2 (Freal F pred J = (5) F 2 real Here, F real and F pred refer to the measured and predicted force, respectively. The values of the parameters in (4) estimated by the optimization algorithm are a = 1.39e 4 kg/m 2 s 2, b =.98 kg/s 2 in case of pre-compression Y of 3 mm. It is worth pointing out that the values of (a,b) directly determine the energy barrier height (given by U = b 2 /4a) as well as the locations (given by x ± = b/a) of the minima and, hence, their separation. In the experimental setup, it is clear that changing the pre-compression, in fact, Load resistance [Ohm] Fig. 7. Power curves as a function of the resistive load and for different frequencies of the sinusoidal stimulus [TRANSDUCERS 213]. adjusts the two parameters (U, x ± ) directly. In turn, this affects the switching dynamics, e.g. the average switching rate. Comparisons between the observed behavior and prediction are shown in Fig. 5a. Fig. 5b shows the elastic potential energy U(x) estimated by Eq. (3). The results shown in Fig. 5 confirm the bistable operation of the device and the possibility of modeling its behavior by an appropriate potential energy function. This point is crucial to the device design as highlighted in Section 3.1. Future efforts will be dedicated to include the piezoelectric mechanical-to-electrical conversion mechanism into the model (4). V piezo [V] 12 1 a RMS = 3.51 m/s Piezoelectrics Accelerometer time [s] (a) Piezoelectrics 3 a RMS = m/s 2 Accelerometer Acceleration [m/s 2 ] V piezo [V] 12 a RMS = 5.63 m/s Piezoelectrics Accelerometer time [s] (b) a Piezoelectrics 3 RMS = m/s 2 Accelerometer Acceleration [m/s 2 ] V piezo [V] Acceleration [m/s 2 ] V piezo [V] Acceleration [m/s 2 ] time [s] (c) time [s] (d) Fig. 8. Experimental results for two values of the stimulus frequency, 4 and 1 Hz, and for two values of the acceleration applied by the shaker. A resistive load of 5 k has been adopted. In particular, the output signals from the piezoelectrics V piezo and the accelerometer for a root mean square (RMS) acceleration of 3.51 and 5.63 m/s 2 at 4 Hz, are shown in (a) and (b), respectively, while the same signals for an RMS acceleration of and m/s 2 at 1 Hz are shown in (c) and (d), respectively.

7 158 B. Andò et al. / Sensors and Actuators A 211 (214) The DP-NLH device As shown in Fig. 1, the DP-NLH device consists of a bistable STB beam, discussed in the previous sections, and two low cost piezoelectric diaphragms exploited to convert beam impacts into electric charge to power electronic devices [13]. An inertial mass of 1 g, placed in the middle of the beam, is used to optimize the trade-off between the operative frequency band and the minimum force that allows the switching. The mass has been designed and installed so that it preserves, as much as possible, the device symmetry thus reducing the beam tilt effect. The two low cost, ultra-thin, and lightweight piezoelectric diaphragms transducers 7BB-35-3L (Murata) have a plate diameter of 35 mm and a piezoelectric element diameter of 25 mm and thickness.53 mm [18]. They are laterally installed to experience beam impacts each time the device switches from one stable state to the other (see Fig. 1). The piezoelectric devices are electrically connected in a parallel configuration to supply the down-line electronics with charges produced during the impacts. As shown in Fig. 6, the DP-NLH device has been packaged in a suitable box which includes the clamping system for the beam pre-compression. The results of a characterization of the electrical performance of the DP-NLH device are discussed in the following subsection. To maintain coherence with the analysis presented in above sections and for the sake of proof of concept of the DP-NLH approach for energy harvesting, the results are presented for a DP-NLH device employing a PET beam 1 cm 1 cm wide with a pre-compression of 3 mm. A mass of 1 g has been attached to the center of the beam in order to reduce the accelerations required for beam switching Electrical behavior of the DP-NLH device To characterize the electrical response of the DP-NLH device, several repeated cycles of mechanical stimulation have been applied by a standard shaker. The shaker was driven by a periodic sinusoidal signal with increasing frequency in the range 4 1 Hz. A reference analog accelerometer Freescale Semiconductor MMA726Q has been used to independently measure the acceleration applied by the shaker. Signals from the reference sensor and the DP-NLH harvester have been acquired on a Lecroy 65A WaveRunner digital scope. A resistive load has been connected to the harvester in order to transduce the current produced by the piezoelectric layer into a voltage signal. An evaluation of the electrical power produced by the DP-NLH device as V 2 RMS /R, where V RMS is the RMS voltage measured across the load R, for different values of R in the range.1 1 k, for different pre-compressions and different values of the acceleration has been performed. Power curves for different frequencies of the sinusoidal stimulus, with a beam pre-compression of 3 mm, and for low acceleration values are shown in Fig. 7. As expected [9], typical P vs load curves have been obtained. In particular, we find that the optimal power transfer takes place with a resistive load of 5 k and the amount of power generated by the DP-NLH harvester is suitable for real applications, e.g. powering wireless sensor nodes. Fig. 1. Signals acquired from the LTC3588-1power supply electronic in case of a vibrational stimulus at 1 Hz producing an RMS acceleration of 9.81 m/s 2 and for the case of resistive load of 1 k, for the two case of (a) one and (b) two input supercapacitors, respectively. For the sake of completeness, the powers experimentally computed by forcing stimuli with the same amplitude producing an acceleration of m/s 2 and increasing frequency are shown in Table 2. As can be observed, although the generated powers weakly depend on the forcing frequency, their values are comparable thus confirming the frequency broad band operation of the device. The power evaluations have been carried out by taking into account the original (i.e. non-normalized) V RMS voltage values. The almost flat response in the considered frequency range is in line with the expected behavior of the nonlinear STB device. Voltage signals V piezo, generated by the piezoelectrics for RMS accelerations of 3.51 and 5.63 m/s 2 at 4 Hz, are shown in Fig. 8a and b, respectively, while the same signals for an RMS acceleration of and m/s 2 at 1 Hz are shown in Fig. 8c and d, respectively. A resistive load of 5 k has been employed. The RMS accelerations, reported in Fig. 8 for the two frequencies, depend on the minimum and maximum amplitude A s of the signal driving the shaker, respectively. The relevant acceleration signals are also shown in Fig. 8a d, for the sake of completeness. The results of Fig. 8 merit additional consideration. First, as can be observed in Fig. 8 and as expected, the voltage amplitude Table 2 Observed electrical power produced by the DP-NLH device on a load R = 5 k, in case of forcing stimuli with the same amplitude producing an acceleration of m/s 2 and increasing frequency. Frequency [Hz] Power [ W] Fig. 9. Schematization of the experimental setup

8 B. Andò et al. / Sensors and Actuators A 211 (214) due to beam impacts on the piezoelectrics depends on the acceleration imposed on the device and, in particular, it increases with acceleration. Actually the root mean square (RMS) value of the output voltage, V RMS, depends on the number of switching events within a defined time slot. From a statistical point of view, the number of switching events would be expected to increase with the amplitude of the mechanical stimulus (especially for acceleration values close to the switching thresholds) and this is clearly demonstrated in Fig. 8, where V RMS increases with the acceleration. We now briefly address some considerations concerning the design flow of the DP-NLH harvester. Assuming that the beam length and width are fixed by design constraints, some issues must be addressed to drive the selection of the beam pre-compression Y and the proof mass. The beam pre-compression will affect the impact force of the beam on the piezoelectric devices and, consequently, the generated voltage amplitude as well as the minimum acceleration required to drive the beam switching. The proof mass will influence both the voltage amplitude generated by beam impacts on the piezoelectric devices and the frequency response of the nonlinear harvester. Hence, it can be affirmed that the DP- NLH characteristics can be fixed once the system specifications (frequency band and strength of mechanical vibrations) have been defined. Fig. 11. Real experimental results in case of stimulus at 1 Hz generating three accelerations, for the resistive loads in the range [.56 1] k. In particular the time, t, required for the first activation of Vo is shown in (a) in case of one and (b) in case of two input supercapacitors while the time interval, t, between consecutive activations of the electronic output is shown in (c) in case of one and in (d) in case of two input supercapacitors. Figs. (e) and (f) show the time, t onpgood for the two cases of one and two supercapacitors, respectively.

9 16 B. Andò et al. / Sensors and Actuators A 211 (214) A case study: the DP-NLH device connected to the LTC electronics In order to demonstrate the compatibility of the DP-NLH device with standard electronics for energy storage, we discuss investigations performed by connecting the DP-NLH device to a commercial piezoelectric energy harvesting power supply circuit LTC by Linear Technology [19]. The LTC is an ultralow quiescent current power supply designed specifically for energy harvesting. It integrates a low-loss full-wave bridge rectifier with a high efficiency buck converter and it is optimized for high output impedance energy sources such as piezoelectric transducers. It is designed to interface directly to a piezoelectric or alternative A/C power source, rectify a voltage waveform, and store harvested energy on an external capacitor (here indicated as C STORAGE ), bleed off any excess power via an internal shunt regulator, and maintain a regulated output voltage by means of a nano-power high efficiency synchronous buck regulator. Four output voltages, 1.8, 2.5, 3.3 and 3.6 V, are pin selectable with up to 1 ma of continuous output current. An input protective shunt set at 2 V enables greater energy storage for a given amount of input capacitance [19]. A schematization of the experimental setup is shown in Fig. 9. To characterize the performance of the DP-NLH device, several repeated cycles of sinusoidal mechanical stimulation at 1 Hz have been applied by a standard shaker. Supercapacitors have been employed and connected at the input (C STORAGE ) and output of the harvesting electronic. Experiments employing one and two input supercapacitors (in parallel) with a capacitance of 47 F to store the electric charges produced by the two piezoelectric transducers, have been performed. Moreover, a supercapacitor of 47 F has been connected to the output of the LTC to store the electric current furnished by the electronics in order to supply the down-line electronics. To investigate the electric performance of the DP-NLH device the voltage across the input capacitor V c, the output voltage V o, and the voltage of the power good output (PGOOD) pin of the device have been observed and acquired on a Lecroy 65A WaveRunner digital oscilloscope. The PGOOD pin, is logic high when the output voltage V O is above 92% of the target value (user selectable). It can be used to enable a sleeping microprocessor or other circuitry connected to the output, when V O reaches regulation. In our experiments the output voltage has been set to 3.3 V which represents the typical supply voltage required by electronics device (e.g. RF transmitters or microcontrollers). Different time parameters have, then, been evaluated. In particular, the parameters evaluated are: the time, t, required for the first activation of the output of the electronic, the time, t onpgood, during which the PGOOD pin stays high, the time interval, t, between consecutive activations of the electronic output. Tests have been performed for different values of the electric load connected to the LTC Examples of the acquired signals in the case of a vibrational stimulus at 1 Hz producing an RMS acceleration of m/s 2 and for the case of resistive load of 1 k, are shown in Fig. 1a and b, for the two case of one and two input supercapacitors, respectively. The evaluation of the time parameters for different frequencies and amplitudes of the vibrational stimulus has been performed for the case of one and two input supercapacitors, and for different resistive loads. Experimental results in the case of three different Hz, and for resistive loads in the range.56 1 k are reported in Fig. 11. In particular, the results for the case of one or two supercapacitors are given by the following presentation: the time, t, required for the first activation of V O is shown in Fig. 11a and b, and the time interval, t, between consecutive activations of the electronic output is shown in Fig. 11c and d. Fig. 11e and f shows the time, t onpgood for the two cases of one and two supercapacitors, respectively. The results show that the time t and the time interval t decrease by increasing the acceleration imposed by the external stimulus. Moreover, as expected, they increase with the number of supercapacitors. The parameter t onpgood, instead, increases with the resistive load but does not appreciably depend on the external acceleration. Actually, for high loads the discharge time becomes significantly long and dependent on the converted power. Since the latter also depends on the acceleration strength, a small increment of the time t onpgood with the acceleration is achieved. In addition, a dependence on the number of input supercapacitors has been observed. This can be easily explained by observing that when the input capacitance is increased, the time required to accumulate a given level of energy increases, together with the time slot t onpgood during which a continuous regulated voltage can be provided to the load. 5. Concluding remarks In this paper, the authors present a low cost solution for energy harvesting based on a bistable clamped-clamped PET beam and two piezoelectric transducers. The beam switching is supposed to be activated by environmental vibrations. The mechanical-toelectrical energy conversion is performed by two piezoelectric transducers laterally installed to experience beam impacts each time the device switches from one stable state to the other. In fact, the intrinsic bistable nature of the conversion methodology, allows for rapid switching (between the two stable states of the bistable configuration) and large displacements, both of which are crucial in power conversion. It has been demonstrated that the proposed solution, the Double Piezo-NonLinear Harvester, is able to supply enough energy to power small electronic devices. In particular, the energy harvester is able to convert low frequency mechanical vibrations into electrical energy. Compared to traditional linear harvesters, the bistable dynamics yields an enhanced device behavior in terms of an extension of the frequency band where the device is able to scavenge energy from mechanical vibrations. Other main advantages of the proposed approach are the wide frequency band that assures high device efficiency at very low cost. Acknowledgements The authors gratefully acknowledge support from the US Office of Naval Research (Global), and the US Army International Technology Center (USAITC). We also thank Dr. Ilenia Medico and Dr. Stefania Medico of the University of Catania, for their contributions to this project. References [1] D. Brunelli, C. Moser, L. Thiele, L. Benini, Design of a solar-harvesting circuit for batteryless embedded systems, Circuits and Systems I: Regular Papers, IEEE Transactions on 56 (11) (29) , /TCSI [2] S. Dalola, M. Ferrari, V. Ferrari, M. Guizzetti, D. Marioli, A. Taroni, Characterization of thermoelectric modules for powering autonomous sensors, Instrumentation and Measurement, IEEE Transactions on 58 (1) (29) 99 17, [3] P. Thurein, E.A. Falkenstein, R. Zane, Z. 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Wang, A review of the recent research on vibration energy harvesting via bistable systems, Smart Materials and Structures 22 (213), [15] J. Qiu, J.H. Lang, A.H. Slocum, A curved-beam bistable mechanism, Journal of Microelectromechanical Systems 13 (2) (24) [16] V. In, A. Palacios, A.R. Bulsara, P. Longhini, A. Kho, J.D. Neff, S. Baglio, B. Andò, Complex behavior in driven unidirectionally coupled overdamped duffing elements, Phys. Rev E73 (6) (26) [17] J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, Convergence properties of the Nelder Mead simplex method in low dimensions, SIAM Journal on Control and Optimization 9 (1) (1998) [18] Piezoelectric Sound Components, Murata Catalog No. P37E-24, Feb.1, 212, on line at [19] LTC Piezoelectric Energy Harvesting Power Supply, device datasheet, available on line at Biographies Bruno Andò received the M.S. in electronic engineering and the Ph.D. in electrical engineering from the Università di Catania, Italy, in 1994 and 1999 respectively. From 1999 to 21, he worked as a researcher with the Electrical and Electronic Measurement Group of the University of Catania DEES. In 22, he became an assistant professor with the same staff. His main research interests are sensors design and optimization, advanced multi-sensors architecture for Ambient Assisted Living, sensor networks, characterization of new materials for sensors, nonlinear techniques for signal processing with particular interest in stochastic resonance and dithering applications and distributed measurement systems. During his activity, he has co-authored several scientific papers, presented in international conferences and published in international journals and books. Salvatore Baglio received the Laurea in electronic engineering and the Ph.D. in electrical engineering from the University of Catania, in 19 and 1994 respectively, where he is currently Associate Professor of electronic instrumentation and measurements. He teaches courses in Electronic measurements systems and Micro and Nano Sensors, he also serves as member of the Board of Ph.D. course in electronic and automation engineering of the University of Catania. He has served as associated Editor of IEEE Transaction on Circuits and Systems-I and distinguished lecturer of IEEE Circuit and Systems Society. Currently, he is associate Editor of the IEEE Transactions on Instrumentation and Measurements. He has focused his scientific interests on integrated micro and nano-transducers, transducers based on nonlinear dynamics, exploitation of smart materials properties toward integrated transducers, energy harvesting. He is principal investigator in several scientific research projects, regarding the development of innovative sensor systems; he has authored more than 3 scientific publications including international journals, books, conferences and patents. He has been recently elevated to IEEE Fellow. Adi R Bulsara received the Ph.D. degree in physics from the University of Texas, Austin, in He is currently a senior researcher with the Space and Naval Warfare Systems Center Pacific, U.S. Navy, San Diego, CA, where he heads a group that specializes in applications of nonlinear dynamics. He is the author of over 1 articles in the physics literature. His primary research interest includes the physics of noisy nonlinear dynamic systems, with a preference for applications. He has recently been elected a fellow of the American Physical Society. Vincenzo Marletta received the M.S. and the Ph.D. degrees from the University of Catania, Italy, in 27 and 211, respectively. He is currently working as temporary research fellow with the DIEEI of the University of Catania. His research interests include sensor design and characterization, new materials for sensors, inkjet printed sensors, energy harvesting, smart multisensor architectures for environmental monitoring and AAL, soft-computing methodologies for instrumentation and measuring systems, exploitation of nonlinear dynamics in sensors, microsensors in standard and dedicated technologies. He is the coauthor of more than 4 scientific publications, which include chapters in books and papers in international journals and proceedings of international conferences.