Energy Harvesting Using an Analog Circuit under Multimodal Vibration

e efficiency of harvesting energy from a vibrating structure using a piezoelectric transducer and a simple analog circuit is investigated experimentally. is analog circuit was originally invented for a synchronized switch damping on inductor (SSDI) technique, which enhances the damping of mechanical vibration. In this study, the circuit is used to implement a synchronized switch harvesting on inductor (SSHI) technique. A multiple degree of freedom (MDOF) structure is excited by single sinusoidal forces at its resonant frequencies and by random forces.e piezoelectric transducer converts this mechanical energy into electrical energy which is harvested using a standard recti�er bridge circuit with and without our analog circuit. Experimental results show that our analog circuit makes it possible to harvest twice as much energy under both single sinusoidal and random vibration excitations.


Introduction
Energy harvesting techniques have been studied extensively in recent years.Energy harvesting is a process by which energy is captured and stored.Energy can be harvested from various power sources, including wind power, solar power, ocean tides, heart, magnetic �elds, and structural vibrations.We focused on the vibration energy of a structure, using the piezoelectric effect to convert structural vibration energy into electrical energy.ere is substantial research on this technique, as reviewed by Sodano et al. [1].Lesieutre et al. [2] addressed the damping associated with energy harvesting from structural vibrations.
Badel et al. [3][4][5] proposed a synchronized switch harvesting on inductor (SSHI) technique to improve energy harvesting.SSHI is based on vibration suppression technique named synchronized switch damping on inductor (SSDI).Both SSHI and SSDI use a piezoelectric transducer attached to the structure and connected to an inductive circuit having an on-off switch [6][7][8][9][10].e switch in the circuit is �ipped at each extremum of displacement of the structure.A displacement sensor and a controller are needed to synchronize the switching commands with the mechanical vibration.In a self-powered system, these sensors and controllers need to be driven using a fraction of the harvested energy.
We previously invented an analog circuit that automatically performs switching without an external energy source [11].We describe in this paper how this analog circuit enhances the energy harvesting performance when used with SSHI.
Although many studies [12][13][14] have been conducted on SSHI, most of them are limited to the sinusoidal vibration of a single degree of freedom (SDOF) structure.is paper focuses on the energy harvesting performance of our analog vibration suppression system for a multiple degree of freedom (MDOF) structure under various excitations.First, we describe the SSDI mechanism.Next, we describe our analog self-powered device.Finally, we present the experimental

With harvesting
Without harvesting 0 results demonstrating the energy harvesting performance of our device for an MDOF structure under sinusoidal and random vibration excitations.

SSDI and SSHI Systems
2.1.Original SSDI Technique.e SSDI mechanism is described in [6][7][8][9][10].For simplicity, we consider the SDOF system shown in Figure 1.e system is composed of a mass, a structure, a piezoelectric transducer attached to the structure, and a switchable inductive circuit.e piezoelectric transducer is modeled by a voltage generator   and a capacitor   .
As shown in [8,10,15], the basic concept of the SSDI technique is to �ip the switch from point B to point A at the moment when displacement  1 or voltage   reaches a maximum, as well as to �ip the switch from point A to point B when  1 or   reaches a minimum.Figure 2 shows the vibration in   .When the displacement of mass reaches F 3: SDOF vibration suppression system with our analog circuit.
T 1: Device parameters of our analog circuit.
a maximum at    1 , the switch is �ipped from point A to point B. Current starts �owing in the inductive circuit shown in Figure 1 and stops when the voltage reaches a positive value  1 , owing to the inductor and diode B in the circuit.
During the subsequent half cycle of mechanical vibration, as the displacement of mass reaches the minimum value, voltage   changes from  1 to  2 .At time    3 , the position of the switch is �ipped from point B to point A, and the piezoelectric voltage changes from  2 to − 1 .is switching technique stores the electric charge in the piezoelectric transducer rather than allowing it to be dissipated, increasing the magnitude of   and thus increasing the force generated by the piezoelectric transducer to suppress the vibration.Furthermore, this switching inverses the polarity of   in synchronism with the mechanical vibration so that the vibration is effectively suppressed.[8,10,15] needs external power for measurement, calculation, and switching.To eliminate the external power supply, we have invented a simple passive analog circuit that performs SSDI switching automatically, as shown in Table 1 and Figure 3.

Analog Self-Powered SSDI. e original SSDI
Figure 3 shows our electric circuit for SSDI.When the voltage across the piezoelectric transducer   passes the maximum and starts to decrease, the anode voltage of the programmable unijunction transistor PUT 1 is maintained at the peak by diode  1 and capacitor  1 .However, the gate voltage of PUT 1 decreases following the decrease in   due to mechanical vibration.erefore, PUT 1 is turned on and the charge stored in  1 �ows through thyristor SCR 1 as its gate current.e gate current turns SCR 1 on, and the charge stored in the capacitor of the piezoelectric transducer,   , �ows through the inductor.Because the thyristor prevents the electric current from �owing in the opposite direction, turning the thyristor on is equivalent to �ipping the switch in Figure 1 to point A. When the value of   reaches a minimum and starts to increase, PUT 2 is similarly turned on, and subsequently, SCR 2 is also turned on.is action is equivalent to �ipping the switch in Figure 1 to point B.
In effect, this analog circuit �ips the switch in Figure 1 to point A when   is approximately at a maximum and �ips the switch to point B when   is approximately at a minimum.erefore, this simple analog circuit performs the functions of a sensor, a controller, and a switch for SSDI.

Energy Harvesting with Original SSHI.
An electric circuit consisting of a piezoelectric transducer connected to an energy harvester and a load resistance   is shown in Figure 4(a).e energy harvester is composed of four diodes and a capacitor   .is is a basic energy harvesting system with a piezoelectric transducer.A bridge circuit with four diodes recti�es the electrical energy from the piezoelectric transducer and stores it in capacitor   .
Figure 4(b) shows a typical system for energy harvesting with SSHI.As shown in this �gure, a switchable inductive circuit is connected to the system shown in Figure 4(a).SSHI tunes the switch in Figure 4(b) just as SSDI does.Because this switching increases the absolute value of   , as mentioned, SSHI can effectively harvest energy.In Figure 2, the broken line shows the vibration in   when some energy is harvested by SSHI, whereas the solid line shows the variation in   when SSDI is used.e �gure shows that when the absolute value of   reaches the voltage of   , the energy starts to �ow into  S .  has a large capacitance, causing   to plateau.5, by replacing the switchable inductive shunt circuit shown in Figure 1 with our analog circuit.Similarly, SSHI is implemented as shown in Figure 5 by replacing the switchable shunt circuit in Figure 4(b) by our analog circuit.6 and 7 show a view of the experimental system, which consists of two masses, a pantograph-type displacement-magni�cation mechanism, a piezoelectric transducer (PSt 1000/10/200-VS18, Piezomechanik GmbH), two cantilevered beams, a spring, a vibration shaker, and a platform.e displacement-magni�cation mechanism is attached to the upper beam, and upper side of the platform is used to accommodate the small elongation of the piezoelectric transducer in response to the large amplitude of vibration.e natural frequencies of the �rst and second vibration modes at a constant electric charge are 20.3 and 36.6 Hz, respectively [16].

Experimental Setup. Figures
e experiment is performed under three types of vibration excitations: a sinusoidal vibration excitation at the �rst mode resonant frequency, a sinusoidal vibration excitation at the second mode resonant frequency, and a random vibration excitation.We investigated the performance in harvesting energy using our system shown in Figure 5 for various values of load resistance   .

Experimental Results with Sinusoidal Excitation. Figure 8(a)
shows the steady-state variations in displacement of the upper mass 1, the voltage of the piezoelectric transducer   , and the harvested voltage   under a sinusoidal excitation at the �rst mode resonant frequency.In this case, the value of   is very large.At each extremum of displacement, the polarity of voltage   reverses.is voltage behavior is a typical feature of SSHI. Figure 8(b) shows a magni�ed view of Figure 8(a).When the absolute value of   is increased to a certain value, energy starts �owing into capacitor   , and as a result,   stays almost constant, making a plateau in the waveform.e difference between the plateau voltage and voltage   is attributed to the forward voltage of the diodes in the recti�er circuit.Figure 8(b) shows that the difference is 1.2 V, which is consistent with the forward voltage of 0.6 V for each diode.Figure 9(a) shows a comparison of the normalized harvested energy for various values of load resistance under a sinusoidal excitation at the �rst and second mode resonant frequencies.e energy dissipated by the load resistance is in�uenced by the value of resistance   .To optimize the harvested power, we apply various load resistances in the electric circuit.e horizontal axis represents the load resistance, and the vertical axis represents the harvested power divided by the mean square of displacement of mass 1, with and without our analog circuit.ese �gures indicate that our system signi�cantly increases the energy harvested from the MDOF structure under sinusoidal vibrations.Although the amount of energy harvested depends on the value of the electric load   , the amount is drastically increased using our circuit under vibration excitation at both the �rst and the second mode resonant frequencies.

Experimental Results with Random
Excitation.We also carried out experiments using random excitation.e vibration shaker connected the upper cantilever through the load cell.A function generator creates an input voltage wave and sends it to vibration shaker.e PSD of the random excitation force is constant over the frequency range from 10 Hz to 50 Hz.
Figure 9(b) shows the normalized harvested energy for various values of load resistances under random excitation.e horizontal axis is the load resistance, and the vertical axis is the harvested power divided by the mean square of displacement of mass 1, with and without our analog circuit.is �gure indicates that our system signi�cantly increases the energy harvested from the MDOF structure under random vibrations.Although the amount of energy harvested depends on the value of the electric load   , the amount is drastically increased using our circuit under random excitation.
e harvested energy can be increased by a factor of at least 2.3 using our simple analog circuit not only under sinusoidal vibration excitation but also under random vibration excitation.

Conclusion
We proposed a simple analog circuit to implement SSHI for harvesting energy from structural vibrations using piezoelectric transducers, and we investigated the resulting performance.Experiments were performed using an MDOF structure under sinusoidal vibration excitation at resonance frequencies and under random vibration excitation.Experimental results show that connecting our simple analog circuit to the standard circuit more than doubles the amount of energy harvested under both single sinusoidal vibration excitation and random vibration excitation.

F 1 :
SDOF vibration suppression system with original SSDI.

F 4 :
(a) SDOF energy harvester connected a piezoelectric transducer.(b) SDOF energy harvester connected a piezoelectric transducer with original SSDI.

F 8 :F 9 :
(a) �ime history of the piezoelectric voltage, harvested voltage, and displacement of mass 1 under �rst mode sinusoidal vibration excitation (  = 47 mF,   = ∞ Ω).(b) Magni�ed view of (a).(a) Comparison of normalized harvest power for various load resistances under sinusoidal vibration excitations.(b) Comparison of normalized harvest power for various load resistances under random vibration excitations.