Patent Publication Number: US-9419546-B2

Title: Piezoelectric energy harvester device with frequency offset vibrational harvesters

Description:
FIELD OF THE INVENTION 
     The present invention relates to a piezoelectric energy harvester device with frequency offset vibrational harvesters, a system comprising the device, and methods of using and designing the system. 
     BACKGROUND OF THE INVENTION 
     Vibrational energy harvester devices offer electrical power generation in environments that lack light, temperature differentials, and/or pressure differentials. Instead, vibrations, and or movements, e.g., emanating from a structural support, which can be in the form of either a vibration at a constant frequency, or an impulse vibration containing a multitude of frequencies can be scavenged (or harvested) to convert movement (e.g., vibrational energy) into electrical energy. One particular type of vibrational energy harvester utilizes resonant beams freely extending from a base as a cantilever that incorporate a piezoelectric material that generates electrical charge when strained during resonance of the beams caused by ambient vibrations (driving forces), such as that described in U.S. patent application Ser. No. 14/173,131 to Vaeth et al. 
     Improvements are needed in the energy harvesting capabilities of such devices in systems which receive multiple impulses. In particular, cantilever based piezoelectric vibrational energy harvesters include a resonator beam that has an inherent resonant frequency. The resonator beam may be excited to vibrate at the inherent resonant frequency by a short acceleration impulse. Additional impulses applied to the vibrational energy harvester may either enhance or suppress the motion of the resonator beam, depending on the timing of the subsequent impulses relative to the resonant frequency. If an additional impulse is applied in phase with the resonator beam motion, the amplitude of the motion is increased. If, however, the additional impulse is applied out of phase with the resonator beam motion, the amplitude of the motion will be decreased. Thus, the performance of the harvester is dependent upon the timing between the impulses applied to the system. 
     By way of example, the timing between impulses is particularly relevant to vibrational energy harvesters utilized in systems such as a tire pressure monitoring system (TPMS), where the harvester experiences impulses as the tire flexes during its rolling motion on the road. When a portion of the tread of the tire where the harvester is located contacts the road surface, that portion of the tire is forced into a short flat shape, which in turn results in a change in the acceleration profile for the harvester, which is attached to the perimeter of the tire. This change in the radial acceleration of the tire is explained in K. B. Singh et al., “Piezoelectric Vibration Energy Harvesting System With An Adaptive Frequency Tuning Mechanism For Intelligent Tires,” Mechantronics 22:970-88 (2012), which is hereby incorporated by reference in its entirety. 
     For the majority of the tire&#39;s rotational period, there is a relatively constant centripetal acceleration for a portion of the tire located at the perimeter of the tire. When that portion of the tire initially contacts the road surface, there is an initial increase in radial acceleration. The initial increase in acceleration is then followed by an abrupt drop in radial acceleration to zero. The abrupt drop to zero provides a first impulse to the vibrational energy harvester, exciting motion of the resonator beam. The radial acceleration then remains at zero during the time it takes for the portion of the tire to rotate through its contact with the road surface. Once the portion of the tire rotates through its contact with the road surface, there is an abrupt positive enhancement in the radial acceleration, followed by a settling back to an equilibrium radial acceleration. The abrupt rise in radial acceleration back to or near equilibrium provides a second impulse to the vibrational energy harvester system. The second impulse will either enhance or suppress the vibration of the resonator beam excited by the first impulse, depending on the temporal width between the first and second pulses. The rotational speed of the tire and the circumference (or diameter) of the tire determine the temporal width. The vibration of the resonator beam, and thus the amount of energy harvested, can vary greatly depending on the speed of the vehicle. Therefore, it would be desirable to develop a piezoelectric energy harvester that provides a more consistent source of electrical energy in a system that is submitted to multiple impulses, such as in a TPMS. 
     The present invention is directed to overcoming these and other deficiencies in the art. 
     SUMMARY OF THE INVENTION 
     One aspect of the present invention relates to a device comprising a plurality of elongate resonator beams. Each of the resonator beams includes a piezoelectric material extending between first and second ends of the resonator beam. One or more bases are connected to the first end of each of the resonator beams, with the second end of the resonator beams being freely extending from the one or more bases as a cantilever. A mass is attached to each of the second ends of the resonator beams. Each of the resonator beams is tuned to a resonant frequency offset relative to each of the other resonator beams by 0.1/W to 0.9/W, wherein W is a temporal width between a first impulse and a second impulse which excite motion of the resonator beams. 
     Another aspect of the present invention relates to a system comprising an electrically powered apparatus and the device of the present invention coupled to the apparatus. 
     Yet another aspect of the present invention relates to a tire comprising the system of the present invention. 
     A further aspect of the present invention relates to a method of powering an electrically powered apparatus. This method involves providing the system according to the present invention and subjecting the system to a plurality of impulses which cause the energy harvester device to generate electrical energy. Electrical energy is transferred to from the energy harvester device to the apparatus to provide power to the apparatus. 
     Another aspect of the present invention relates to a method for designing an energy harvesting device tuned to impulses encountered by a tire. The method involves determining the rotational period P of the tire at a given speed. A temporal width between a first impulse generated when a point on an outer circumference of the tire contacts a road surface and a second impulse generated when the point on the outer circumference of the tire is withdrawn from contact with the road surface at the determined rotational period P is determined. The system of the present invention is provided with a first resonator beam of the plurality of resonator beams tuned to a first resonant frequency that is an integer multiple M of the inverse of the temporal width W, wherein M is greater than or equal to 3, and a second resonator beam of the plurality of resonator beams tuned to a second resonant frequency offset relative to the first resonant frequency of the first resonator beam by 0.1/W to 0.9/W. The system is connected to the tire. 
     The energy harvester device of the present invention provides resonator beams that act as cantilevers with slightly offset resonant frequencies. The offset in resonant frequencies provides an energy harvester that yields a more consistent source of energy when the system is subjected to multiple impulses by limiting the effect of subsequent impulses on the overall average energy output from the harvester. In particular, the resonant frequencies are chosen in a manner such that, as one resonator beam experiences a decrease in motion due to improper phasing with respect to the received impulses, another resonator beam experiences increased motion due to favorable phasing of the received impulses. Additional resonator beams may be applied to provide further consistency in the amount of energy produced at different impulse rates. This device provides a more predictable and consistent source of energy for systems that receive multiple impulses at varying rates, which leads to better device performance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a top view of an embodiment of an energy harvester device of the present invention with a plurality of energy harvesters. Each of the plurality of energy harvesters includes an elongate resonator beam comprising a piezoelectric material, the resonator beam extending between first and second ends; a base connected to the resonator beam at the first end with the second end being freely extending from the base as a cantilever; and a mass attached to the second end of the resonator beam. 
         FIG. 2  is a top view of another embodiment of an energy harvester device of the present invention with an energy harvester comprising two elongate resonator beams comprising a piezoelectric material. The resonator beams are freely extending as cantilevers from a common base, with a separate mass attached at the freely extending end of both resonator beams. 
         FIG. 3  is a perspective view of an exemplary single energy harvester of the present invention shown in  FIG. 1 . 
         FIGS. 4A-4C  illustrate an embodiment of a system of the present invention in which a tire pressure monitoring system is electrically coupled to the energy harvester device of the present invention to power the tire pressure monitoring system.  FIGS. 4A and 4B  illustrate the attachment of the system directly to the tire (e.g., underneath the tire tread.  FIG. 4C  is a partial side view and partial block diagram of the system shown attached to the tire in  FIGS. 4A and 4B . 
         FIG. 5A  illustrates the position of the system shown in  FIGS. 4A-4C  during the rotation of the tire. 
         FIG. 5B  illustrates a radial acceleration profile for the system at the various positions as illustrated in  FIG. 5A . 
         FIG. 6  is a graph illustrating the power output of an energy harvester device with two energy harvesters with a resonant frequency offset of 0.635/W with W approximately equal to 8.45 ms. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention relates to a piezoelectric energy harvester device with frequency offset vibrational harvesters, a system comprising the device, and methods of using and designing the system. The energy harvester device of the present invention has improved energy harvesting consistency in systems that are subject to multiple impulses. 
     One aspect of the present invention relates to a device comprising a plurality of elongate resonator beams. Each of the resonator beams includes a piezoelectric material extending between first and second ends of the resonator beam. One or more bases are connected to the first end of each of the resonator beams, with the second end of the resonator beams being freely extending from the one or more bases as a cantilever. A mass is attached to each of the second ends of the resonator beams. Each of the resonator beams is tuned to a resonant frequency offset relative to each of the other resonator beams by 0.1/W to 0.9/W, where W is a temporal width between a first impulse and a second impulse which excite motion of the resonator beams. 
       FIG. 1  is a top view of an embodiment of an energy harvester  10  device of the present invention including a plurality of energy harvesters  11 ( 1 )- 11 ( n ). Although energy harvesters  11 ( 1 )- 11 ( n ) are each shown located on separate, individual die, it is to be understood that two or more of energy harvesters  11 ( 1 )- 11 ( n ) could be co-located on a single die. The elements of energy harvesters  11 ( 1 )- 11 ( n ) will be described with respect to exemplary energy harvester  11 ( 1 ) as each of the energy harvesters  11 ( 1 )- 11 ( n ) includes the same elements as will be described with respect to energy harvester  11 ( 1 ), except that energy harvesters  11 ( 1 )- 11 ( n ) are tuned to operate at different resonant frequencies f 1 -f n . Resonant frequencies f 1 -f n  of energy harvesters  11 ( 1 )- 11 ( n ) are offset from one another as further described below. 
     Energy harvester  11 ( 1 ) includes elongate resonator beam  12 ( 1 ). Resonator beam extends between first end  14 ( 1 ) and second end  16 ( 1 ). First end  14 ( 1 ) is connected to base  18 ( 1 ) while second end  16 ( 1 ) is freely extending from base  18 ( 1 ) as a cantilever. Mass  20 ( 1 ) is attached to second end  16 ( 1 ) of resonator beams  12 ( 1 ). 
     Energy harvester  11 ( 1 ) may be formed in an integrated, self-packaged unit. In particular, as illustrated in  FIG. 1 , package  18 ( 1 ), which also forms the base to which first end  16 ( 1 ) of resonator beam  12 ( 1 ) is attached, is shown to surround the cantilever structure (i.e., resonator beam  12 ( 1 ) and mass  20 ( 1 )) so that it encloses (at least partially) the cantilever structure. In the present invention, the package can completely enclose the energy harvester device, or can be formed so as to vent the energy harvester device to the atmosphere. When it completely encloses the energy harvester device, the pressure within the enclosed package may be higher, equal to, or lower than atmospheric pressure. In one embodiment, the atmosphere in the enclosed package is less than atmospheric, for example, below 1 Torr. 
     In one embodiment, as shown in  FIG. 2 , energy harvester  110  includes package  118 , which may include two separate cantilever structures freely extending from package  118  in opposite directions. Resonator beams  112 ( 1 ) and  112 ( 2 ) of the cantilever structures may be tuned to resonant frequencies that are slightly offset from one another as further described below. One or more of energy harvesters  11 ( 1 )- 11 ( n ) as shown in  FIG. 1  may be replaced by energy harvester  110  shown in  FIG. 2 . 
     Referring again to  FIG. 1 , in one embodiment, package  18 ( 1 ) may further comprise a compliant stopper connected to the package (e.g., on an inside wall of the package), where the stopper is configured to stabilize motion of the cantilever to prevent breakage. Suitable compliant stoppers according to this embodiment of the energy harvester device are illustrated and described in U.S. patent application Ser. No. 14/173,131 to Vaeth et al., which is hereby incorporated by reference in its entirety. The compliant stopper of the energy harvester device may be constructed of a variety of materials. The stopper may be made compliant through material choice, design, or both material choice and design. According to one embodiment, the stopper is made from a material integral to the package. Suitable materials according to this embodiment may include, without limitation, glass, metal, silicon, oxides or nitrides from plasma-enhanced chemical vapor deposition (PECVD), or combinations thereof. According to another embodiment, the stopper is not integral to the package. Suitable materials for the stopper according to this embodiment may include, without limitation, glasses, metals, rubbers and other polymers, ceramics, foams, and combinations thereof. Other suitable materials for the compliant stopper include polymers with low water permeation, such as, but not limited to, cycloolefin polymers and liquid crystal polymers. Liquid crystal polymers can be injection molded. 
     In an alternative embodiment, resonator beam  12 ( 1 ) may be configured to have a stopper feature which is configured to stabilize motion of the cantilever. Suitable stopper features according to this embodiment are illustrated in U.S. patent application Ser. No. 14/145,560 to Andosca et al., which is hereby incorporated by reference in its entirety. According to this embodiment, a stopper is formed on the mass and/or the second end of the resonator beam, and is configured to prevent contact between the second end of the resonator beam and the package. 
       FIG. 3  is a side cross-sectional view of an exemplary energy harvester  11 ( 1 ), which is representative of energy harvesters  11 ( 1 )- 11 ( n ) shown in  FIG. 1 . According to one embodiment, resonator beam  12 ( 1 ) comprises a laminate formed of a plurality of layers. Resonator beam  12 ( 1 ) includes at least piezoelectric stack layer  22 ( 1 ) over cantilever layer  24 ( 1 ) on oxide layer  26 ( 1 ), although resonator beam  12 ( 1 ) may include other layers in other configurations. Non-limiting examples of other layers include those described in U.S. patent application Ser. No. 14/173,131 to Vaeth et al., which is hereby incorporated by reference in its entirety. In one particular embodiment, the plurality of layers comprises at least two different materials. 
     Cantilever layer  24 ( 1 ) may be any suitable material such as silicon, polySi, metal (e.g., Cu or Ni), or other metal oxide semiconductor (CMOS) compatible material, or a high temperature polymer such as polymide. In one embodiment, cantilever layer  24 ( 1 ) has a thickness range of about 10 μm to about 200 μm, about 10 μm to about 75 μm, or about 10 μm to about 50 μm. In one embodiment, cantilever layer  24 ( 1 ) is a high Q resonator with a specific resonant frequency. Oxide layer  26 ( 1 ), according to one embodiment, is a silicon layer with a thickness of about 1 μm. 
     Piezoelectric stack layer  22 ( 1 ) of resonator beam  12 ( 1 ) includes a piezoelectric material. Suitable piezoelectric materials include, without limitation, aluminum nitride, zinc oxide, polyvinylidene fluoride (PVDF), and lead zirconate titanate based compounds. Piezoelectric materials are materials that when subjected to mechanical strain become electrically polarized. The degree of polarization is proportional to the applied strain. Piezoelectric materials are widely known and available in many forms including single crystal (e.g., quartz), piezoceramic (e.g., lead zirconate titanate or PZT), thin film (e.g., sputtered zinc oxide), screen printable thick-films based upon piezoceramic powders (see, e.g., Baudry, “Screen-printing Piezoelectric Devices,”  Proc.  6 th    European Microelectronics Conference  (London, UK) pp. 456-63 (1987) and White &amp; Turner, “Thick-film Sensors: Past, Present and Future,”  Meas. Sci. Technol.  8:1-20 (1997), which are hereby incorporated by reference in their entirety), and polymeric materials such as polyvinylidenefluoride (“PVDF”) (see, e.g., Lovinger, “Ferroelectric Polymers,”  Science  220:1115-21 (1983), which is hereby incorporated by reference in its entirety). 
     Piezoelectric materials typically exhibit anisotropic characteristics. Thus, the properties of the material differ depending upon the direction of forces and orientation of the polarization and electrodes. The level of piezoelectric activity of a material is defined by a series of constants used in conjunction with the axes of notation. The piezoelectric strain constant, d, can be defined as 
     
       
         
           
             d 
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                   strain 
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                   developed 
                 
                 
                   applied 
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                   field 
                 
               
               ⁢ 
               m 
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     (Beeby et al., “Energy Harvesting Vibration Sources for Microsystems Applications,”  Meas. Sci. Technol.  17:R175-R195 (2006), which is hereby incorporated by reference in its entirety 
     Piezoelectric stack layer  22 ( 1 ) of resonator beam  12 ( 1 ) also includes one or more electrodes  28 ( 1 ) in electrical contact with piezoelectric stack layer  22 ( 1 ). According to one embodiment, electrodes  28 ( 1 ) comprise a material selected from the group consisting of molybdenum and platinum, although other materials suitable for forming electrode structures may also be used. In additional, energy harvester  11 ( 1 ) may further include electrical harvesting circuitry in electrical connection with one or more electrodes  28 ( 1 ) to harvest electrical energy from the piezoelectric material of resonator beam  12 ( 1 ). As described in further detail below, the electrical harvesting circuitry can be electrically coupled to an electrically powered apparatus to provide power generated from the piezoelectric material and supplied to the apparatus. 
     In energy harvester  11 ( 1 ), resonator beam  12 ( 1 ) has second end  16 ( 1 ), which is freely extending from base  18 ( 1 ) as a cantilever. A cantilever structure comprising piezoelectric material is designed to operate in a bending mode thereby straining the piezoelectric material and generating a charge from the d effect (Beeby et al., “Energy Harvesting Vibration Sources for Microsystems Applications,”  Meas. Sci. Technol.  17:R175-R195 (2006), which is hereby incorporated by reference in its entirety). A cantilever provides low resonant frequencies, reduced further by the presence of mass  20 ( 1 ) attached at second end  16 ( 1 ) of resonator beam  12 ( 1 ). 
     Resonator beam  12 ( 1 ) may have sidewalls that take on a variety of shapes and configurations to help tune resonator beam  12 ( 1 ) and to provide structural support. According to one embodiment, resonator beam  12 ( 1 ) has sidewalls which are continuously curved within the plane of resonator beam  12 ( 1 ), as described in U.S. patent application Ser. No. 14/145,534 to Vaeth et al., which is hereby incorporated by reference in its entirety. 
     Energy harvester  11 ( 1 ) includes mass  20 ( 1 ) at second end  16 ( 1 ) of resonator beam  12 ( 1 ). Mass  20 ( 1 ) is provided to lower the frequency of resonator beam  12 ( 1 ) and also to increase the power output of resonator beam  12 ( 1 ) (i.e., generated by the piezoelectric material). Mass  20 ( 1 ) may be constructed of a single material or multiple materials (e.g., layers of materials). According to one embodiment, mass  20 ( 1 ) is formed of silicon wafer material. Other suitable materials include, without limitation, copper, gold, and nickel deposited by electroplating or thermal evaporation. 
     In one embodiment, a single mass  20 ( 1 ) is provided per resonator beam  12 ( 1 ). However, more than one mass may also be attached to resonator beam  12 ( 1 ). In other embodiments, mass  20 ( 1 ) is provided, for example, at differing locations along resonator beam  12 . 
     One or more electrodes  28 ( 1 ) output an electrical signal from the piezoelectric materials of resonator beam  12 ( 1 ) as resonator beam  12 ( 1 ) is subject to movement, such as an impulse motion applied to the energy harvester device  10 ( 1 ). Accordingly, electrodes  28 ( 1 ) are in electrical communication with the piezoelectric materials of resonator beam  12 ( 1 ). Electrical energy collected from the piezoelectric materials of resonator beam  12 ( 1 ) is then communicated to additional circuitry. In one embodiment, the additional circuitry is formed on device  10  at or near electrodes  28 ( 1 ). In another embodiment, the circuitry may be a separate chip or board, or is present on a separate chip or board. 
     Referring again to  FIG. 1 , in the energy harvester device of the present invention, each of the energy harvesters  11 ( 1 )- 11 ( n ) in energy harvester device  10  includes resonator beam  12 ( 1 )- 12 ( n ) that is tuned to a respective resonant frequency f 1 -f n . As those skilled in the art will readily appreciate, resonator beam  12 ( 1 )- 12 ( n ) can be tuned by varying any one or more of a number of parameters, such as the cross-sectional shape of resonator beam  12 ( 1 )- 12 ( n ), cross-sectional dimensions of resonator beam  12 ( 1 )- 12 ( n ), the length of resonator beam  12 ( 1 )- 12 ( n ), the mass of mass  20 ( 1 )- 20 ( n ), the location of mass  20 ( 1 )- 20 ( n ) on resonator beam  12 ( 1 )- 12 ( n ), and the materials used to make resonator beam  12 ( 1 )- 12 ( n ). 
     The resonant frequencies of energy harvesters  11 ( 1 )- 11 ( n ) of the present invention in operation may include frequencies of about 50 Hz to about 4,000 Hz, about 100 Hz to about 3,000 Hz, about 100 Hz to about 2,000 Hz, or about 100 Hz to about 1,000 Hz. Each resonant frequency f 1 -f n  of energy harvesters  11 ( 1 )- 11 ( n ) is offset relative to the resonant frequencies of the other energy harvesters by 0.1/W to 0.9/W, where W is a temporal width between a first impulse and a second impulse which excite motion of resonator beams  12 ( 1 )- 12 ( n ), although the offset may be 0.2/W to 0.8/W, 0.3/W to 0.7/W, 0.4/W to 0.6/W, or 0.45/W to 0.55/W. The resonator beams  12 ( 1 )- 12 ( n ) are tuned to an offset in resonant frequencies such that one or more of the energy harvesters  11 ( 1 )- 11 ( n ) will experience the proper phasing with respect to the timing of the received impulses as will be described further below. The offset in resonant frequencies f 1 -f n  provides a consistent source of the output of the electrical signal from one or more electrodes  28 ( 1 ) for impulses received at various different temporal widths W between impulses which excite motion of resonator beams  12 ( 1 )- 12 ( n ) of energy harvester device  10 . 
     Energy harvesters  11 ( 1 )- 11 ( n ) of the energy harvester device of the present invention may be made in accordance with the methods set forth, e.g., in U.S. patent application Ser. No. 14/145,534 to Andosca &amp; Vaeth; U.S. patent application Ser. No. 14/173,131 to Vaeth et al.; and U.S. patent application Ser. No. 14/201,293 to Andosca et al., which are hereby incorporated by reference in their entirety. For example, according to one embodiment, a method of producing an energy harvester device involves providing a silicon wafer having a first and second surface. A first silicon dioxide (SiO 2 ) layer is deposited on the first surface of the silicon wafer. A cantilever material is deposited on the first silicon dioxide layer. A second silicon dioxide layer is deposited on the cantilever material. A piezoelectric stack layer is deposited on the second silicon dioxide layer. The piezoelectric stack layer, the second silicon dioxide layer, the cantilever material, and the first silicon dioxide layer are patterned. The second surface of the silicon wafer is etched to produce the energy harvester device. 
     Another aspect of the present invention relates to a system comprising an apparatus and the device of the present invention. In one embodiment, the device is electrically coupled to the apparatus. Yet another aspect of the present invention relates to a tire comprising the system of the present invention. 
     For example, according to one embodiment, the system of the present invention is a wireless sensor device containing a sensor to monitor pressure in a tire, although the system of the present invention may be applied to wireless sensors to monitor, e.g., any one or more various environmental properties (temperature, humidity, light, sound, vibration, wind, movement, pressure, etc.). The energy harvester system of the present invention is coupled to the sensor to provide power to the sensor. 
     Turning now to  FIGS. 4A-4C , according to one embodiment, the system of the present invention is a tire pressure monitoring system (“TPMS”)  30 , which includes housing  32 , although the system of the present invention could be applied to other systems that are excited by impulse motion. TPMS  30  is coupled to tire  36  on the underside of tire  36  (i.e., under tire tread  38  and between tread  38  and wheel rim  40 . In this embodiment, TPMS  30  includes sensor component  42  to monitor tire pressure, energy storage  44 , and energy harvester device  10  of the present invention, all of which are in electrical communication and are located within housing  32 . According to this embodiment, energy harvester device  10  provides a standalone source of energy to power sensor  42  of TPMS  30 , which is used in place of, or in conjunction with, another standalone energy source. The energy harvester device of the present invention may also power an electrically powered apparatus by charging energy storage  44  associated with the electrically powered apparatus. Energy storage  44  may be a capacitor bank or a super-capacitor, although in other applications energy storage  44  may be a rechargeable battery. For example, the energy harvester device may provide a trickle charge to energy storage  44  which powers the electrically powered apparatus. 
     TPMS  30  is mounted directly to tire  36  such that motion of resonator beams  12 ( 1 )- 12 ( n ) of energy harvester device  10  is excited as a result of impulses generated as tire  36  enters the footprint region of rotation (i.e., as tire  36  meets the road at the point where TPMS  30  is attached to tire  36 ).  FIG. 5A  shows the various positions ( 1 - 6 ) of TPMS  30  during rotation of tire  36  through a full 360 degree rotation of tire  36 , including in footprint region  46 .  FIG. 5B  shows an associated radial acceleration profile for TPMS  30  when attached to tire  36  throughout the rotation of tire  36 , including the radial acceleration at positions  1 - 6 . 
     TPMS  30  travels at an equilibrium radial acceleration outside of footprint region  46 , i.e., at positions  1 ,  2 , and  6 . At position  3 , the TPMS  30  enters footprint region  46  and experiences a sudden increase in radial acceleration, followed by a sudden decrease in radial acceleration to zero. The sudden decrease provides a first impulse to excite motion of resonator beams  12 ( 1 )- 12 ( n ) of energy harvester device  10 . TPMS  30  remains at zero radial acceleration throughout footprint region  46 , including at position  4 . At position  5 , TPMS  30  exits footprint region and experiences a sudden increase in radial acceleration before settling back to the equilibrium radial acceleration. The sudden increase at position  5  provides a second impulse to excite motion of resonator beams  12 ( 1 )- 12 ( n ) of energy harvester device. The temporal width or time duration (W) between the first impulse and the second impulse is determined by the rotational period (P) of tire  36 , which is determined by the speed of the vehicle on which tire  36  is located. 
     In one example, energy harvester device  10  of TPMS  30  may include two energy harvesters  11 ( 1 ) and  11 ( 2 ) with corresponding resonant frequencies f 1  and f 2 . In this example, resonant frequency f 1  of energy harvester  11 ( 1 ) is tuned based on the temporal width W at a given speed, such that the resonant frequency f 1  is defined by the equation f 1 =n/W, wherein n is a positive integer. In one example, n&gt;4, although higher values of n may be utilized to provide optimal power generation based on the characteristics of the energy harvester  11 ( 1 ), such as size by way of example. Energy harvester  11 ( 1 ) may be tuned to resonant frequency f 1  using methods known in the art. By way of example, resonator beam  12 ( 1 ) can be tuned by varying any one or more of a number of parameters, such as the cross-sectional shape of resonator beam  12 ( 1 ), cross-sectional dimensions of resonator beam  12 ( 1 ), the length of resonator beam  12 ( 1 ), the mass of mass  20 ( 1 ), the location of mass  20 ( 1 ) on resonator beam  12 ( 1 ), and the materials used to make resonator beam  12 ( 1 ). 
     In this example, energy harvester  11 ( 2 ) is tuned to resonant frequency f 2 , which is slightly offset from resonant frequency f 1 . In this example, the offset between f 1  and f 2  is 0.1/W to 0.9/W, i.e., the absolute value of f 1 -f 2  is equal to 0.1/W to 0.9W, although the offset may be 0.2/W to 0.8/W, 0.3/W to 0.7/W, 0.4/W to 0.6/W, or 0.45/W to 0.55/W. Energy harvester  11 ( 2 ) may be tuned to resonant frequency f 2  using methods known in the art. By way of example, resonator beam  12 ( 2 ) can be tuned by varying any one or more of a number of parameters, such as the cross-sectional shape of resonator beam  12 ( 2 ), cross-sectional dimensions of resonator beam  12 ( 2 ), the length of resonator beam  12 ( 2 ), the mass of mass  20 ( 2 ), the location of mass  20 ( 2 ) on resonator beam  12 ( 2 ), and the materials used to make resonator beam  12 ( 2 ). 
     In operation, motion of resonant beams  12 ( 1 ) and  12 ( 2 ) of energy harvesters  11 ( 1 ) and  11 ( 2 ) is excited by the first impulse received when TPMS  30  enters footprint region  46  at position  3 , as shown in  FIG. 5A . The second impulse is received when TPMS  30  footprint region  46  at position  5 . The first impulse and second impulse are separated by temporal width W. Resonant beam  12 ( 1 ) vibrates with a period of T 1 =1/f 1 , while resonant beam  12 ( 2 ) vibrates with a period of T 2 =1/f 2 . In the event that temporal width W is approximately an integer multiple of either T 1  or T 2 , the motion of the associated energy harvester will be out of phase for the second impulse. This is because the second impulse is a sharp increase in acceleration, while the first impulse is a sharp reduction in acceleration. Therefore, this harvester will be degraded. However, if the temporal width W is an integer n+/−½ times the period of either T 1  or T 2 , the motion of the associated energy harvester will be enhanced. The offset between f 1  and f 2  ensures that, when one energy harvester is slightly out of phase with the temporal width W, the other energy harvester is likely to be in phase, in order to make the power output from the energy harvester device  10  more even at various values for temporal width W. Although this example utilizes two energy harvesters, it is to be understood that additional energy harvesters with offset resonant frequencies may be utilized to provide a more uniform source of power at various speeds. In one example, the additional energy harvesters include resonator beams with resonant frequencies that are offset relative to each of the other resonator beams in the plurality of resonator beams by 0.1/W to 0.9/W, although the offset may be 0.2/W to 0.8/W, 0.3/W to 0.7/W, 0.4/W to 0.6/W, or 0.45/W to 0.55/W. 
     A further aspect of the present invention relates to a method of powering an electrically powered apparatus. This method involves providing the energy harvester system of the present invention. The energy harvester is subjected to a plurality of impulses to generate electrical energy from the piezoelectric material. The electrical energy is transferred from the piezoelectric material to electrically powered apparatus to provide power to the apparatus. In one example, the method is carried out in conjunction with a vehicle tire in use and said apparatus is a tire pressure monitoring system or a component of a tire pressure monitoring system as described above. 
     Another aspect of the present invention relates to a method for designing an energy harvesting device tuned to impulses encountered by a tire. The method involves determining the rotational period P of the tire at a given speed. A temporal width between a first impulse generated when a point on an outer circumference of the tire contacts a road surface and a second impulse generated when the point on the outer circumference of the tire is withdrawn from contact with the road surface at the determined rotational period P is determined. The system of the present invention is provided with a first resonator beam of the plurality of resonator beams tuned to a first resonant frequency that is an integer multiple M of the inverse of the temporal width W, wherein M is greater than or equal to 3, and a second resonator beam of the plurality of resonator beams tuned to a second resonant frequency offset relative to the first resonant frequency of the first resonator beam by 0.1/W to 0.9/W. The system is connected to the tire. 
     Referring to  FIGS. 1-5B , an exemplary method for designing energy harvesting device  10 , which is tuned to impulses encountered by tire  36  is described. The rotational period P of tire  36  at a given speed is determined. The rotational speed and tire diameter (or circumference) may then be utilized to determine the temporal width W between a first impulse generated when a point on the outer circumference of tire  36  contacts a road surface, as shown in position  3  in  FIG. 5A , and a second impulse generated when the point on the outer circumference of tire  36  is withdrawn from contact with the road surface, as shown in position  5  in  FIG. 5A . The temporal width W is dependent on the rotational period P, such that the value of P/W remains fairly constant at various vehicle speeds. 
     Next, TPMS  30  of the present invention is provided with resonator beams  12 ( 1 )- 12 ( n ) comprising a piezoelectric material. Resonator beams  12 ( 1 )- 12 ( n ) are freely extending from bases  18 ( 1 )- 18 ( n ) as cantilevers. An exemplary resonator beam  12 ( 1 ) is illustrated in  FIG. 3 . Resonator beams  12 ( 1 )- 12 ( n ) may be located on the same die as illustrated, by way of example only, in  FIG. 2 , or may be located separately within energy harvester device  10 , as individual harvesters  11 ( 1 )- 11 ( n ), as illustrated in  FIG. 1 . 
     First resonator beam  12 ( 1 ) is tuned to first resonant frequency f 1  that is an integer multiple M of the inverse of the temporal width W of tire  36  at a given speed. In one example, M is greater than or equal to 3, although different values of M may be utilized depending on the desired performance characteristics of TPMS  30 . First resonator beam  12 ( 1 ) may be tuned to resonant frequency f 1 =M/W using methods known in the art. By way of example, first resonator beam  12 ( 1 ) can be tuned by varying any one or more of a number of parameters, such as the cross-sectional shape of first resonator beam  12 ( 1 ), cross-sectional dimensions of first resonator beam  12 ( 1 ), the length of first resonator beam  12 ( 1 ), the mass of mass  20 ( 1 ) attached to the end of first resonator beam  12 ( 1 ), the location of the mass  20 ( 1 ) on first resonator beam  12 ( 1 ), and the materials used to make first resonator beam  12 ( 1 ). 
     Second resonator beam  12 ( 2 ) is then tuned to second resonant frequency f 2  which is offset relative to first resonant frequency f 1  of first resonator beam  12 ( 1 ) by 0.1/W to 0.9/W, although the offset may be 0.2/W to 0.8/W, 0.3/W to 0.7/W, 0.4/W to 0.6/W, or 0.45/W to 0.55/W. Second resonator beam  12 ( 2 ) may be tuned to resonant frequency f 2  using methods known in the art. By way of example, second resonator beam  12 ( 2 ) can be tuned by varying any one or more of a number of parameters, such as the cross-sectional shape of second resonator beam  12 ( 2 ), cross-sectional dimensions of second resonator beam  12 ( 2 ), the length of second resonator beam  12 ( 2 ), the mass of mass  20 ( 2 ) attached to the end of second resonator beam  12 ( 2 ), the location of mass  20 ( 2 ) on second resonator beam  12 ( 2 ), and the materials used to make second resonator beam  12 ( 2 ). 
     TPMS  30  may include additional harvesters with resonator beams tuned to an offset from the other resonator beams by an offset of 0.1/W to 0.9/W relative to resonator beams  12 ( 1 )- 12 ( n ). In one example, third resonator beam  12 ( 3 ) may have resonant frequency f 3  offset from resonant frequency f 1  of first resonant beam  12 ( 1 ) by 0.25/W to 0.75/W, while fourth resonator beam  12 ( 4 ) may have resonant frequency f 4  offset from resonant frequency f 2  of second resonator beam  12 ( 2 ) by 0.25/W to 0.75/W, although additional number of resonator beams with other offsets may be utilized. Additionally, the method may include determining the rotational period of tire  36  at another given speed and tuning the resonant frequency of two or more resonator beams with a frequency interval based on the rotational period P of tire  36  at the another given speed. The additional resonator beams will provide a more consistent source of power to the system when subjected to impulse motion at various different speeds. 
     EXAMPLES 
     The following examples are provided to illustrate embodiments of the present invention but are by no means intended to limit its scope. 
     Example 1 
     Power Output of a Device with Two Energy Harvesters with a Resonant Frequency Offset of 0.635/W, with W=8.45 ms 
     A system was constructed to provide impulses to one or more harvesters at delay intervals between a first and second impulse, or an impulse pair, similar to that experienced by a rolling tire. This system was operated at various repeat rates of these impulse pairs and the output power of the harvesters was monitored. Using a temporal width W of 8.45 ms as a reference point, the system was loaded with a vibrational energy harvester with a resonant frequency of 581 Hz. Over an operating frequency of 7 to 10 Hz (equivalent to a rotational period of 143 ms to 100 ms), the average power produced was 4.3 uW, with almost no average power being produced at 7 and 8.5 Hz rotational frequency. 
     The system was then fitted with a vibrational energy harvester with a resonant frequency of 581 Hz and a second vibrational energy harvester with a resonant frequency of 506 Hz, representing a 75 Hz difference in harvester resonant frequencies, (or 0.635/W, with W=8.45 ms as a reference point) offset between the two frequencies. Referring to  FIG. 6 , the dashed line shows the power output for the energy harvester with a resonant frequency of 581 Hz, while the solid line shows the power output for the energy harvester with a resonant frequency of 506 Hz. The use of two energy harvesters with the frequency offset of 0.635/W in the system provides a more even power output from the system. The average power produced from this system over the operating frequency of 7 to 10 Hz (equivalent to a rotational period of 143 ms to 100 ms) was 9.9 uW, with no bands of zero average power production. 
     Although preferred embodiments have been depicted and described in detail herein, it will be apparent to those skilled in the relevant art that various modifications, additions, substitutions, and the like can be made without departing from the spirit of the invention and these are therefore considered to be within the scope of the invention as defined in the claims which follow.