DESCRIPTION

FIELD OF THE INVENTION

The invention relates to the field of resonating devices, in particular to devices that can be used for energy harvesting or as actuators.

The project leading to this application has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 952039.

BACKGROUND ART

The study of novel metamaterial devices has attracted growing interest within the research community working in several fields such as electromagnetism (1; 2), acoustics (3; 4) and elasticity (5), amongst others.

In the context of elastic waves, initial designs based around Bragg scattering and material contrast were used to create bandgaps (6; 7; 8; 9; 10) that often drew upon ideas from the photonic crystal community.

To push the operational regime toward lower frequencies, the exploitation of local resonance has received considerable attention (4; 11; 12; 13) for applications in geophysics, mechanical and civil engineering (14; 15; 16) involving common ambient spectra. While the concept of bandgap was initially employed for vibration isolation, it was then linked to a variety of phenomena including lensing (19; 20; 21), localization (22) or topological edge states (23; 24).

To capitalize on these recent metamaterial designs, energy harvesting is an attractive application. Vibration-based energy harvesting has received considerable attention over the last two decades, aiming at powering devices using vibrational energy. The opportunity to harvest energy from the environment may potentially remove the cost associated with battery replacement and avoid the chemical waste of conventional batteries (25).

Among the various possible energy harvesting methods, piezoelectric materials are widely used due to their large power densities and ease of application (26; 27).

A recent line of work exploits methods to locally increase the vibrational energy in the attempt to enhance the efficiency of piezoelectric devices. For instance, this can be achieved by focusing or localizing acoustic/ elastic wave energy at the harvester location using mirrors, funnels (28), defect modes (29) or lenses (30; 31).

Another approach to amplify the wavefield relies on the rainbow effect, that effectively slows down waves and spatially separate frequency components. These systems are based around gradually varying periodic arrays to take advantage of local bandgaps to control wave propagation. The underlying physics, capable of spatial segregation of frequency components, relies on the ability to isolate the dispersion curves of the locally periodic structures inside the array. A graded array is formed by smoothly varying a particular parameter, or set of parameters, of neighboring elements in subsequent unit cells. Originally discovered in electromagnetism using axially non- uniform, linearly tapered, planar waveguides with cores of negative index material (32), there has been a flurry of intensive research translating the rainbow effect into all flavors of classical wave propagation fields including acoustics (33; 34; 35; 36), water waves (37) and fluid loaded elastic plates (38), amongst others. Particular advances have been recently reported in elastic devices made of arrays of resonant rods for deep elastic substrates (17; 18; 39; 40) to mode convert Rayleigh (R) into Shear (S) or Pressure (P) waves. Such graded line arrays of resonators have been theorized, designed and manufactured also for energy harvesting applications (41; 42; 43; 44). In this context, rainbow reflection and trapping mechanisms are employed to enhance the interaction time between waves and the harvesting system, reporting higher power output as compared to ungraded designs.

De Ponti et al. (41) disclose a metamaterial including an aluminum beam with section 10mm x 30mm which is augmented by an array of 30 resonating rods of varying length and square cross section. In this work, a piezoelectric harvester is placed at one edge of one of the rods with cantilever electrodes free to oscillate as an input wave travels along the beam. De Ponti et al. show that rainbow effect can be used to decrease the speed of the wave in the beam and to confine wave energy on proximity of the rods, thereby increasing energy harvesting. In this paper, the resonating rods are placed on one same side of the aluminum beam and the cantilever electrodes are placed in a plane orthogonal to the longitudinal axis of the rod.

Devices using cantilever resonators with piezoelectric elements are also known by some patents.

US 8,169,124 discloses a physical /biochemical sensor using piezoelectric microcantilever resonators. An array of resonators is placed on one side of a silicon substrate. Each resonator includes a supporting layer supporting a piezoelectric thin layer laying between a lower electrode and an upper electrode. The supporting layers of the resonators are arrayed in a manner that their lengths are gradually reduced. The resonators have different spring constants depending on their length; therefore, they are sensitive to different mass loading and surface stress. In the example described in this patent, a human antibody is immobilized on the resonators. The experiments show that each resonator of the array suffer a different frequency shift, therefore the sensor can be used to detect different target materials by comparing the detected frequency shifts with those determined by target materials.

US 6,858,970 discloses a multifrequency energy harvester. A piezoelectric device connected to a vibration source converts vibration energy to electrical current. A plurality of pairs of oppositely polarized piezoelectric wafers deflect to produce an electrical current. Each pair of wafers are arranged back-to-back and electrically joined. The plurality of pairs of wafers are each connected to a set of micro-machined parts. Each pair of wafers form a bimorph, configured as a cantilevered beam attached to a set of parts to form an element. Each cantilevered beam has a mass weighted first end and is fixedly attached to one or more flexible sheaths on a second end.

CN106856380 discloses a piezoelectric energy collecting device, which comprises a base skeleton, a cantilever rod array, magnets, and piezoelectric power generation pieces. The base skeleton is composed of metal tubes distributed according to three cartesian axis. The cantilever rod array is composed of multiple cantilever rods which are arranged sequentially from the shorter to the longer. Each metal tube of the base skeleton is provided with a cantilever rod array orthogonal to the metal tube. The tail end of each cantilever rod in the cantilever rod array is provided with a magnet. The magnets of two adjacent cantilever rods are placed with same magnetic poles facing each other. The piezoelectric power generation piece is adhesive to the root of each cantilever rod.

Although several solutions have been proposed for energy harvesting using piezoelectric elements, there's a need for devices which can be easily manufactured, and which provide efficient energy harvesting.

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OBJECTS AND BRIEF SUMMARY OF THE INVENTION

It is an object of the present invention to overcome the drawbacks of the prior art.

In particular, an object of the invention is to provide a compact resonator device which can be used for efficient energy harvesting or as an actuator.

A further object of the invention is to provide a broadband energy harvesting device which can efficiently harvest energy transported by mechanical vibrations at different frequencies.

These and further objects of the present invention are achieved by means of a piezoelectric energy harvesting device incorporating the features of the appended claims, which form an integral part of the present description.

In one aspect, the invention is directed to a resonator device comprising a waveguide for propagating a mechanical wave, and a graded array of cantilever resonators arranged on one side of the waveguide. Each resonator of the array comprises a supporting layer supporting a piezoelectric element. The waveguide is laminar in shape and has same thickness of the resonators' supporting layers. Moreover, two ends of the waveguide are connected each to a respective supporting element raising the waveguide with respect to a lower plane and allowing the waveguide to oscillate in a plane orthogonal to a plane comprising a main face of the waveguide.

This solution allows efficiently harvesting energy from propagation of mechanical waves, in particular flexural waves propagating in the waveguide. The graded array allows exploitation of the rainbow effect, increasing interaction of waves at different frequencies with respective resonators in the graded array, thereby increasing the transfer of energy from the wave to the piezoelectric elements.

In one embodiment, the lengths of the cantilever resonators are graded according to a straight line inclined of an angle 0, with respect to the longitudinal axis of the waveguide, which is preferably comprised between 3° (three degrees) and 7° (seven degrees) and more preferably is 5,2° (five point two degrees). Although other ways for grading the array are possible, e.g. the length could increase according to an exponential or parabolic law, several tests have provided this configuration to be preferred.

In one embodiment, the resonator device further comprises a second graded array of cantilever resonators, said second graded array of cantilever resonators being identical to said graded array of cantilever resonators and being arranged on a second side of the waveguide opposite to the other graded array.

The symmetry of this solution reduces torsional movements of the waveguide during propagation of the mechanical wave. This increases the efficiency of the resonator when used in an energy harvesting system.

Preferably, the waveguide and the resonators' supporting layers are made of a single piece. This solution also appears to increase energy transfer from the wave to the resonators, thereby increasing efficiency of the device.

In one embodiment, both the support layer and the piezoelectric element of each cantilever resonator are laminar in shape, and the piezoelectric element is arranged upon a main face of the support layer. This solution is preferred compared to others wherein the piezoelectric layer is not parallel to the supporting layer because manufacture of the same is easier.

According to a second aspect, the invention is directed to an energy harvesting system comprising a resonator device as described above and more in detail in the following description. The system also comprises energy storage means electrically connected to the resonators' piezoelectric elements for storing electric energy generated by the piezoelectric elements when the waveguide oscillates.

In one embodiment, the harvesting system further comprises an electric interface allowing access to the energy stored in the storage means.

According to a third aspect, the invention is directed to a method for energy harvesting with an energy system as described above and more in detail in the following description. According to the method, the supporting elements of the resonator device are connected to a supporting surface and the waveguide is oriented in such a way that a flexural wave, caused by vibration of the supporting surface, propagates in the waveguide in a direction from the resonator with lower length to the resonator of higher length.

Energy harvesting is more efficient by orienting the waveguide in this way.

In one embodiment, the supporting elements of the resonator device are beams. The method therefore provides for connecting the ends of each beam to the supporting surface, preferably leaving the intermediate portion of the beam free to oscillate. This solution makes energy harvesting more efficient.

According to a fourth aspect, the invention is directed to an actuating system comprising a resonator device as described above and more in detail in the following description.

In one embodiment, the actuating system also comprises an electric signal generator and a control unit. The electric signal generator is electrically connected to the resonators' piezoelectric layers. The control unit is operatively connected to the electric signal generator and adapted to control it for generating an electric signal at a predetermined frequency, thereby causing oscillation at least a resonator having resonating frequency equal to the predetermined frequency.

In another embodiment, the actuating system comprises a vibrator mechanically coupled to one of the supporting elements, in particular to the one being closest to the shorter of the cantilever resonators. The vibrator being adapted to generate flexural waves within the waveguide at frequencies corresponding to the resonating frequencies of the cantilever resonators.

Further features and objects of the present invention will be more apparent from the following description.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described hereinbelow with reference to certain examples provided by way of non-limiting example and illustrated in the accompanying drawings. These drawings illustrate different aspects and embodiments of the present invention and reference numerals illustrating structures, components, materials and/or similar elements in different drawings are indicated by similar reference numerals, where appropriate.

Figure 1 is a perspective view of a resonator device according to an embodiment of the invention;

Figure 2 is a cross sectional view of the device of figure 1 in the plane A- A;

Figure 3 is cross sectional view of a device alternative to that of figure 1;

Figure 4 is a cross sectional view of a device alternative to that of figure 1 or 2;

Figure 5 is top view of the device of figure 1; Figure 6a and 6b show respectively a top view and a cross section of a cell of the device of figure 1;

Figure 7 illustrates dispersion curves in an ideal periodic system comprising an infinite number of cells of the type of figure 6a and 6b;

Figure 8 illustrates comparative results of energy generated by the single cell device (lone resonator) of figure 9b and by the graded array of figure 9a;

Figure 9a illustrates a graded array resonator device according to figure 1 with evidence of a cell generating energy;

Figure 9b illustrates a lone resonator device with evidence of a cell generating energy;

Figure 10 illustrates a vibration applied to the graded array device of figure 9a and to the lone resonator device of figure 9b to measure the results of figure 8;

Figure 11 illustrates a simulation of energy harvesting results when a large band vibration, illustrated in figure 11, is applied to the device of figure 1;

Figure 12 illustrates an energy harvesting system comprising the resonator device of figure 1;

Figure 13 illustrates an actuating system using the resonator device of figure 1.

DETAILED DESCRIPTION OF THE INVENTION

While the invention is susceptible to various modifications and alternative constructions, certain preferred embodiments are shown in the drawings and are described hereinbelow in detail. It is in any case to be noted that there is no intention to limit the invention to the specific embodiment illustrated rather on the contrary, the invention intends covering all the modifications, alternative and equivalent constructions that fall within the scope of the invention as defined in the claims.

The use of "for example", "etc.", "or" indicates non-exclusive alternatives without limitation, unless otherwise indicated. The use of "includes" or "comprises" means respectively "includes, but not limited to", and "comprises, but not limited to", unless otherwise indicated.

Figure 1 illustrates a device 1 that can be operated as an energy harvester or as an actuator.

The device 1 comprises an elastic waveguide 2 connected between two supporting elements, in particular two supporting beams 3. Each supporting beam 3 comprises a lower face 30 intended to rest over a vibrating surface. The shape of the supporting beams 3 and the way the supporting beams are connected to the vibrating surface can be different, e.g. in one embodiment only the two opposite ends 31 and 32 of each supporting beam can be fixed, e.g. via glue or screws or other fixing means, to the vibrating surface, thereby allowing the central portion 33 of the supporting beam to be free to move in the Z direction. Operatively, the device 1 will be fixed to the vibrating surface with the waveguide 2 disposed in the direction where the vibration of the vibrating surface is expected to propagate.

The waveguide is connected to the supporting beams such that the waveguide is raised over the vibrating surface and is therefore free to oscillate if a mechanical vibration is applied on one of the supporting beams, in particular in the point P indicated in figure 1.

Two arrays of cantilever resonators 4 are placed at two opposite sides of the elastic waveguide 2. Each array comprises a plurality of resonators 4 having linearly increasing lengths.

As shown in figure 2, each resonator comprises a lower elastic supporting layer 40 and an upper thin piezoelectric layer 41. Preferably the elastic supporting layer 40 and the waveguide are made of the same elastic material.

When a mechanical vibration is generated in P, e.g. as a consequence of movements of the surface on which the supporting beams 3 are placed, a mechanical wave propagates along the waveguide 2 and causes oscillation of one or more resonators 4, thereby causing the piezoelectric layer 41 to generate an electric charge that can be collected in a storage device (not shown in figure 1), through a pair of electrodes properly connected to the piezoelectric layers 41 of the resonators 4. The storage device can be any device suitable for storing electric charge, e.g. a capacitor or a battery.

In the same way, if a voltage having opportune frequency and amplitude is applied to the piezoelectric layers through the electrodes, the resonators 4 bends due to the piezoelectric layers converting the electric current into mechanical vibrations. In this way, it is possible to use the device 1 as an efficient actuator, wherein a control unit generates a control voltage that is applied to the electrodes and that causes bending of one or more resonators 4.

The electrodes can be any type of known electrodes suitable for being connected to the piezoelectric layers 41, e.g. they can be electric cables or electric tracks connected on two opposite surfaces of the piezoelectric layers 41.

In the example of figure 3, one of the electrodes includes a conductive layer 5, not shown in figure 1, which lays over the piezoelectric layers 41 of the resonators and over an electrically insulating layer 6 that is placed on the waveguide 2. The conductive layer 5 can be made of any conductive material, e.g. copper or gold. The other electrode, instead, includes the supporting layer 40 which, in this example, is made of an electrically conductive material, e.g. aluminium or copper.

In an additional example illustrated in figure 4, the piezoelectric layer 41 is placed in between two conductive layers 50, 51 acting as electrodes, and the lower electrode 51 is separated from the supporting layer 40 by means of an electrically insulating layer 61. An electrically insulating layer 60 is also placed between the two conductive layers 50 and 51 in the region above the waveguide 2 and between two opposite piezoelectric layers 41.

In a preferred embodiment, the arrays of resonators 4 are graded according to an monotone increasing law that, in the embodiment of figure 1, is represented by a straight line 7 inclined of an angle 0 which is preferably comprised between 3° and 7° and more preferably is 5,2°. In other words, in the embodiment of figure 1 and 5, the midpoints of the free edge of each resonator 4 of a same array, lies on the straight line 7 which is inclined of an angle 0 with respect to the longitudinal axis X of the waveguide 2.

In different embodiment, the midpoints of the free edge of each resonator 4 of a same array are arranged according to a different monotone increasing law, e.g. according to an exponential or parabolic line.

The resonating frequency fi of each resonator decreases as the length L of the resonator increases. Therefore, as shown in figure 1, by applying a mechanical vibration in P, the wave propagates through the waveguide 2 in X direction and meets resonators having decreasing resonant frequency, i.e./i >fi >f _n .

The device 1 includes a plurality of cells 10, nine in the example of figure 5, each including a pair of resonators 3 as shown in figure 6a (top view) and 6b (side view). Cells 10 are all the same size D, wherein D is comprised in the following range:

— < £) < — (1)

15 2 ^V ’

Where Xo is the wavelength of the fundamental flexural wave (A0) propagating in a device 1 having no cantilever resonator, but only a waveguide 2 suspended between two supporting elements. In particular, Xo can be calculated according to the following formula: where: p:=Material density

A:=Cross section of the waveguide

®:=Operating angular frequency

E:=Young modulus

I:=Moment of inertia of the waveguide section

The dimensions D of the cells 10 therefore depends on the application the device is intended for.

These distribution of the lengths (and consequently of the frequencies) of the resonators allows exploiting the rainbow effect and provides several advantages as shown by the following data.

Figure 7 shows a dispersion curve showing the relation existing between wave number (k) and wave frequency (f) as the wave propagates in a system constituted by an infinite number of cells 10 having identical dimensions. The example of figure 7 is obtained as a simulation for cells having the following dimensions:

• Length of the cell, D = 128pm

• Width of the waveguide, Lw =60 pm

• Length of the resonator, L =223pm

• Width of the resonator, d= 50pm

• Thickness of the cell's skeleton, Ws =17pm

• Thickness of the piezoelectric layer, Wp =2pm

As it is known, the derivate of the dispersion curve indicates the group velocity v _g ), in X direction, of the wave in the cell.

In figure 7, the continuous line Ao represents the dispersion curve of the fundamental mode of a flexural wave, obtained by exciting the device in P in the Z direction, propagating in a cell having only a waveguide and no resonators. Lines with dots represents dispersion curves of waves, obtained by exciting the device in P in the Z direction, propagating in the system with infinite number of cells. The line with square points represents the dispersion curve of a wave oscillating only in the XY plane.

Focusing on propagation of waves oscillating only in the XZ plane (indicated by lines with dots), we see that one curve 700 has group velocity null in XQ, i.e. the wave having frequency fi and entering the cell slows down while part of the energy is reversed and propagates back. By using a graded array, the group velocity of such wave is smoothly reduced, allowing to decrease the wave reflections. Moreover, the resonators with resonant frequency / <fi create a bandgap, thus enhancing the wave confinement. The interplay of these two effects maximises the transfer of energy between the wave and the resonators. Parallel to this, the presence of several resonators with different resonant frequency increases the broadband capabilities of the system.

This is clear from figure 8 which shows a comparison of the energy transferred by a wave having frequency//- to a resonating cell 80 of a graded array system (figure 9a) and to a resonating cell 81 of a device having only one resonating cell (figure 9b). The results clearly show that the piezoelectric layers of the cell 80, that is part of the graded array, generate much more electric energy (proportional to the square of the Voltage indicated in Figure 8) compared to the energy produced by the single cell 81 of figure 9b. The results of figure 8 relates to a particular embodiment wherein: the device comprises an aluminium structure (Young modulus Ea = 70 GPa, Poisson ratio o _a = 0.33, and density p _a = 2710 kg/m ³ ) endowed with monomorph PZT-5H patches placed upon the top of the resonators (Young modulus Ep = 61 GPa, Poisson ratio o _p = 0.31, density p _p = 7800 kg/m ³ , dielectric constant £33/^0 = 3500, with e ₀ = 8.854 pF/m the free-space permittivity, and piezoelectric coefficient e ₃₁ = -9.2 C/ m ² ); the cell 80 has the same dimensions of the cell of figure 6 discussed above,

The graded array of figure 9a includes nine cells arranged according to the schematic of figure 5 with an angle 0=5,2°;

Both devices of figure 9a and 9b are solicited by a signal p(t) as shown in figure 10 while being clamped at the four ends 31,32 of the supporting elements 3.

The results of figure 8 have been obtained by using a numerical model based on a finite element discretization of the system through ABAQUS CAE 2018. In particular, the waveguide and the resonators are modelled through full 3D stress quadratic elements (C3D20), while the electromechanical interactions are addressed by linear 3D piezoelectric elements (C3D8E). The dispersion relation is obtained by performing modal analyses with a parametric sweep over the wave vector k along the edges of the Irreducible Brillouin Zone (IBZ). Time domain results are obtained with implicit analyses based on the Hilber-Hughes-Taylor operator, with a constant time increment dt = 0.1 ps.

Figure 11 shows the behavior of device 1 in broadband, i.e. when it is stimulated by a signal with a frequency between the resonance frequency of the last resonator (f _n ) and the resonance frequency of the first resonator (fi). The two graphs in Figure 11 (indicated by (a) and (b) ) show that the resonators farthest from the signal's entry point P (having lower resonating frequencies) are activated first, followed by those closest to the signal's entry point (having higher resonating frequencies). In particular, graph (b) allows to appreciate the rainbow effect, i.e. the separation in space of the frequencies.

In view of the above, it is clear that the device according to the invention allows efficient harvesting of energy transported by mechanical in a broad range of frequencies. Figure 12 shows a harvesting system 100 comprising the device of the invention. The harvesting system 100 further comprises storage means 101, e.g. a capacitor or a battery, for storing electric energy generated by the piezoelectric layers 41 when a mechanical wave propagates in the waveguide 2. The storage means are electrically connected to the piezoelectric layers of the resonators 4 by means of electrodes 102, 103. The system 100 also comprises an electric interface 104 allowing access to the energy stored in the storage means 101, e.g. the electric interface may comprise a connector or a switch electrically connected to the storage means, thereby allowing an electric load to receive the electric energy once connected to the connector.

In order to harvest energy with the harvesting system 100, the supporting elements 3 of the resonator device 1 are connected to a supporting surface that is expected to vibrate. By connecting the supporting elements 3 to the supporting surface, the waveguide 2 is oriented in such a way that a Sectional wave, caused by vibration of the supporting surface, propagates in the waveguide 2 in a direction from the resonator with lower length to the resonator of higher length. If the supporting elements are beams, as in the example described, preferably the ends of each beam are connected to the supporting surface, while the intermediate portion of the beam is left free to oscillate.

In the same way, the above-mentioned results show that the device can be efficiently operated as an actuator of an actuating system. Figure 13 shows such an actuating system 1000 comprising a device 1 according to the invention and an electric signal generator 130. The electric signal generator is configured to generate an electric signal at a predetermined frequency that can be selected by a control unit 131 operatively connected to the electric signal generator 130 and adapted to control it. The electric signal generator 130 applies the electric signal to the electrodes 132 and 133 that are connected to the piezoelectric layers of the resonators. By applying an electric signal having frequency fi, the system causes oscillation of the i-th resonator having resonating frequency fi.

In another embodiment, the actuating system comprises a vibrator mechanically coupled to one of the supporting elements, in particular to the one being closest to the shorter of the cantilever resonators. The vibrator being adapted to generate flexural waves within the waveguide at frequencies corresponding to the resonating frequencies of the cantilever resonators.

From the above description it is clear that the invention provides several advantages. The person skilled in the art will also understand that several modification can be made to the embodiments above illustrated and that features described with reference to one embodiment can be applied also to others, as an example, the systems of figure 12 and 13 have been described with reference to the resonator device of figure 1, but a resonator device with the features illustrated in figures 2-4 could be well be used in these systems. In the same way, the invention is not limited to a resonator device having the dimensions described above. While the above described embodiments relate to devices wherein the resonators have dimensions of the order of tens or hundreds of microns, tests have been successfully carried out also on devices with resonators having dimensions one thousand time grater, i.e. of the order of tens or hundreds of millimeters. As an example, a test has been carried out on a resonator device wherein the array is made of 9 unit cells of size D = 15 mm, with a linear grading law for the lengths of the resonators, from 16.75 mm to 27.75 mm, resulting in a grading angle of approximately 5.2°. The test provided very good harvesting results.