Abstract:
A transducer for use with a boundary-stiffened panel has an inter-digitated electrode (IDE) and a piezoelectric wafer portion positioned therebetween. The IDE and/or the wafer portion are triangular, with one edge or side aligned with a boundary edge of the panel. The transducer generates and transmits an output force to the panel in response to an input voltage signal from a sensor, which can be another transducer as described above or an accelerometer. A controller can generate an output force signal in response to the input voltage signal to help cancel the input voltage signal. A method of using the transducer minimizes vibration in the panel by connecting multiple transducers around a perimeter thereof. Motion is measured at different portions of the panel, and a voltage signal determined from the motion is transmitted to the transducers to generate an output force at least partially cancelling or damping the motion.

Description:
TECHNICAL FIELD 
     The present invention relates to a dual-function or dual-use transducer used for generating a transverse point load and/or for measuring a transverse velocity on a rib-stiffened or other boundary-stiffened panel, and a method of using the same. 
     BACKGROUND OF THE INVENTION 
     Active control systems are often used to suppress noise and/or vibration in certain structures. For example, aboard aerospace structures, noise and vibration reduction can be achieved using compact, surface-mounted piezoelectric actuators. As will be understood by those of ordinary skill in the art, the term “piezoelectric” generally describes the natural capability of certain classes of crystalline materials, e.g., quartz, tourmaline, lead zirconate titanates, barium titanate, etc., to produce a proportional voltage in response to an applied mechanical force or pressure. Piezoelectric materials can also change their shape and/or dimensions in response to an applied electric field, thereby making piezoelectric materials potentially useful as actuators in a host of different applications. 
     In one particularly simple and robust vibration control strategy referred to as “active damping,” the output of a velocity sensor is fed back to a point force actuator via a fixed control gain. The control approach is guaranteed to be stable for any value of the control gain if the actuator and sensor are matched. However, actuator/sensor pairs in actuality are never perfectly matched, thus necessitating the limitation of any applied control gain to minimize spillover and other system stability issues. Often, an electromagnetic shaker can be used to generate a point force while the integrated response from an accelerometer is used to measure velocity. While the transducers may not be perfectly matched, they are often adequate for vibration control applications. Unfortunately, shakers tend to be large, bulky, and require an inertial base from or against which to react. 
     Due to the severe space and weight constraints associated with many applications, and in aerospace applications in particular, considerable research has focused on piezoelectric patch actuators, which are compact and can be integrated into the structure. For instance, in U.S. Pat. No. 4,849,668 to Crawley et al., a laminate structural member is provided having embedded piezoelectric elements for sensing and control. Similarly, U.S. Pat. No. 4,565,940 to Hubbard Jr. describes a method for using piezoelectric film to control or damp vibrations in mechanical systems. 
     Other work has explored the advantages of spatially weighting distributed transducers. For instance, U.S. Pat. No. 5,054,323 of Hubbard Jr., et al. utilizes multiple triangularly-shaped segmented electrodes to characterize the pressure distribution on a rigid surface. By shaping a distributed transducer, researchers are able to vary how the device couples to the structural response. For instance, a triangular shape has been shown to couple to the flexural response of a cantilevered beam in exactly the same way as a point load or sensor applied at the tip of the transducer. However, this result has not been extended to two-dimensional structures such as plates. 
     Research pertaining to shaped piezoelectric transducers has established that the Laplacian of the spatial distribution determines how the transducer couples to the flexural response of a given structure. Generally triangular-shaped piezoelectric actuators have been demonstrated as capable of producing transverse point forces at each vertex of the actuator, and bending moments along each edge of the actuator. If the base edge of the actuator is aligned along a fixed boundary of a panel structure, then the point forces or loads and the line moment along the base of the actuator do not couple to the structural response. Therefore, a single point sensor that is positioned at a vertex of the actuator opposite the base edge can yield a substantially, although not perfectly, matched sensor/actuator pair. However, line moments created along the lateral edges of the actuator can cause undesirable high-frequency phase problems, which in turn can destabilize certain control methodologies such as negative rate-feedback control. 
     SUMMARY OF THE INVENTION 
     Accordingly, a dual-use transducer is provided herein. The transducer in accordance with the invention has potential utility in many industries, such as in an exemplary application wherein active noise and/or dissipative vibration control is highly desirable, and with particular utility when used in conjunction with a boundary-stiffened panel. As used herein, boundary-stiffened panels are characterized by a compliant substructure that is divided or segmented into individual sections or bays by one or more ribs or other suitably rigid stiffener portions. If the stiffener portions approximate a theoretically clamped boundary, then the distribution of a plurality of the shaped transducers of the invention around the perimeter of the panel in conjunction with the present invention can form an effective active control system for reducing the severity of vibrations in the panel. 
     Within the scope of the invention, the transducer is piezoelectric in nature, and is multi-functional or dual-use in the sense that it can generate a predetermined transverse point load when employed as an actuator, and can measure a transverse point response or transverse velocity when employed as a sensor. The transducer includes a piezoelectric wafer portion and one or more inter-digitated electrodes (IDE), at least one of the piezoelectric wafer portion and IDE being substantially triangular in shape. When used in its capacity as an actuator, the IDE applies a predetermined electric field in a preferred in-plane direction. When used in its capacity as a sensor, the same IDE can collect an electrical charge that is proportional to the flexural vibration at the tip of the sensor. In either capacity, the requisite substantially triangular shape has a base side or edge that is aligned along a fixed edge or boundary edge of the panel. 
     More particularly, the transducer is a compact and light-weight device that can be surface-mountable or embeddable with respect to the panel, and which includes a piezoelectric material or wafer portion attached to one IDE or sandwiched or positioned between two IDE, with the IDE enabling the application of a predetermined electric field in a preferred in-plane direction. The transducer does not generate destabilizing line moments along its lateral edges, and can be used with a separate point sensor or itself configured as a point sensor to measure motion at a single point on the panel structure, with the charge output of the transducer proportional to the flexural vibration at the tip or vertex of the actuator/sensor. Alternately, the transducer can be used solely as an actuator in conjunction with a corresponding point sensor such as a miniaturized accelerometer. 
     As provided herein, in at least one advantageous embodiment of the present invention, an apparatus for minimizing vibration in a stiffened panel includes a transducer having a pair of or a single set of IDE and a piezoelectric wafer portion positioned between the pair of IDE or on one side of a single IDE depending on the particular configuration. The transducer generates a force on the stiffened panel in response to an input voltage signal. The apparatus also includes a sensor that is operable for measuring the vibration at a surface portion of the stiffened panel, and that generates an output voltage signal in proportion to the measured vibration. A controller is electrically connected to the transducer and the sensor, with the controller configured to generate an output force signal in response to the input voltage signal. At least one of the piezoelectric wafer portion and the IDE is substantially triangularly in shape, with the output force signal adapted to induce the output force. 
     In accordance with a least one advantageous embodiment of the present invention, a method controls or minimizes vibration in a stiffened panel, and includes connecting triangular transducers around a perimeter of the stiffened panel such that a base edge of each transducer is aligned with a boundary of the perimeter. Each transducer includes a piezoelectric wafer attached to one or two IDE as described above. The method includes measuring a quantity of motion such as linear velocity at different surface portions of the stiffened panel, determining a proportional voltage signal from the quantity of motion. The proportional voltage signal for each of the different surface portions is transmitted to a corresponding transducer, here acting as an actuator, to generate a corresponding output force in proximity to the surface portion. This output force at least partially cancels the quantity of motion in proximity to the surface portion. 
     The above features and advantages and other features and advantages of the present invention are readily apparent from the following detailed description of the best modes for carrying out the invention when taken in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic perspective view of an exemplary rib-stiffened panel depicting various point forces and line moments; 
         FIG. 2  is a schematic perspective side view of a baseline or unshaped multi-use transducer having inter-digitated electrodes (IDE); 
         FIG. 3A  is a schematic perspective view of a shaped transducer according to one embodiment of the invention; 
         FIG. 3B  is a schematic perspective view of shaped transducer according to another embodiment of the invention; 
         FIG. 4A  is a schematic plan view of a boundary-stiffened panel having a distributed plurality of shaped transducers with closed-loop vibration controls; and 
         FIG. 4B  is a schematic side view of a boundary-stiffened panel having a plurality of shaped transducers according to another embodiment. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to the drawings wherein like reference numbers represent like components throughout the several figures, and beginning with  FIG. 1 , an exemplary panel  10  is configured as a rib-stiffened panel structure of the type known in the art. That is, one or more stiffener portions or ribs  19  divide or segment a compliant substructure  11  into individual sections or bays  20 ,  22 . The compliant substructure  11  is constructed of a generally compliant material suited to the intended use of the panel  10 . For example, when the panel  10  is intended for use in forming an aircraft fuselage the panel  10  can be constructed of a suitable light weight material, e.g., 6061-T6 aluminum, etc. 
     Regardless of its ultimate use, the panel  10  has suitably rigid edges or boundaries  16  around its perimeter that approximate clamped boundaries. As shown, a pair of substantially triangular-shaped transducers  14  are surface mounted to an inner surface  17  of the compliant substructure  11 . The shaped transducers  14  are constructed at least partially of a suitable piezoelectric material. As will be understood by those of ordinary skill in the art, piezoelectric materials can be crystalline structures or ceramics which produce a proportional output voltage when a mechanical force or stress is applied thereto. Since this effect also applies in the reverse manner, an input voltage applied to a sample piezoelectric material such as the shaped transducers  14  will produce a proportional mechanical force or stress, which can be imparted to the panel  10 . The activation of a typical piezoelectric material can result in a change in dimension of approximately 0.1% for piezo-ceramics and 1% for piezo-polymers. Suitably designed transducer structures made from these particular materials can therefore be made that bend, expand, or contract as desired when a voltage is applied thereto. 
     The shaped transducers  14 , being triangular in design, each have three vertices, and are able to generate or produce transverse point forces or loads (f b , f t ) at each vertex, wherein the subscript “b” refers to the base edge of each shaped transducer  14 . The shaped transducer  14  also produces or generates bending moments (m b , m 1 ) along each of its sides or edges. In particular, and with special reference to Gardonio, P. and Elliott, S. J. (2005), “Smart panels with velocity feedback control systems using triangularly shaped strain transducers”,  Journal of the Acoustical Society of America,  117(4), 2046-2064, the moment excitation along the lateral edges of a triangular-shaped transducer such as the transducer  14  can be mathematically defined as m 1 (t)=h s /2(m 2 e 31 +e 32 )v e (t), wherein the variable (h s ) is the combined thickness of the compliant substructure  11  and the shaped transducer  14 , the variable (m) is the slope of the lateral edge of the shaped transducer  14 , and the variable (e 31 ) is a piezoelectric material constant relating the electric field applied in the 3 or z direction to the stress induced in the 1 or x direction. Likewise, the variable (e 32 ) is the piezoelectric material constant relating the electric field applied in the 3 or z direction to the stress induced in the 2 or y direction, with the variable v c (t) describing the applied or input voltage. 
     Similarly, the moment excitation along the base edge  24  of the transducer  14  is defined as m b (t)=h s /2(e 31 )v c (t), while the point forces f b  generated at the base vertices of the shaped transducer  14  are defined as f b (t)=2 m(h s /2)(e 31 )v c (t). The point force f t  at the tip of the shaped transducer  14  is defined as f t (t)=(−4 m)(h s /2)(e 31 )v c (t). It is noted that when the base edge  24  of the shaped transducer  14  is aligned along a fixed boundary such as the boundary  16  of the substructure  11 , then the point forces (f b ) and the line moment (m b ) along the base edge  24  of the shaped transducer  14  do not couple to the structural response. Therefore, a single point sensor  12 , such as a miniaturized accelerometer, that is placed at the tip of the shaped transducer  14 , i.e., the vertex opposite the base edge  24 , can yield a substantially matched sensor/transducer pair. However, the line moments (m 1 ) along the lateral edges of the shaped transducer  14  can still cause undesirable high-frequency phase problems which can destabilize certain vibration control methodologies and systems. 
     Referring to  FIG. 2 , within the scope of the invention the shaped transducers  14  of  FIG. 1  each can include one or a pair of inter-digitated electrodes or IDE  28 . An unshaped transducer  15  is shown in  FIG. 2  to more clearly show the IDE  28 , with the shaped transducers  14 A,  14 B, and  14 C of the invention discussed below with reference to  FIGS. 3A ,  3 B,  4 A, and  4 B. A piezoelectric wafer  30  is attached or connected to one IDE  28  or interposed or sandwiched between a pair of the IDE  28 . Unlike a conventional monolithic shaped transducer  14  of the type shown in  FIG. 1 , in which the electric field couples to both in-plane directions equally, the IDE pattern used within the scope of the invention enables the application of an electric field in a preferred in-plane direction. The Macro-Fiber Composite (MFC) actuator distributed by Smart Material Corporation of Sarasota, Fla., provides such an IDE pattern. More importantly, the sign of the piezoelectric material constants (e 11 , e 12 ) in the respective  1  and  2  directions are opposite using the IDE  28 . Therefore, using a piezoelectric transducer with IDE in accordance with the invention can provide a zero lateral edge moment m 1 (t), i.e., h s /2(e 11+ e 12 )v c (t)=0. 
     To optimize noise and vibration control aboard an aircraft, it is advantageous to eliminate the destabilizing line moments (m 1 ) of  FIG. 1  along the lateral edges of any distributed transducers. This can be accomplished by using anisotropic or directionally-dependent devices such as the shaped transducer  14 A,  14 B,  14 C described below with reference to  FIGS. 3A ,  3 B,  4 A, and  4 B to generate a tensile stress in one in-plane direction and a comprehensive stress in the other in-plane direction. Use of the IDE pattern shown in  FIG. 2  in conjunction with a substantially triangular shape of either the piezoelectric wafer  30  or the IDE  28  itself helps to achieve this, with the IDE pattern allowing application of an electric field in the 1-direction as noted above. 
     Referring to  FIGS. 3A ,  3 B,  4 A, and  4 B, in accordance with the invention a shaped transducer  14 A,  14 B,  14 C provides a substantially triangular shape in conjunction with the IDE  28 ,  128  to zero the destabilizing line moments (m 1 )(see  FIG. 1 ) along the lateral edges of the transducer  14 A,  14 B,  14 C. The desired triangular shape can be achieved in at least three manners: (a) by shaping the piezoelectric wafer  30  of  FIG. 2  into a substantially triangular-shaped wafer  130  as shown in  FIG. 3A , (b) by shaping the IDE  28  of  FIG. 2  to form a substantially triangular-shaped IDE  128 , without modifying the shape of the piezoelectric wafer  30  of  FIG. 2 , or (c) by shaping both the piezoelectric wafer  30  of  FIG. 2  and the IDE  28  of  FIG. 2  to form a substantially triangular-shaped transducer  14 C as shown in  FIGS. 4A and 4B . 
     If the shaped transducer  14 A,  14 B,  14 C is properly aligned with a clamped edge or barrier  16  of the panel  10  (see  FIG. 1 ), then the point forces and line moments along the base edge  24  (see  FIG. 1 ) of the shaped transducer  14 A,  14 B,  14 C will not couple to the response of the panel  10 . Additionally, the shaped transducers  14 A,  14 B,  14 C couple to the flexural vibration of the compliant substructure  11  of  FIG. 1  in exactly the same way as would a single transverse point load or sensor  12  (see  FIG. 1 ) located at the tip of the shaped transducer  14 A,  14 B,  14 C. 
     Referring to  FIG. 4A , the panel  110  is configured as a boundary-stiffened panel structure with a distributed plurality of shaped transducers  14 C attached to the interior surface  17  of the panel  110  around the perimeter of the compliant substructure  11 . While four shaped transducers  14 C are shown in  FIG. 4A , those of ordinary skill in the art will recognize that the number and/or relative size of the shaped transducers  14 C can vary within the scope of the invention, with additional shaped transducers  14 C providing greater control authority, and with an increasing size of the shaped transducers  14 C generally leading to an increased sensitivity to boundary conditions. Likewise, while the shaped actuator  14 C is shown in  FIGS. 4A and 413  for simplicity, the description below also applies to the shaped transducers  14 A of  FIGS. 3A and 14B  of  FIG. 3B . In one embodiment, the shaped transducer  14 C is approximately 2.5 to 5 mm thick, has a base width (W) of approximately 0.03 to 0.04 meters (m), and has a height (H) of approximately 0.06-0.07 m, although other sizes can be used within the scope of the invention. 
     In the embodiment of  FIG. 4A , the shaped transducers  14 C are each attached to the interior surface  17  of the compliant substructure  11 , which as noted above can represent an internal surface or pressurized side of an aircraft fuselage or other similar structure subject to vibration and noise in a similar fashion. A point sensor  12  is positioned at the peak of each shaped transducer  14 C. The point sensor  12  can be configured as a miniaturized accelerometer adapted to precisely measure, sense, or otherwise determine the value of a linear acceleration of a portion of the compliant substructure  11  in immediate proximity to that particular point sensor  12  performing the measurement. A feedback signal  34  describing the measured vibration or force, such as in the form of a raw linear acceleration value (α), is transmitted or relayed from each point sensor  12  to an electronic control unit or controller  40 . 
     The controller  40  receives the transmitted feedback signal  34  and calculates or otherwise determines a linear velocity (v) value therefrom. After calculating the linear velocity, the controller  40  generates a control signal  36  as a calibrated or proportional voltage signal (V), which is then transmitted to the shaped transducer  14 C as an input command. The shaped transducer  14 C is adapted to apply a predetermined force or vibration signal to the compliant substructure  11  in response to the proportional voltage of the control signal  36 . As used herein, the term “proportional voltage” describes a scaled negative voltage producing motion in the compliant substructure  11  that effectively cancels or at least partially offsets or damps the vibration or motion that is measured, detected, or otherwise determined by the point sensor  12 . 
     The controller  40  can be configured as a general purpose closed-loop control device. As such, the controller  40  has the necessary operational amplifiers, capacitors, and/or other necessary electronic circuitry components required for manipulating one or more control variables, including the feedback signal  34 , in order to generate the scalar negative or proportional voltage (V) signal as the control signal  36 . However configured, the controller  40  is operable for processing the raw data transmitted from a corresponding point sensor  12 , determining the linear acceleration (α) of the compliant substructure  11  in close proximity to that point sensor  12 , and for calculating a linear velocity (v) value therefrom. From this intermediate value, the controller  40  generates a scalar negative or proportional voltage signal (V) as the output signal  36 , which can be modified as needed via a calibrated applied gain (k), i.e., a constant of proportionality, as needed to thereby affect the desired vibrational attenuation in the compliant substructure  11 . 
     Referring to  FIG. 4B , the panel  110  is shown in side view to present an alternate embodiment in which the point sensors  12  are not used. Instead, a matching set of shaped actuators  14 C are used, with one placed on the reverse side  17 R of the compliant substructure  11 , i.e., the side opposite the internal surface  17  previously described hereinabove, and one on the internal surface  17 . When the panel  110  is configured as an integral portion of an aircraft fuselage as described above, the reverse side  17 R would correspond to the depressurized or external surface of the fuselage. Therefore, such a configuration may be less than optimal in terms of accessibility, although such a configuration may retain utility in other vibration or noise control applications. 
     When shaped transducers  14 C are used without a corresponding point sensor  12 , as shown in  FIG. 4B , a shaped transducer  14 C on the inner surface  17  can be positioned precisely opposite to the shaped transducer  14 C on the reverse surface  17 R, such that the apexes of the shaped transducers  14 C that are coincident with the position of the point sensor  12  of  FIG. 4A  are positioned directly opposite each other, with only the thickness of the compliant substructure  11  interposed therebetween. One set of the shaped transducers  14 C, such as the set that is surface-mounted to or embedded within the reverse surface  17 R, is configured to generate a voltage in response to motion of the compliant substructure  11  at that location. This voltage is fed to the controller  40  (see  FIG. 4A ) described above, where it is processed in the same manner therein to provide the control signal  36  back to the other set of shaped transducers  14 C. 
     While the best modes for carrying out the invention have been described in detail, those familiar with the art to which this invention relates will recognize various alternative designs and embodiments for practicing the invention within the scope of the appended claims.