Flexural wave absorption system

A flexural wave absorption system may include a pair of resonators disposed on the structure and separated from each other by a separation distance. The pair of resonators are arranged on the structure in a direction substantially similar to the direction of the flexural wave acting on the structure. As to the separation distance, this distance may be approximately one-quarter of the wavelength of the flexural wave acting on the structure.

TECHNICAL FIELD

The present disclosure generally relates to systems for absorbing flexural waves acting upon a structure.

BACKGROUND

The background description provided is to present the context of the disclosure generally. Work of the inventors, to the extent it may be described in this background section, and aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present technology.

Flexural waves, sometimes referred to as bending waves, deform the structure transversely as they propagate. Flexural waves are more complicated than compressional or shear waves and depend on material and geometric properties. Airborne noises can be created by flexural waves when an object comes into contact with a structure subjected to a flexural wave. Flexural vibrations of thin structures, such as beams, plates, and shells are the most common source of noise caused by flexural waves.

To reduce noise caused by flexural waves, traditional sound absorption methods have been utilized, including installing sound absorbing materials that absorb radiated sound, applying damping materials to reduce vibration, and/or adding high mass structures to prevent the passage of vibrations. However, these traditional sound absorption methods only reduce the airborne noise and do not significantly impact the flexural wave, which is the root cause of the airborne noise. As a result, noise may still be transmitted to other locations through the structure.

SUMMARY

This section generally summarizes the disclosure and is not a comprehensive disclosure of its full scope or all its features.

In one example, a system for absorbing a flexural wave acting on a structure includes a pair of resonators disposed on the structure and separated from each other by a separation distance. The pair of resonators are arranged on the structure in a direction substantially similar to the direction of the flexural wave acting on the structure. As to the separation distance, this distance may be approximately one-quarter of the wavelength of the flexural wave acting on the structure.

In another example, a system for absorbing a flexural wave acting on a structure includes at least one elongated slot formed within the structure and extending in a direction substantially similar to the direction of the flexural wave acting on the structure. The at least one elongated slot defines a channel located between the at least one elongated slot and either another elongated slot or perimeter of the structure. A pair of resonators are disposed on the channel are and separated from each other by a separation distance and generally are arranged in a direction substantially similar to the direction of the flexural wave acting on the structure. Like before, the separation distance may be approximately one-quarter of the wavelength of the flexural wave acting on the structure.

Further areas of applicability and various methods of enhancing the disclosed technology will become apparent from the description provided. The description and specific examples in this summary are intended for illustration only and are not intended to limit the scope of the present disclosure.

DETAILED DESCRIPTION

Described are different examples of flexural wave absorption systems that can substantially absorb a flexural wave in a beam or plate-like structure. When the structure is a beam, the flexural wave absorption system may include a pair of resonators disposed on the beam in a substantially similar direction to the flexural wave acting on the beam. The resonators may be separated from one another at a distance that is approximately one-quarter of the wavelength of the flexural wave acting on the beam.

Each resonator forming the pair of resonators may be similar to one another. In one example, the resonators include a solid member acting as a mass and a flexible member attached to the solid member that acts as a spring and damper. Generally, the resonators may have a resonant frequency that is substantially similar, but may vary slightly, from the frequency of the flexural wave acting on the beam. In one example, the natural frequency of the resonators is approximately 5% greater than the frequency of the flexural wave acting on the beam. This frequency shift can be explained because the beam or plate, while an elastic structure, has some stiffness that must be accounted for.

The flexural wave absorption system can also absorb flexural waves acting on a plate-like structure. When the structure is a plate, the structure includes one or more elongated slots that define a channel within the structure that is located between the elongated slots or between an elongated slot and an edge of the plate. A pair of resonators are disposed on the channel in a substantially similar direction to the direction of the flexural wave acting upon the plate. Generally, the length of the channel defines a direction that is also substantially similar to the direction of the flexural wave acting upon the plate as well.

Like before, the distance between the resonators forming the pair is generally one-quarter of the wavelength of the flexural wave acting upon the plate and the resonant frequency of the resonators is substantially similar to the frequency of the flexural wave acting upon the plate but may vary slightly. As explained previously, the resonant frequency of the resonators may be approximately 5% greater than the frequency of the flexural wave acting on the plate.

Referring toFIGS.1and2, illustrated is one example of a flexural wave absorption system10. As will be explained, the flexural wave absorption system10can substantially absorb a flexural wave14acting upon the structure. In this example, the structure is in the form of a beam12. The beam12can vary from application to application and can be made of different types of materials and have different types of dimensions, such as length, width, and thickness. Generally, the longer portion of the beam is the length, while the shorter portion of the beam is the width wb.

The beam12includes a top side16A and a bottom side16B that generally oppose one another. In this example, a pair of resonators18, including a first resonator20A and a second resonator20B, are disposed on the top side16A of the beam12. Generally, the first resonator20A and the second resonator20B are disposed on the beam12in a substantially similar direction of travel of the flexural wave14acting upon the beam12. In some cases, the direction that the first resonator20A and the second resonator20B are disposed on the beam12may be such that they are substantially similar to a direction defined by the length of the beam12.

The first resonator20A and the second resonator20B are generally separated from each other by a separation distance d. The separation distance d is generally dependent on the wavelength of the flexural wave14acting upon the beam12and may be approximately one-quarter of the wavelength of the flexural wave14. Depending on what frequency range of flexural waves are targeted for absorption, the separation distance d can vary accordingly.

As mentioned previously and shown inFIGS.1and2, the pair of resonators18may be disposed on the top side16A of the beam12. However, it should be understood that the pair of resonators18may be alternatively disposed on the bottom side16B of the beam12. Further still, one resonator of the pair of resonators18may be disposed of on the top side16A, while the other resonator of the pair of resonators18may be disposed of on the bottom side16B. For example, referring toFIG.3, illustrated is an example wherein the first resonator20A is disposed of on the top side16A of the beam12and the second resonator20B is disposed of on the bottom side16B of the beam12. Notably, the separation distance d remains the same regardless of the configuration. As mentioned before, the separation distance d depends on the frequency of the flexural wave14to be absorbed and is generally one-quarter of the wavelength of the flexural wave14.

Generally, the first resonator20A and the second resonator20B are substantially similar to each other, such that they have a similar frequency response. As such, they may also be physically similar to each other. For example, referring toFIG.4A, illustrated is a more detailed view of a resonator20that may be similar to the first resonator20A and/or the second resonator20B or any of the other resonators described in this description, such as the resonators120A-120G that will be described later. Here, the resonator20includes a solid member22and a flexible member24. Generally, the solid member22acts as a mass in a mass-spring-damper system and may be made of a rigid material, such as steel, iron, aluminum, ceramics, plastics, and the like. However, the solid member22may be made of any suitable material that allows the solid member22to act as a mass in a mass-spring-damper system.

As to the flexible member24, the flexible member24acts as a spring and damper in a mass-spring-damper system and may be made of a flexible material, such as rubber and soft plastics, such as thermoplastic elastomers, and/or thermoplastic polyurethane. However, the flexible member may be made of any suitable material that allows the flexible member24to act as a spring and damper in a mass-spring-damper system.

The solid member22may be attached to the flexible member24using adhesives. However, the solid member22may be attached to the flexible member24using a number of different methodologies, such as press-fitting, over-molding, crimping, and/or the use of retainers, such as screws. The flexible member24may be attached to the beam12using similar methodologies, such as adhesives, press-fitting, over-molding, crimping, and/or the use of retainers, such as screws. When the resonator20is attached to the beam12, the flexible member24is located between the beam12and the solid member22.

The resonator20may also have a cross-sectional area26that may be based on the width wbof the beam12ofFIG.1. Moreover, cross-sectional areas of the solid member22and/or the flexible member24may be directly proportional to the width wbof the beam12ofFIG.1. In particular, the characteristic dimension of the cross-sectional area26is between 15% to 20% of the width wbof the beam12ofFIG.1.

The resonator20may have a resonant frequency that is substantially similar to the resonant frequency of the flexural wave acting upon the structure to which the resonator20is attached. Moreover, when using a pair of resonators, such as the resonators20A and20B ofFIG.1, both the resonators20A and20B will have substantially similar resonant frequencies, which are substantially similar to the frequency of the flexural wave that is acting upon the structure. However, it should be understood that the similarity of the resonant frequencies of the resonators20A and20B and that of the flexural wave14may vary slightly (approximately 20% or less) to accommodate for the stiffness of the flexible member24. For example, the resonant frequencies of the resonators20A and20B may be greater than the frequency of the flexural wave. In one particular example, the resonant frequencies of the resonators20A and20B may be approximately 5% greater than the frequency of the flexural wave14.

Since the resonator20is a spring-mass-damper system, the lumped mass M of the solid member22may be represented as M=ρAh1, wherein ρ is the density of the material that makes up the solid member22, A is the cross-sectional area of the resonator20(in particular, the cross-sectional area of the solid member22), and h1is the height of the solid member22. Since the mass of the flexible member24may be negligible, the mass of the solid member22could be taken as the mass of the resonator20.

The lumped stiffness of the resonator20may be represented as κ=EA/(βh2), where E is the Young's modulus of the material that makes up the flexible member24, A is the cross-sectional area of the resonator20(in particular, the cross-sectional area of the flexible member24), and h2is the height of the flexible member24. The damping property C of the material that makes up the flexible member24comes from the viscous damping in the material, which can be modeled as the imaginary part of Young's modulus.

It should be understood that the overall shape of the resonator20can vary from application to application. For example,FIG.4Aillustrates that the resonator20is substantially cylindrical in shape, wherein both the solid member22and the flexible member24are cylindrical, giving the both the solid member22and the flexible member24substantially circular cross-sectional areas. However, the resonator20can take other shapes as well. For example,FIG.4Billustrates the resonator20as being cubic in shape.FIG.4Cillustrates the resonator20is being hexagonal in shape. Again, the examples given inFIGS.4A-4Care merely examples, and the resonator20can vary significantly. Further, it should be understood that resonators of different shapes can be utilized to form the pair of resonators18. For example, one resonator could be cylindrical, while the other could be cubic. However, the frequency response of both resonators may be substantially similar.

Returning toFIG.1, upon incidence of the flexural wave14such that it acts upon the beam12, the vibrations of the resonators20A and20B will be excited. When the frequency of the flexural wave14is substantially similar to the resonant frequency of the resonators20A and20B, the resonators20A and20B vibrate up and down with high amplitude. The resonators20A and20B are treated as one unit. The monopole and dipole resonances may occur at the same frequency by tuning the size of resonators20A and20B and the distance d between them.

Moreover, when the resonators20A and20B are subject to the flexural wave14, the monopole and dipole responses cancel each other in a backward direction so that there is no reflection. While the resonators20A and20B have constructive interference in the forward direction resulting in a scattered forward wave, the forward scattered wave cancels the incident wave in the forward direction beyond the resonators20A and20B. In this way, the flexural wave14is fully absorbed by the resonators20A and20B.

As mentioned before, the flexural wave absorption system10ofFIG.1is incorporated within the beam12to absorb the flexural wave14acting upon the beam12. However, similar principles can also be applied to absorbing a flexural wave acting upon a structure that is a plate. Plates differ from beams in that plates are significantly wider than beams. As such, there are some difficulties with absorbing flexural waves acting upon plates. Nevertheless, referring toFIGS.5and6, illustrated is one example of a flexural wave absorption system100that can absorb a flexural wave114acting upon a plate112.

The plate112is a structure that includes a top side116A and a bottom side116B. Similar to the beam12ofFIG.1, the plate112can be made out of any one of a number of different materials and can vary in dimensions significantly. The plate112generally has a perimeter119that defines the outer edge of the plate112and extends around the plate112.

Here, the plate112includes elongated slots130A-130C formed within the plate112that have channels140A-140D defined between the elongated slots130A-130C and/or the perimeter119. Each of the elongated slots130A-130C may either partially or completely pass through the thickness of the plate112. In this example, three elongated slots130A-130C have been defined within the plate112. However, it should be understood that the number of elongated slots130A-130C can vary based on the size and shape of the plate112.

Moreover, the channel140A is defined between the elongated slot130A and the perimeter119, the channel140B is defined between elongated slot130A and the elongated slot130B, the channel140C is defined between the elongated slot130B and the elongated slot130C, and the channel140D is defined between the elongated slot130C and the perimeter119. Generally, the channels140A-140D have widths wpthat are substantially similar. Disposed within the channels140A-140D are pairs of resonators118A-118D, respectively.

With particular attention toFIG.6, illustrated is a more detailed view of the channel140B formed between elongated slot130A and the elongated slot130B. It should be understood that the description provided of the channel140B can be equally applied to the other channels140A,140C, and140D. Here, disposed on the channel140B are pair of resonators118B that include a first resonator120C and a second resonator120D. It should be understood that the first resonator120C and the second resonator120D may be similar to the resonators20A and20B, shown inFIGS.1and2and previously described. As such, any description regarding the resonators20A and20B is equally applicable to the first resonator120C and the second resonator120D. Further still, any description regarding the resonators20A and20B is also applicable to any of the other resonators forming the pairs of resonators118A-118D.

The first resonator120C and the second resonator120D are separated by a separation distance d. Like before, separation distance d is generally dependent on the wavelength of the flexural wave114acting upon the plate112and may be approximately one-quarter of the wavelength of the flexural wave114acting upon the plate112. Depending on what frequency range of flexural waves are targeted for absorption, the separation distance d can vary accordingly.

The width wpof the channel140B can vary based on the size of the plate112as well as the cross-sectional area of the resonators120C and120D. In particular, the characteristic dimension of the cross-sectional areas of the resonators120C and120D is between 15% to 20% of the width wpof the channel140B. As mentioned previously, the width wpof each of the channels140A-140D may be substantially similar.

The resonators120C and120D are shown to be attached to the channel140B and are located on the top side116A of the plate112. However, similar to what was described inFIG.3, the resonators120C and/or120D may be located on the bottom side116B of the plate112and/or may be disposed such that the first resonator120C is located on the top side116A and the second resonator120D is located on the bottom side116B. However, the separation distance d between the first resonator120C and the second resonator120D should remain the same regardless of which side of the plate112the resonators120C and120D are located.

As previously explained when describing the resonator20ofFIG.4A, which is equally applicable to any of the resonators forming the pairs of resonators118A-118D, the first resonator120C and the second resonator120D have resonant frequency substantially similar (within 20%) to the frequency of the flexural wave114acting upon the plate112. In some cases, the resonant frequency of the first resonator120C and the second resonator120D may be greater than the frequency of the flexural wave114, such as 5% greater.

The elongated slots130A-130D and the perimeter119of the plate112guide the flexural wave114into the channels140A-140D. When the flexural wave114reaches the channels140A-140D, the monopole and dipole responses of the pairs of resonators118A-118D cancel each other in a backward direction so that there is no reflection. While the resonators that form each of the pairs of resonators118A-118D have constructive interference in the forward direction resulting in a scattered forward wave, the forward scattered wave cancels the incident wave in the forward direction beyond the resonators that form each of the pairs of resonators118A-118D. In this way, the flexural wave114is fully absorbed by resonators that form each of the pairs of resonators118A-118D.

To better illustrate the performance of the flexural wave absorption system10ofFIG.1and/or the flexural wave absorption system100ofFIG.5, reference is made toFIG.7. Here, illustrated are the transmission202, absorption204, and reflection206of flexural waves by a system similar to the flexural wave absorption systems10and/or100. As shown inFIG.7, there is near total absorption of flexural waves having a frequency of approximately 2725 Hz, with minimum reflection across all frequency ranges.

The preceding description is merely illustrative and is in no way intended to limit the disclosure, its application, or its uses. The phrase at least one of A, B, and C should be construed to mean a logical (A or B or C), using a non-exclusive logical “or.” It should be understood that the various steps within a method may be executed in different order without altering the principles of the present disclosure. Disclosure of ranges includes disclosure of all ranges and subdivided ranges within the entire range.

The headings (such as “Background” and “Summary”) and sub-headings used herein are intended only for the general organization of topics within the present disclosure and are not intended to limit the disclosure of the technology or any aspect thereof. The recitation of multiple embodiments having stated features is not intended to exclude other embodiments having additional features or other embodiments incorporating different combinations of the stated features.

As used herein, the terms “comprise” and “include” and their variants are intended to be non-limiting, such that recitation of items in succession or a list is not to the exclusion of other like items that may also be useful in the devices and methods of this technology. Similarly, the terms “can” and “may” and their variants are intended to be non-limiting, such that recitation that an embodiment can or may comprise certain elements or features does not exclude other embodiments of the present technology that do not contain those elements or features.

The broad teachings of the present disclosure can be implemented in various forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the specification and the following claims. Reference herein to one aspect or various aspects means that a particular feature, structure, or characteristic described in connection with an embodiment or particular system is included in at least one embodiment or aspect. The appearances of the phrase “in one aspect” (or variations thereof) are not necessarily referring to the same aspect or embodiment.