Superstructure beam with low broadband vibration reduction and one-way transmission characteristics

Abstract

The invention discloses a superstructure beam with low broadband vibration reduction and one-way transmission characteristics, the superstructure beam is composed of three or more materials, primitive cells comprise two periods: a main period and an internal period, a periodic material interface is increased, and band gap attributes are changed. Compared with the prior art, the antenna has the advantages of wider-band low-frequency band gap, higher vibration attenuation capability and the like. First-order inherent frequencies exist in band gaps of the superstructure beams with different primitive cell numbers, and vibration modes corresponding to the first-order inherent frequencies show obvious asymmetry. The wavelength of the vibration mode corresponding to the inherent frequency in the band gap is close to the length of the primitive cell, the inherent frequency is close to the first-order inherent frequency of the primitive cell, and non-reciprocity transmission of vibration can be achieved near the inherent frequency. The superstructure beam with the low-broadband vibration reduction characteristic is not only suitable for low-broadband vibration reduction, but also can be applied to one-way transmission of vibration, and is wide in application range.

Description

Technical Field

[0001] The invention relates to the technical field of low-frequency vibration reduction and noise reduction, and in particular to a superstructure beam with low-bandwidth vibration reduction and unidirectional transmission characteristics. Background Art

[0002] As one of the cutting-edge technologies for vibration control, superstructures have elastic wave bandgap characteristics, which can attenuate or block the propagation of elastic waves within a certain frequency range. Currently, two types of band gaps have been revealed, Bragg band gaps and local resonance band gaps. In traditional primitives, the frequency of the Bragg band gap is relatively high, and multiple cycles are required to achieve a good attenuation effect; although the local resonance band gap can achieve a lower frequency band gap, it is often narrower in frequency band and has higher design requirements for the oscillator and its installation position. Therefore, it is difficult for conventional superstructures to have both low-frequency and wide-band gaps to achieve good low-frequency vibration control effects. Summary of the invention

[0003] In order to overcome the shortcomings of high Bragg band gap frequency and weak attenuation of traditional primitive cells, the purpose of the present invention is to propose a superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics. By innovating the primitive cell form and nesting the internal period in the main period, a significant widening of the low-frequency band gap and effective attenuation of vibration elastic waves are achieved. In addition, it has asymmetric vibration modes under simply supported boundaries and fixed supported boundaries, which can realize unidirectional transmission of elastic waves.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] A superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics, the superstructure beam is a slender uniform cross-section beam with a rectangular cross-section, the cross-section width is b, the thickness is h, the length of the unit cell, that is, the lattice constant is a; one unit cell is counted as one period, and multiple unit cells are periodically arranged in one-dimensional direction to form the superstructure beam; one unit cell contains (2n+1) components connected in sequence and periodically arranged in one-dimensional direction, two material periods exist in one unit cell at the same time, ABCBC constitutes a main period, and BC nested in the main period constitutes an internal period; wherein n is the number of times the internal period BC is repeated, which is a positive integer greater than or equal to 2.

[0006] The primitive cell should be made of at least three different materials, and the Young's modulus and density of different materials are greatly different. Material A is polytetrafluoroethylene, nylon, polypropylene, plexiglass or TPU, material B is aluminum, copper, lead or resin, and material C is steel, aluminum, nickel or tungsten. No repeated materials shall appear in materials A, B and C.

[0007] When there are five components, they are respectively a first component (1), a second component (2), a third component (3), a fourth component (4) and a fifth component (5) arranged in sequence; wherein the material A of the first component (1) has a length a1, the material B of the second component (2) and the fourth component (4) has a length a2, and the material C of the third component (3) and the fifth component (5) has a length a3.

[0008] The interfaces of the components in the primitive cell are fixedly connected by an adhesive.

[0009] The superstructure beam has a first-order asymmetric vibration mode at a simply supported boundary and a fixed supported boundary, and its natural frequency is located within the band gap.

[0010] In the elastic wave propagation path of the superstructure beam, the sequence of ABCBC is called forward propagation, and CBCBA is called reverse propagation;

[0011] When the superstructure beam is excited in the middle in the vertical direction and the excitation frequency is within the band gap, the elastic waves propagate to the two ends of the superstructure beam respectively. Due to the asymmetry of the structure, the propagation characteristics in the two directions are also different, showing non-reciprocity; when the elastic wave propagates in the forward direction, since the structure is arranged periodically, the elastic wave with a frequency within the band gap will be affected by Bragg scattering, and strong destructive interference will be generated after scattering. The average attenuation rate within the length of 6 primitive cells reaches more than 92%, so that the elastic wave is difficult to propagate, and a good vibration reduction effect is achieved; when the elastic wave propagates in the reverse direction, due to the change in the propagation path, its transmission characteristics are also changed accordingly, and the elastic wave with a frequency within the band gap is affected by Bragg scattering, and only elastic waves of some frequencies undergo weak destructive interference, and the attenuation degree is much weaker than that of the forward propagation, so it can propagate in the reverse direction.

[0012] Compared with the prior art, the present invention has the following advantages:

[0013] (1) Compared with the traditional single-period superstructure beam, the present invention has two periods at the same time, which can enhance the destructive interference of elastic waves and thus has a wider low-frequency band gap;

[0014] (2) The multi-period design of the present invention enables more material interfaces in the unit cell, thereby enhancing the attenuation capability within the band gap, which is beneficial to low-frequency and broadband vibration and noise reduction.

[0015] (3) The superstructure beam of the present invention has a first-order frequency in the band gap when the number of primitive cells is different, and the vibration mode corresponding to the frequency shows obvious asymmetry. Due to the presence of asymmetric vibration modes in the band gap, in addition to the vibration reduction capability, the non-reciprocal transmission of elastic waves can be realized near a specific frequency, which broadens the application range of the superstructure beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of the original cell structure of the present invention.

[0017] Figure 2 Schematic diagram of the size of the primitive cell of the present invention.

[0018] Figure 3 It is a schematic diagram of the arrangement of the superstructure beams of the present invention.

[0019] Figure 4 Schematic diagram of the energy band curve of the present invention.

[0020] Figure 5 It is a transmission rate curve diagram of the forward propagation of the present invention.

[0021] Figure 6 It is a transmission rate curve diagram of reverse propagation of the present invention.

[0022] Figure 7 It is the N-order vibration mode diagram of the present invention.

[0023] Figure 8 It is a schematic diagram of the non-reciprocal transmission of the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0025] like Figure 1 , Figure 2 and Figure 3 As shown, the present embodiment involves a superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics, which is composed of a plurality of unit cells arranged periodically, each unit cell has five components, composed of three materials, including two periods. A low-frequency broadband Bragg band gap is formed by periodic arrangement to achieve vibration attenuation. The five components are the first component 1, the second component 2, the third component 3, the fourth component 4 and the fifth component 5 arranged in sequence; wherein the material of the first component 1 is A, the length is a1, the material of the second component 2 and the fourth component 4 is B, the length is a2, the material of the third component 3 and the fifth component 5 is C, the length is a3.

[0026] In the elastic wave propagation path of the superstructure beam of the present invention, the order of ABCBC is called forward propagation, and CBCBA is called reverse propagation; when the superstructure beam is excited in the middle in the vertical direction and the excitation frequency is within the band gap, the elastic wave propagates to the two ends of the superstructure beam respectively, and due to the asymmetry of the structure, the propagation characteristics in the two directions are also different, showing non-reciprocity; when the elastic wave propagates in the forward direction, since the structure is arranged periodically, the elastic wave with a frequency within the band gap will be affected by Bragg scattering, and strong destructive interference will be generated after scattering, and the average attenuation rate within the length of 6 primitive cells reaches more than 92%, so that the elastic wave is difficult to propagate, and a good vibration reduction effect is achieved; when the elastic wave propagates in the reverse direction, due to the change in the propagation path, its transmission characteristics are also changed accordingly, and the elastic wave with a frequency within the band gap is affected by Bragg scattering, and only the elastic wave of some frequencies undergoes weak destructive interference, and the attenuation degree is much weaker than the forward propagation, so it can propagate in the reverse direction.

[0027] A specific implementation of the present invention is given below, and Table 1 shows the structure and material parameters.

[0028] Table 1

[0029]

[0030] In this embodiment, material A is polytetrafluoroethylene, material B is epoxy resin, and material C is aluminum.

[0031] In this embodiment, the superstructure beam is a rectangular beam with a uniform cross-section, and its cross-sectional thickness h is 5 mm and its cross-sectional width b is 10 mm.

[0032] In this embodiment, the boundary condition of the superstructure beam is simply supported.

[0033] like Figure 4 As shown, the first-order band gap of the superstructure beam is 42.27 Hz to 107.16 Hz, and the wave vector in the band gap has an imaginary part value, which represents damping, indicating that it has the ability to attenuate vibrations in the band gap.

[0034] like Figure 5 As shown, it is the forward transmission curve of this embodiment. After finite element verification, when the vibration propagates forward in the superstructure beam, the transmission rate in the band gap is less than zero, indicating that the vibration in the band gap is attenuated, so that the vibration is difficult to propagate, and it has a good low-bandwidth vibration reduction effect.

[0035] like Figure 6 As shown, it is the reverse transmission curve of this embodiment. After finite element verification, when the vibration propagates in the superstructure beam in the reverse direction, the transmission rate in the band gap is not less than zero, and there is a peak value above 0dB, indicating that there is a resonance peak in the band gap, and the attenuation amplitude is much weaker than the forward propagation.

[0036] like Figure 7 As shown, this is the bending vibration mode of the embodiment whose natural frequency is within the band gap. The vibration mode is obviously asymmetric, with the amplitude at the left end being much larger than the amplitude at the right end, and the natural frequency is within the band gap range, which can affect the transmission characteristics within the band gap.

[0037] like Figure 8 The figure shows the displacement distribution of this embodiment under constant frequency excitation. The excitation frequency is close to the natural frequency, and the vibration can propagate in the reverse direction to the left; it is difficult for the vibration to propagate in the forward direction to the right, and the amplitude is greatly suppressed. This shows that due to the different propagation paths and the existence of asymmetric vibration modes in the band gap, the propagation of vibration in the superstructure beam exhibits non-reciprocity. The vibration with a frequency within the band gap is greatly attenuated in the positive direction and is difficult to propagate, but it is only slightly attenuated in the reverse direction and can propagate. Therefore, the structural beam of the present invention has a unidirectional transmission characteristic.

[0038] Compared with the prior art, the superstructure beam of the present invention has a lower frequency and wider band gap, achieves stronger vibration attenuation capability, and can also realize non-reciprocal transmission of elastic waves. It provides a new idea for the design of superstructure beams, expands the function of superstructures, and has important application value.

[0039] The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementations. All implementation schemes within the scope of the claims shall be subject to the constraints of the present invention.

Claims

1. A superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics, characterized in that: The superstructure beam is a slender uniform cross-section beam with a rectangular cross-section, a cross-section width of b, a thickness of h, a unit cell length, i.e., a lattice constant of a, one unit cell is counted as one period, and multiple unit cells are periodically arranged in one-dimensional direction to form a superstructure beam. One unit cell contains (2n+1) sequentially connected components arranged periodically in one-dimensional direction. Two material periods exist simultaneously in one unit cell, ABCBC constitutes a main period, and BC nested in the main period constitutes an internal period, wherein n is the number of times the internal period BC is repeated, which is a positive integer greater than or equal to 2.

2. The superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics according to claim 1, characterized in that: The primitive cell should be made of at least three different materials, and the Young's modulus and density of different materials are greatly different. Material A is polytetrafluoroethylene, nylon, polypropylene, plexiglass or TPU, material B is aluminum, copper, lead or resin, and material C is steel, aluminum, nickel or tungsten. No repeated materials shall appear in materials A, B and C.

3. The superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics according to claim 1, characterized in that: When there are five components, they are respectively a first component (1), a second component (2), a third component (3), a fourth component (4) and a fifth component (5) arranged in sequence, wherein the first component (1) is made of material A and has a length a1, the second component (2) and the fourth component (4) are made of material B and have a length a2, and the third component (3) and the fifth component (5) are made of material C and have a length a3.

4. The superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics according to claim 1, characterized in that: The interfaces of the components in the primitive cell are fixedly connected by an adhesive.

5. The superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics according to claim 1, characterized in that: The superstructure beam has a first-order asymmetric vibration mode at a simply supported boundary and a fixed supported boundary, and its natural frequency is located within the band gap.

6. The superstructure beam with low broadband vibration reduction and unidirectional transmission characteristics according to claim 1, characterized in that: In the elastic wave propagation path of the superstructure beam, the sequence of ABCBC is called forward propagation, and CBCBA is called reverse propagation; When the superstructure beam is excited in the middle in the vertical direction and the excitation frequency is within the band gap, the elastic waves propagate to the two ends of the superstructure beam respectively. Due to the asymmetry of the structure, the propagation characteristics in the two directions are also different, showing non-reciprocity; when the elastic wave propagates in the forward direction, since the structure is arranged periodically, the elastic wave with a frequency within the band gap will be affected by Bragg scattering, and strong destructive interference will be generated after scattering. The average attenuation rate within the length of 6 primitive cells reaches more than 92%, so that the elastic wave is difficult to propagate, and a good vibration reduction effect is achieved; when the elastic wave propagates in the reverse direction, due to the change in the propagation path, its transmission characteristics are also changed accordingly, and the elastic wave with a frequency within the band gap is affected by Bragg scattering, and only elastic waves of some frequencies undergo weak destructive interference, and the attenuation degree is much weaker than that of the forward propagation, so it can propagate in the reverse direction.

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