A non-periodic layered vibration isolator and its design method
By designing a non-periodic layered vibration isolator, connecting rubber and metal layers of different thicknesses in series, and optimizing the isolator parameters, the problem of standing wave effect in the high-frequency range of the periodic vibration isolator was solved, achieving a wider range of mid-to-high frequency vibration isolation effects and noise reduction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-01-06
- Publication Date
- 2026-05-26
AI Technical Summary
Existing periodic vibration isolators exhibit significant bandgap characteristics in the mid-to-high frequency bands, and the standing wave effect makes it difficult to eliminate vibration peaks, thus limiting their vibration isolation effect in the mid-to-high frequency range.
A non-periodic layered vibration isolator is designed by connecting multiple sets of rubber and metal layers of different thicknesses in series. The non-periodic unit structure reduces the standing wave effect and widens the mid-to-high frequency filtering range. The parameters of the vibration isolator are optimized by analyzing the dynamic stiffness matrix and transfer matrix.
It broadens the wave-blocking frequency range of the vibration isolator, reduces the peak value of mid-to-high frequency vibration, reduces noise radiation, and has a simple structure and compact space.
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Figure CN116070428B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of vibration isolation and damping technology, and relates to a non-periodic layered vibration isolator and its design method. Background Technology
[0002] Vibration isolators are one of the most effective devices for reducing vibration and sound radiation in mechanical structures. Different mechanical structures have different frequency characteristics of their vibration sources, and often the suppression effect of a single type of vibration isolator varies depending on the application. Traditional vibration isolator technology offers wide-band vibration reduction, but lacks filtering characteristics specific to a particular frequency range. When the vibration frequency of the mechanical source is high, vibration peaks may occur in the mid-to-high frequency range due to insufficient stiffness of the supporting structure and the wave effect of the isolator itself, thus degrading the vibration isolation effect of traditional vibration isolators. Therefore, engineering applications require a method that can improve the mid-to-high frequency vibration isolation effect and effectively suppress vibrations at different mechanical sources.
[0003] In recent years, the rise of phonon crystal theory in condensed matter physics has provided new methods for controlling mechanical vibration waves. During the structural design phase, introducing periodic impedance mismatches into the structure can lead to the reinforcement of incident, reflected, and transmitted elastic waves within certain frequency ranges, generating passband and stopband phenomena for sound waves. Elastic waves can propagate within the passband, but cannot propagate within the stopband (also known as the bandgap). The bandgap characteristics of periodic structures are related to the size and material parameters of individual periodic units; therefore, the attenuation of vibration waves at different frequencies can be achieved by designing the size and material parameters of the periodic structure. Periodic structures offer a new approach to enhancing the vibration isolation performance of traditional vibration isolators.
[0004] In recent years, combining traditional vibration isolation technology with the concept of periodic structure vibration reduction, some novel vibration isolator devices and design methods containing periodic structures have been proposed. Relevant literature includes: Chinese patent document CN201320865573.1U discloses a mechanical vibration isolation platform with a periodic structure effect, achieving mechanical filtering of the isolator through multi-layer mass units and elastic units, and enhancing the damping of the isolator through damping filler and comb-shaped damping materials. Chinese patent document 201610939527.X discloses a metamaterial vibration isolator, using polymer or rubber materials as the base material, with the vibration isolation components being artificially designed periodic honeycomb-shaped periodic structures. Chinese patent document 201510872673.0 discloses a periodic cavity type low-frequency bandgap vibration isolator and its preparation method, containing a thin plate with small bending rigidity and an annular cavity with large bending rigidity and connecting parts as periodic units.
[0005] Current periodic vibration isolators possess bandgap characteristics in the mid-to-high frequency range, exhibiting a more significant attenuation effect on mid-to-high frequency vibrations compared to traditional isolators. While effective at suppressing mid-to-high frequency vibrations in flexible support foundations, current periodic isolators struggle to eliminate vibrations caused by the isolator's wave effect. To reduce the peak vibration caused by the isolator's wave effect, a non-periodic layered vibration isolator structure was designed. This non-periodic layered vibration isolator connects multiple unit structures composed of rubber and metal layers of varying thicknesses in series, effectively improving mid-to-high frequency vibration isolation and reducing peak vibrations caused by flexible foundation vibrations and wave effects. Summary of the Invention
[0006] Technical problems to be solved
[0007] To overcome the shortcomings of existing technologies, this invention proposes an aperiodic layered vibration isolator and its design method, which solves the problem that current periodic vibration isolators have significant standing wave effects and limited vibration isolation effects in the mid-to-high frequency range. This invention provides an aperiodic layered vibration isolator that improves the vibration damping characteristics of the isolator through a periodic structure, reduces the standing wave effect of the isolator by utilizing aperiodic units, and widens the filtering frequency range in the mid-to-high frequency range.
[0008] Technical solution
[0009] A design method for an aperiodic layered vibration isolator, characterized in that: the aperiodic layered vibration isolator includes... N A series of aperiodic unit structures are connected together. Each group of aperiodic unit structures includes a rubber layer and a metal layer. The design steps are as follows:
[0010] Step 1: Determine the dynamic stiffness matrix of each metal layer and rubber layer to obtain the transfer matrix of the vibration isolator's metal and rubber layers:
[0011] The N The thickness of each metal layer is HM i The cross-sectional area of the metal layer is A M The material density of the metal layer is ρ M The Young's modulus of the metal layer is E M ;
[0012] No. i The dynamic stiffness matrix of the metal layer is KM :
[0013] in, k M The longitudinal wave number of the metal layer, k M The expression is , ω Angular frequency;
[0014] The N The thickness of each layer of rubber is HR i The cross-sectional area of the rubber layer is A R The material density of the rubber layer is ρ R The Young's modulus of the rubber layer material is E R ;
[0015] No. i The dynamic stiffness matrix of the rubber layer is KR i :
[0016]
[0017] in, k R The longitudinal wave number of the rubber layer. k R The expression is , ω Angular frequency;
[0018] Step 2: Determine the total transfer matrix of the aperiodic layered vibration isolator, and obtain its wave propagation characteristics through eigenvalue analysis:
[0019] No. i The transfer matrix of the metal layer is TM i :
[0020]
[0021] No. i The transfer matrix of the rubber layer is TR i :
[0022]
[0023] Total transfer matrix of non-periodic layered vibration isolator T Transfer matrix to each unit TM i and TR i The product of:
[0024] ;
[0025] The eigenvalues of the wave transfer matrix T of the aperiodic layered vibration isolator are λ ( f Wave propagation constantα ( f ) is defined as:
[0026]
[0027] Where Re is the symbol for the real part;
[0028] Step 3: Adjust the thickness of the metal layer of the non-periodic layered vibration isolator HM i and rubber layer thickness HR i Avoid using mid-to-high frequency bands ( f 1, f 2) Within Hz α ( f Design parameters that are 0 or close to 0 are selected in the mid-to-high frequency band. f 1, f 2) Wave propagation constant of non-periodic layered vibration isolators within Hz α ( f () greater than the average propagation constant of the wave in that frequency band α The design parameters are set to 0 to meet the vibration isolation requirements in the mid-to-high frequency range.
[0029] The N ≥2.
[0030] An aperiodic layered vibration isolator obtained by the design method of the aforementioned aperiodic layered vibration isolator is characterized by: the aperiodic layered vibration isolator... N In the aperiodic unit structure, the rubber and metal layers of each unit have different thicknesses, and the thickness of each metal layer is... HM i (i=1,2,…,N), the thickness of each rubber layer is HR i (i=1,2,…,N).
[0031] The geometry of the non-periodic layered vibration isolator is either a block structure or a ring structure.
[0032] The cross-sectional geometry of the metal layer and the rubber layer includes, but is not limited to, cylindrical, matrix, and hexagonal shapes.
[0033] The aforementioned N The rubber layer material includes, but is not limited to, nitrile rubber.
[0034] The aforementioned N The metal layer material includes, but is not limited to, iron and aluminum.
[0035] The aforementioned N Layered metal structure and N The layers of rubber are bonded together through vulcanization.
[0036] Beneficial effects
[0037] This invention proposes an aperiodic layered vibration isolator and its design method. The aperiodic layered vibration isolator includes... N A series of multiple aperiodic unit structures are connected in series, with each group of aperiodic unit structures including a rubber layer 1 and a metal layer 2. The design method of the aperiodic layered vibration isolator includes the following steps: determining the dynamic element stiffness matrix of each metal layer and rubber layer to obtain the unit transfer matrix of the vibration isolator; determining the overall transfer matrix of the aperiodic layered vibration isolator. N The wave propagation characteristics of the isolator are obtained by multiplying the transfer matrices of each unit and analyzing the eigenvalues of the transfer matrix of the isolator; the thickness of each metal layer of the aperiodic layered isolator is adjusted. HM i and rubber layer thickness HR i The design parameters selected cover a wide range of wave-blocking frequencies. This invention improves upon existing periodic vibration isolators, broadening their wave-blocking frequency range. The layered structure also features simple design and compact space.
[0038] The beneficial effects of this invention are as follows: 1. This invention further optimizes existing periodic vibration isolators, broadens the damping frequency range of periodic vibration isolators, and reduces high-frequency vibrations that are difficult to isolate due to resonance within the isolator and resonance in the flexible foundation support structure of the isolator, thereby reducing the noise radiation of the structure. 2. The non-periodic layered vibration isolator of this invention has the characteristics of simple structural design and compact space. Attached Figure Description
[0039] Figure 1 It is a cylindrical, non-periodic, layered vibration isolator.
[0040] Figure 2 It is a block-shaped, non-periodic, layered vibration isolator.
[0041] Figure 3 It is a circular non-periodic layered vibration isolator.
[0042] Figure 4 This is a comparison of the transfer constant curves of non-periodic layered vibration isolators and periodic layered vibration isolators.
[0043] Explanation of reference numerals in the attached figures: 1. Cylindrical metal layer; 2. Cylindrical rubber layer; 3. Square metal layer; 4. Square rubber layer; 5. Circular rubber layer; 6. Circular metal layer. Detailed Implementation
[0044] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:
[0045] Specific implementation method one: Combining Figure 1This invention discloses a cylindrical aperiodic layered vibration isolator comprising four sets of aperiodic units connected in series. Each set of aperiodic units includes a metal cylindrical layer 1 and a rubber cylindrical layer 2. The rubber layer and the metal layer are connected by a vulcanization process. The cylindrical aperiodic layered vibration isolator and its design method are characterized by the following specific steps:
[0046] Step 1: Confirm N Design parameters for the N=4 metal layers: N The thickness of each metal layer is HM i The cross-sectional area of the metal layer is A M The material density of the metal layer is ρ M The Young's modulus of the metal layer is E M ;
[0047] Step 2: Confirm N Design parameters for the rubber layer: N The thickness of each layer of rubber is HR i The cross-sectional area of the rubber layer is A R The material density of the rubber layer is ρ R The Young's modulus of the rubber layer material is E R ;
[0048] Step 3: Confirm N Dynamic stiffness matrix of the metal layer: i The dynamic element stiffness matrix of the layered metal is KM i :
[0049] in, k M The longitudinal wave number of the metal layer, k M The expression is , ω ω is the angular frequency.
[0050] Step 4: Confirm N Dynamic stiffness matrix of the rubber layer: i The dynamic element stiffness matrix of the rubber layer is KR i :
[0051]
[0052] in, k RThe longitudinal wave number of the rubber layer. k R The expression is , ω ω is the angular frequency.
[0053] Step 5: Confirm N Transfer matrix of the first metal layer: i The transfer matrix of the metal layer is TM i :
[0054]
[0055] Step 6: Confirm N Transfer matrix of the rubber layer: i The transfer matrix of the rubber layer is TR i :
[0056]
[0057] Step 7: Determine the total transfer matrix of the aperiodic layered vibration isolator: Total transfer matrix of the aperiodic layered vibration isolator T Transfer matrix to each unit TM i and TR i The product of:
[0058]
[0059] Step 8: Calculate the wave propagation characteristics of the aperiodic layered vibration isolator: The eigenvalues of the wave transfer matrix T of the aperiodic layered vibration isolator are... λ ( f Wave propagation constant α ( f ) is defined as:
[0060]
[0061] Where Re is the symbol for taking the real part.
[0062] Step 9: Adjust the thickness of the metal layer of the non-periodic layered vibration isolator HM i and rubber layer thickness HR i Avoid using mid-to-high frequency bands ( f 1, f 2) Within Hz α ( f Design parameters that are 0 or close to 0 are selected in the mid-to-high frequency band. f 1, f 2) Wave propagation constant of non-periodic layered vibration isolators within Hzα ( f (greater than the propagation constant) α The design parameters are set to 0 to meet the vibration isolation requirements in the mid-to-high frequency range.
[0063] Specific Implementation Method Two: Combining Figure 2 This invention provides a block-shaped aperiodic layered vibration isolator comprising three sets of aperiodic units connected in series. Each set of aperiodic units includes a metal block layer 3 and a rubber block layer 4. The rubber layer and the metal layer are connected by vulcanization. The method for determining the design parameters of the rubber layer and the metal layer is the same as steps 1-9 of specific embodiment one.
[0064] Specific implementation method three: Combining Figure 3 This invention provides a ring-shaped aperiodic layered vibration isolator comprising two sets of aperiodic units connected in series. Each set of aperiodic units includes a rubber ring layer 5 and a metal ring layer 6. The rubber and metal layers are connected by vulcanization. The method for determining the design parameters of the rubber and metal layers is the same as steps 1-9 of specific embodiment one.
[0065] To further illustrate the effectiveness of this method, a cylindrical aperiodic layered vibration isolator and a cylindrical periodic layered vibration isolator are analyzed, and their filtering characteristics are compared. The wave propagation constants of the cylindrical aperiodic layered vibration isolator and the cylindrical periodic layered vibration isolator are also discussed. α ( f The calculation results are as follows: Figure 4 As shown. Figure 4 Calculation results show that cylindrical aperiodic layered vibration isolators, compared to cylindrical periodic layered vibration isolators, broaden the blocking frequency range in the mid-to-high frequency band (1000Hz, 5000Hz). In other words, cylindrical aperiodic layered vibration isolators... α ( f In the mid-to-high frequency range (1000Hz, 5000Hz), the value equal to or close to 0 is significantly improved compared to the cylindrical periodic layered vibration isolator.
Claims
1. A design method for a non-periodic layered vibration isolator, characterized in that: Non-periodic layered vibration isolators include N A series of aperiodic unit structures are connected together. Each group of aperiodic unit structures includes a rubber layer and a metal layer. The design steps are as follows: Step 1: Determine the dynamic stiffness matrix of each metal layer and rubber layer to obtain the transfer matrix of the vibration isolator's metal and rubber layers: The N The thickness of each metal layer is HM i The cross-sectional area of the metal layer is A M The material density of the metal layer is ρ M The Young's modulus of the metal layer is E M ; No. i The dynamic stiffness matrix of the metal layer is KM : in, k M The longitudinal wave number of the metal layer, k M The expression is , ω Angular frequency; The N The thickness of each layer of rubber is HR i The cross-sectional area of the rubber layer is A R The material density of the rubber layer is ρ R The Young's modulus of the rubber layer material is E R ; No. i The dynamic stiffness matrix of the rubber layer is KR i : in, k R The longitudinal wave number of the rubber layer. k R The expression is , ω Angular frequency; Step 2: Determine the total transfer matrix of the aperiodic layered vibration isolator, and obtain its wave propagation characteristics through eigenvalue analysis: No. i The transfer matrix of the metal layer is TM i : No. i The transfer matrix of the rubber layer is TR i : Total transfer matrix of non-periodic layered vibration isolator T Transfer matrix to each unit TM i and TR i The product of: ； The eigenvalues of the wave transfer matrix T of the aperiodic layered vibration isolator are λ ( f Wave propagation constant α ( f ) is defined as: Where Re is the symbol for the real part; Step 3: Adjust the thickness of the metal layer of the non-periodic layered vibration isolator HM i and rubber layer thickness HR i Avoid using mid-to-high frequency bands ( f 1, f 2) Within Hz α ( f Design parameters that are 0 or close to 0 are selected in the mid-to-high frequency band. f 1, f 2) Wave propagation constant of non-periodic layered vibration isolators within Hz α ( f () greater than the average propagation constant of the wave in this frequency band α The design parameters are set to 0 to meet the vibration isolation requirements in the mid-to-high frequency range.
2. The design method of the non-periodic layered vibration isolator according to claim 1, characterized in that: The N ≥2.
3. An aperiodic layered vibration isolator obtained by the design method of the aperiodic layered vibration isolator according to claim 1 or 2, characterized in that: Non-periodic layered vibration isolators N In the aperiodic unit structure, the rubber and metal layers of each unit have different thicknesses, and the thickness of each metal layer is... HM i Let i = 1, 2, ..., N, and the thickness of each rubber layer be... HR i , i=1,2,…,N.
4. The non-periodic layered vibration isolator according to claim 3, characterized in that: The geometry of the non-periodic layered vibration isolator is either a block structure or a ring structure.
5. The non-periodic layered vibration isolator according to claim 3, characterized in that: The cross-sectional geometry of the metal layer and the rubber layer includes cylindrical, matrix, and hexagonal shapes.
6. The non-periodic layered vibration isolator according to claim 3, characterized in that: The aforementioned N The rubber layer material includes nitrile rubber.
7. The non-periodic layered vibration isolator according to claim 3, characterized in that: The aforementioned N The metal layer materials include iron and aluminum.
8. The non-periodic layered vibration isolator according to claim 3, characterized in that: The aforementioned N Layered metal structure and N The layers of rubber are bonded together through vulcanization.