CN111985135B - Board shell super structure integrating bearing and vibration isolation and design method thereof - Google Patents
Board shell super structure integrating bearing and vibration isolation and design method thereof Download PDFInfo
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Abstract
The invention discloses a plate-shell super structure integrating bearing and vibration isolation and a design method thereof, belonging to the technical field of plate-shell vibration isolation. Comprises a plate shell and a plurality of microstructure components; the microstructure component is a block structure with a uniform cross section, the cross section contour line of the microstructure component consists of a bottom edge and two arcsine-like function curves, and the intersection point of the two arcsine-like function curves forms a beak tip; the bottom surface of the microstructure component is connected with the board shell; and a plurality of microstructure components are periodically arranged to form an array for separating the vibration source and the protected object. When the elastic wave excited by the vibration source propagates to the periphery of the array from any direction along the plate shell, the microstructure components bend and vibrate in a torsional mode under the influence of the elastic wave, and the microstructure can exert force and moment on the plate shell, so that the propagation of the elastic wave in the plate shell is restrained, and isolation of the incident elastic wave in any direction of a high frequency band in the plate shell is realized. Simple structure, processing is convenient, can keep apart protected object and vibration source simultaneously, has good bearing and vibration isolation ability concurrently.
Description
Technical Field
The invention belongs to the technical field of plate shell vibration isolation, and particularly relates to a plate shell super structure integrating bearing and vibration isolation and a design method thereof.
Background
The plate and shell structure is widely used for fixing various instruments and equipment in the fields of aerospace, civil engineering, vehicles, ships and the like. In practical engineering, some devices generate impact and vibration during operation, and the impact and vibration excite elastic waves in the plate shell, and the elastic waves propagate to other devices in the plate to cause other devices to fail or destroy. Thus, vibration isolation of specific areas in the panel housing structure is an important issue.
The existing vibration isolation technology is classified into passive vibration isolation (external power supply is not required) and active vibration isolation (external power supply is required) according to whether the vibration isolation device requires external power supply. The passive vibration isolation means that a spring damping vibration isolator is designed for the protected object, and the energy transmitted from a vibration source is absorbed, so that the vibration of the protected object is reduced; the active vibration isolation technology utilizes an active control strategy to enable the vibration isolator to have broadband vibration isolation characteristics by actively adjusting parameters such as rigidity, damping and the like.
However, the existing vibration isolator has the following disadvantages: 1) The existing vibration isolator is large in volume and large in additional mass, and is not beneficial to miniaturization and light weight of the vibration isolator; 2) The damping materials of the existing vibration isolator are mostly rubber, the Young modulus of the rubber materials is 4 to 5 orders of magnitude lower than that of metal materials such as 304 steel, and the like, so that the damping vibration isolator is low in rigidity, large in deformation and low in bearing capacity; 3) The existing damping vibration isolator has a complex structure, is different from a bearing structure (formed by processing metals such as steel, aluminum and the like) in material, and has large integrated processing difficulty due to the design of separating the vibration isolating structure from the bearing structure; 4) The rubber can be aged under the influence of mechanical stress, light, heat and the like, and cracks, softening, stickiness and the like are generated, so that the vibration isolation effect of the damping vibration isolator is influenced; 5) The geometric parameters, elastic rigidity, damping characteristics and the like of the conventional vibration isolator cannot be changed once designed, and when the protected object is changed, the whole vibration isolator needs to be redesigned, so that the use cost is high.
Disclosure of Invention
In order to solve the existing problems, the invention aims to provide a board shell super structure with integrated bearing and vibration isolation and a design method thereof, which have the advantages of simple structure, convenient processing, capability of isolating a protected object and a vibration source and good bearing and vibration isolation capability.
The invention is realized by the following technical scheme:
the invention discloses a bearing vibration isolation integrated plate shell super structure, which comprises a plate shell and a plurality of microstructure components; the microstructure component is a block structure with a uniform cross section, the cross section contour line of the microstructure component consists of a bottom edge and two arcsine-like function curves, and the intersection point of the two arcsine-like function curves forms a beak tip; the bottom surface of the microstructure component is connected with the board shell; and a plurality of microstructure components are periodically arranged to form an array for separating a vibration source and a protected object.
Preferably, the plate shell and the microstructure component are made of the same material and are integrally formed.
Preferably, the distance from the array to the vibration source or protected object is greater than the wavelength of the vibration source elastic wave.
Preferably, the beak tips of the microstructure elements face away from the vibration source.
Preferably, the expressions of the two arcsine-like function curves in the microstructure element cross-section are:
wherein a is the horizontal distance from the midpoint of the bottom edge of the microstructure component to the beak tip, and the value is 1/2-1 of the wavelength of the vibration source elastic wave; b is the height of the microstructure component, and the value is 1/2-1 of the wavelength of the vibration source elastic wave; m is a constant greater than zero, ε is a function of the length t of the bottom edge of the microstructure element (ε=t/a) m ) S is defined as [0, a]The value of t is 1/4-1/2 of the wavelength of the vibration source elastic wave.
Preferably, the array forms a plurality of non-communication areas, and the vibration source and the protected object are respectively arranged in the non-communication areas.
The invention discloses a design method of the bearing vibration isolation integrated plate shell super structure, which comprises the following steps:
step 1: determining the vibration frequency f of a vibration source needing to be isolated;
step 2: establishing a plate shell super-structure finite element model comprising a plate shell, a microstructure component and a reflected wave absorption layer;
step 3: simulating the plate-shell super-structure finite element model established in the step 2 by using a three-dimensional entity unit;
step 4: applying bending waves with different incident angles and frequency f at the vibration source;
step 5: scanning the interval H and different incidence angles of adjacent microstructure components in the array, and calculating the transmittance of different intervals H and different incidence directions;
step 6: calculating the average transmittance of bending waves corresponding to different intervals H according to the transmittance obtained in the step 5, and drawing an interval-average transmittance relation curve;
step 7: and (3) selecting an integer value of the interval from the valley region in the interval-average transmittance relation curve obtained in the step (6) as an arrangement interval H of microstructure components in the array, and completing the design of the plate-shell super structure with integrated bearing and vibration isolation.
Preferably, in step 1, the plate shell super-structure finite element model is built according to the material density, young's modulus and Poisson's ratio of the plate shell and the microstructure elements.
Preferably, in step 1, when building the plate-shell super-structure finite element model, periodic boundary conditions are added at two sides H/2 of one microstructure component.
Preferably, in step 7, an integer value of the interval is selected as the arrangement interval H of the microstructure elements in the array in the middle of the valley region in the interval-average transmittance relation.
Compared with the prior art, the invention has the following beneficial technical effects:
according to the plate shell super structure with integrated bearing and vibration isolation, the vibration source and the protected object are separated through the periodic array structure formed by the microstructure components, when elastic waves excited by the vibration source propagate to the periphery of the periodic array along the plate shell from any direction, the microstructure components bend and vibrate in a torsional mode under the influence of the elastic waves, and according to the Darby principle, the microstructure can exert force and moment on the plate shell, so that propagation of the elastic waves in the plate shell is restrained, and isolation of incident elastic waves in any direction of a high frequency band in the plate shell is realized. The array protection area is adjusted according to specific protected equipment, the number and the enveloping area of the microstructure components of the array are adjusted, the array formed by the microstructure components can protect a plurality of objects, isolate a plurality of vibration sources, isolate the protected objects and the vibration sources at the same time, and can be suitable for various structures and has wide application occasions. The design cost is reduced. The microstructure components are of a uniform-section block structure, the volume is small, the weight is light, the arrangement interval of the components in the periodic array is large, the overall structure does not influence the distribution of other devices on the plate shell, and excessive additional load is not added; the microstructure components adopt non-damping materials which are the same as the bearing structure, and have the characteristics of high rigidity, no large deformation, long service life and the like, so that the defects caused by the existing damping materials such as rubber and the like are avoided; the micro-structural component is directly attached to the plate shell, the structure is simple, the processing is convenient, the strength is high, the reliability is high, compared with vibration isolation forms such as drilling holes, the strength of the plate shell of the attached micro-structural component array is not affected, and the plate shell has the bearing and vibration isolation capabilities.
Further, the microstructure components are made of the same material as the plate shell and are integrally formed, and the plate shell is simple to process, high in strength and high in reliability.
Further, the array forms a plurality of non-communicated areas, the vibration source and the protected object are respectively arranged in the non-communicated areas, so that the vibration isolation effect is all-dimensional, and the vibration isolation effect is good.
Further, the distance from the array to the vibration source/the protected object is larger than the wavelength, so that enough space is ensured for placing the vibration source and the protected object, meanwhile, elastic waves penetrating through the array are reduced, and the vibration isolation effect is improved.
Further, the beak tip of the component faces away from the vibration source (toward the protected object), so that the vibration amplitude of the protected object near the design frequency can be further reduced.
The invention discloses a design method of the bearing vibration isolation integrated plate shell super structure, which designs and simulates a microstructure component array and a plate shell through a finite element method. When the microstructure components and the array thereof are designed, calculated and optimized, a parameterized modeling method is adopted, and simulation results of different geometric dimensions and different materials can be obtained only by scanning design parameters.
Furthermore, when the plate shell super-structure finite element model is built, periodic boundary conditions are added on two sides of a microstructure component corresponding to the plate shell structure, so that the function of simulating the whole vibration isolation bearing integrated plate shell super-structure by using the microstructure component and the corresponding plate shell structure is realized, and the calculation efficiency is greatly improved. When the interval design is carried out on the microstructure element array elements, the average transmissivity of each angle is used as a measurement index, and the isolation capability of the microstructure element array on incident bending waves in all directions is improved.
Further, when the interval value is determined by the valley region in the interval-average transmittance relation curve, the middle part of the valley region is selected, so that the two sides of the selected numerical value are ensured to be respectively left with a margin, and the influence of factors such as processing errors, working frequency changes and the like in practical application is reduced.
Drawings
FIG. 1 is a schematic diagram of the overall structure of a microstructure component of the present invention;
FIG. 2 is a schematic side view of a microstructure component of the present invention;
FIG. 3 is a schematic diagram of a periodically arranged array of microstructure elements according to the present invention;
FIG. 4 is a schematic diagram of a linear array arrangement of microstructure elements according to the present invention;
FIG. 5 is a graph of average transmittance of a microstructure element linear array superstructure of the present invention for incident waves at different angles;
FIG. 6 is a graph of the amplitude field distribution of a 6kHz point source acting outside of a quadrilateral array superstructure;
FIG. 7 is a graph of the amplitude field distribution of a 6kHz point source acting within a quadrilateral array superstructure;
FIG. 8 is a graph of the amplitude field distribution of a point source operating at 6kHz inside a double circular array superstructure;
FIG. 9 is a plot of frequency response of center point relative displacement amplitude for a protected region of a double circular array superstructure;
FIG. 10 is a plot of frequency response versus amplitude of center point relative displacement for a protected region of a dual circular array superstructure for different beak tip orientations.
In the figure: 1-plate shell, 2-microstructure component, 3-array, 4-vibration source and 5-protected object.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings and specific examples, which are given by way of illustration of the invention and not by way of limitation:
the invention relates to a bearing and vibration isolation integrated plate shell super structure which comprises a plate shell 1 and a plurality of microstructure components 2; the microstructure component 2 is of a uniform section block structure, the section contour line of the microstructure component consists of a bottom edge and two arcsine-like function curves, and the intersection point of the two arcsine-like function curves forms a beak tip; the bottom surface of the microstructure component 2 is connected with the board shell 1, preferably, the board shell 1 and the microstructure component 2 are made of the same material, and can be integrally formed by 3D printing. The microstructure elements 2 are periodically arranged to form an array 3, and the vibration source 4 and the protected object 5 are separated.
The length, width and thickness of the plate shell 1 are L, W and h respectively as shown in fig. 4, and the material is determined by working conditions.
The microstructure component 2 has a thickness H as shown in figures 1 and 2 0 1/15 to 1/10 wavelength is taken. The cross-sectional profile is formed by two arcsine-like function curves and a bottom edge, the abscissa of the arcsine-like function curve points is given by formula (1),
x＝s±ε(a-s) m
wherein a represents the horizontal distance from the midpoint of the bottom edge of the microstructure component to the beak tip, and the wavelength is 1/2 to 1 time; b represents the height of the microstructure component, and takes 1/2 to 1 times of wavelength; m is a constant greater than zero; epsilon is a function of the length t of the bottom edge of the microstructure element (epsilon=t/a) m ) T is 1/4 to 1/2 wavelength; s is an independent variable, the definition domain is [0, a]. The structural parameters of the components are determined through the wavelength of the elastic wave, so that the design has wide adaptability; the component 2 determined in the above-described manner is capable of producing a suppressing effect on the propagation of elasticity, which lays a foundation for the subsequent determination of H in the array 3.
As shown in fig. 3 and 4, the microstructure elements 2 are arranged in a linear array at intervals by taking H as a space, the beak tips face the protected object 5, and the microstructure elements 2 and the plate shell 1 are connected in a mode of 3D printing integrated formation or gluing and the like; the array 3 formed by the microstructure elements 2 divides the plate shell 1 into two or more areas, including a vibration source 4 placement area and a protected object 5 placement area, and the number of the microstructure elements 2 and the shape of the array 3 are based on the fact that the vibration source 4 and the protected object 5 can be separated. As shown in fig. 5, the circular array is arranged at intervals corresponding to the distance between the center points of the bottom surfaces of the two microstructure elements 2. When vibration is generated by the vibration source 4 to excite the elastic wave, the elastic wave propagates to the array 3 formed by the microstructure elements 2 to cause the microstructure elements 2 to generate motion, and the microstructure elements 2 apply force and moment to the plate shell 1 to resist the motion under the action of inertia, so that the elastic wave is reduced, and vibration isolation is realized. The distance of the array 3 to the protected object/vibration source is larger than the wavelength, and the above-mentioned design parameter H is determined by the design method.
The following explains the structure and design method of the board-and-shell super structure with integrated bearing and vibration isolation according to the present invention with specific embodiments:
as shown in fig. 6 and 7, the length, width and thickness of the plate shell 1 of the quadrangular array super structure are l=600 mm, w=600 mm and h=0.95 mm respectively; as shown in fig. 8, the length, width and thickness of the plate shell 1 of the double circular array super structure are l=800 mm, w=600 mm and h=0.95 mm respectively; the microstructure component 2 and the plate shell 1 are integrally formed, the material is 304 steel, and the density, young modulus and Poisson ratio of the material are 7900kg/m3, 200GPa and 0.3 respectively; the bending wave with the frequency of 6kHz has the wavelength of 38.8mm in the plate shell 1, and the geometric parameters of the microstructure component 2 are respectively a=20mm, b=20mm and H 0 ＝3mm，t＝10mm，m＝1；
The design method comprises the following steps:
a finite element model is built by adopting COMSOL Multiphysics software, and the model comprises a plate shell 1, a microstructure component 2 and a reflected wave absorption layer. The microstructure element 2 coordinate system shown in fig. 1 coincides with the software default coordinate system; the length of the plate shell 1 is L, the width is H, and the thickness is H; the geometry of the microstructure element 2 is as described above; the reflected wave absorption layers are positioned at two ends of the plate shell 1, the length is 50mm (larger than the wavelength) of the end face of the plate shell 1, and the width and the thickness are H and H respectively; the microstructure component 2 is positioned in the center of the upper surface of the plate shell 1; the reflected wave absorption layer is positioned on the plate shell 1; the plate shell 1 and the microstructure component 2 are divided by adopting a combination of a free triangle mesh and a mapping mesh, and the reflection wave absorption layer is divided by adopting a sweep mesh; endowing the whole model material with properties including density, young's modulus and Poisson's ratio; setting frequency domain analysis research, and setting periodic boundary conditions on a plane of the plate shell 1 perpendicular to the y direction; adopting COMSOL Multiphysics software, generating bending waves with different incidence directions, wherein the amplitude of the bending waves is 1N/m < 2 >, and the frequency of the bending waves is 6kHz at the vibration source 4 by the plate shell 1; adding parameterized scanning of structural parameters H of the microstructure element array 3, and calculating the transmittance of bending waves at different angles of incidence under different H; calculating the average transmittance of the bending wave under different parameters H by using the transmittance of the bending wave under different angles of incidence under different parameters H, as shown in FIG. 5; the intermediate integer h=25 mm is selected from the average transmittance valleys as the gap-preferred structural parameter for periodic arrangement of microstructure elements. Thus, the design of the parameters of the microstructure component array is completed.
In COMSOL Multiphysics, the designed plate-shell superstructure is simulated, and the microstructure elements 2 are arranged in an array of different shapes such as quadrangles and circles at a pitch h=25 mm to form a closed area, and the vibration source 4 and the protected object 5 are separated, as shown in fig. 6, 7 and 8. The geometry of the plate shell 1 is as described above, and the length, width and thickness are respectively L=600 mm, W=600 mm and h=0.95 mm; the periphery of the plate shell 1 is provided with a reflected wave absorbing layer, and the boundary of the plate shell is 50mm inwards. Applying amplitude of 1N/m at vibration source 4 2 And calculating displacement amplitude field by micro-vibration simple harmonic force with frequency of 6kHz, wherein the distribution condition is as follows:
fig. 6 is a graph showing the amplitude field distribution of the point source acting at 6kHz outside the microstructure element quadrilateral array superstructure, the minimum distance from the point source to the array being 100mm, and it can be seen that when the elastic wave excited by the vibration source 4 propagates along the plate shell 1 to the periodic array superstructure formed by the microstructure elements 2, the elastic wave is blocked by the array 3 formed by the microstructure elements 2 and cannot enter the area where the protected object 5 is located. Fig. 7 is a diagram showing an amplitude field distribution of a point source acting at 6kHz inside a microstructure of the microstructure element quadrilateral array, wherein the shortest distance from the vibration source to the array is 68mm, and it can be seen that when an elastic wave excited by the vibration source 4 propagates to the microstructure element array 3 along the plate shell, the elastic wave is limited in an isolation region and cannot enter the region where the protected object 5 is located.
Fig. 8 is a graph showing the amplitude field distribution of a 6kHz point source acting inside a microstructure element double circular array superstructure, wherein the shortest distance from the vibration source to the array is 42.7mm, and it can be seen that the elastic wave excited by the vibration source 4 is confined in an isolation region by the array 3 composed of microstructure elements 2. The relationship between the relative displacement amplitude of the center point of the microstructure and the vibration source frequency is calculated by adopting COMSOL Multiphysics software to change the vibration frequency of the vibration source 4 in fig. 8, and the result is shown in fig. 9, wherein the relative displacement amplitude of the microstructure component array is far smaller than that of the microstructure component array. The relationship between the relative displacement amplitude and the frequency of the central point of the super structure is calculated by adopting COMSOL Multiphysics software to change the beak tip orientation of the component 2 around the vibration source in fig. 8, and as a result, as shown in fig. 10, it can be found that the beak tip orientation is not obviously different near the design frequency of 6kHz, but in the range of 3 to 5.5kHz, the beak tip faces away from the vibration source 4, and the form of the beak tip facing the protected object 5 obviously reduces the vibration amplitude of the central point, so that the protected object 5 is protected in the process of increasing the vibration source frequency to the design frequency.
By designing the structural parameters of the microstructure elements 2 and the gaps H of the microstructure elements 2 in the array 3, isolation of incident elastic waves in any direction within a wide frequency band of 6.0 to 9.5kHz in the plate shell 1 is realized, and the relative displacement amplitude of a super structure is far smaller than that of a non-super structure. The microstructure components 2 are respectively arranged into a quadrilateral array, a circular array and the like according to the design interval, so that the protected object 5 and the vibration source 4 are isolated, the shape of the array 3 can be adjusted according to the number of the actual protected objects 5 and the vibration source 4, the application occasion is wide, and the design cost is reduced. The maximum geometric dimension of the microstructure component 2 is 20mm, the volume is small, the weight is light, the arrangement interval of the components in the periodic array is large, the unit thickness is only 3mm, and the miniaturization and the light weight of the vibration isolation structure are realized; the micro-structural component 2 and the plate shell 1 can be made of 304 steel, and have the characteristics of high rigidity, no large deformation, long service life and the like, and the micro-structural component 2 is directly attached to the plate shell 1, so that the whole vibration isolation bearing super structure can be manufactured by adopting integrated forming technologies such as 3D printing and the like. The method for designing the component gaps of the array 3 has high calculation efficiency and reduces the design cost; the 3-component interval of the microstructure component array is designed through average transmissivity, so that the isolation capability of the super structure to bending waves in all directions is improved.
It should be noted that the foregoing description is only one of the embodiments of the present invention, and all equivalent modifications of the system described in the present invention are included in the scope of the present invention. Those skilled in the art can substitute the described specific examples in a similar way without departing from the structure of the invention or exceeding the scope of the invention as defined by the claims, all falling within the scope of protection of the invention.
Claims (5)
1. The board shell super structure with integrated bearing and vibration isolation is characterized by comprising a board shell (1) and a plurality of microstructure components (2); the microstructure component (2) is of a uniform section block structure, the section contour line of the microstructure component consists of a bottom edge and two arcsine-like function curves, and the intersection point of the two arcsine-like function curves forms a beak tip; the bottom surface of the microstructure component (2) is connected with the board shell (1); a plurality of microstructure components (2) are periodically arranged to form an array (3) for separating a vibration source (4) and a protected object (5); the plate shell (1) and the microstructure component (2) are made of the same material and are integrally formed; the distance from the array (3) to the vibration source (4) or the protected object (5) is larger than the wavelength of the elastic wave of the vibration source (4); the beak tip of the microstructure component (2) faces away from the vibration source (4); the array (3) forms a plurality of non-communicated areas, and the vibration source (4) and the protected object (5) are respectively arranged in the non-communicated areas;
the expressions of the two arcsine-like function curves in the section of the microstructure component (2) are as follows:
wherein a is the horizontal distance from the midpoint of the bottom edge of the microstructure component (2) to the beak tip, and the value is 1/2-1 of the wavelength of the elastic wave of the vibration source (4); b is the height of the microstructure component (2), and the value is 1/2-1 of the wavelength of the elastic wave of the vibration source (4); m is a constant greater than zero, ε is a function of the bottom edge length t of the microstructure element (2) (ε=t/a) m ) S is defined as [0, a]The value of t is 1/4-1/2 of the wavelength of the elastic wave of the vibration source (4).
2. The design method of the board shell super structure with integrated bearing and vibration isolation as claimed in claim 1, which is characterized by comprising the following steps:
step 1: determining the vibration frequency f of a vibration source (4) to be isolated;
step 2: establishing a plate shell super-structure finite element model comprising a plate shell (1), a microstructure component (2) and a reflected wave absorption layer;
step 3: simulating the plate-shell super-structure finite element model established in the step 2 by using a three-dimensional entity unit;
step 4: applying bending waves with different incident angles and frequency f at the vibration source (4);
step 5: scanning the interval H and different incidence angles of adjacent microstructure components (2) in the array (3), and calculating the transmittance of different intervals H and different incidence directions;
step 6: calculating the average transmittance of bending waves corresponding to different intervals H according to the transmittance obtained in the step 5, and drawing an interval-average transmittance relation curve;
step 7: and (3) selecting an integer value of the interval from the valley region in the interval-average transmittance relation curve obtained in the step (6) as the arrangement interval H of the microstructure components (2) in the array (3), and completing the design of the plate-shell superstructure of the bearing vibration isolation integrated plate-shell superstructure.
3. The method for designing the bearing vibration isolation integrated plate and shell superstructure according to claim 2, wherein in the step 1, the plate and shell superstructure finite element model is built according to the material density, young's modulus and poisson ratio of the plate and shell (1) and the microstructure component (2).
4. The method for designing a plate-shell superstructure with integrated bearing and vibration isolation according to claim 2, wherein in step 1, when a plate-shell superstructure finite element model is built, periodic boundary conditions are added at the positions H/2 on both sides of one microstructure component (2).
5. The method for designing a plate-and-shell superstructure with integrated vibration isolation according to claim 2, wherein in step 7, the integer value of the interval is selected as the arrangement interval H of the microstructure elements (2) in the array (3) at the middle of the valley region in the interval-average transmittance relation curve.
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| CN202010844647.8A CN111985135B (en) | 2020-08-20 | 2020-08-20 | Board shell super structure integrating bearing and vibration isolation and design method thereof |
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| WO2001030528A1 (en) * | 1999-10-25 | 2001-05-03 | Alliedsignal Inc. | Process for manufacturing of brazed multi-channeled structures |
| WO2004008069A1 (en) * | 2002-07-12 | 2004-01-22 | Luka Optoscope Aps | Method and apparatus for optically measuring the topography of nearly planar periodic structures |
| CN111102319A (en) * | 2020-01-17 | 2020-05-05 | 北京理工大学 | Low-frequency vibration isolation superstructure |
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| WO2001030528A1 (en) * | 1999-10-25 | 2001-05-03 | Alliedsignal Inc. | Process for manufacturing of brazed multi-channeled structures |
| WO2004008069A1 (en) * | 2002-07-12 | 2004-01-22 | Luka Optoscope Aps | Method and apparatus for optically measuring the topography of nearly planar periodic structures |
| CN111102319A (en) * | 2020-01-17 | 2020-05-05 | 北京理工大学 | Low-frequency vibration isolation superstructure |
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| 冯岩 ; 杜国君 ; 马玉娇 ; 高崇一 ; .周期性弧形凸起凹凸板等效刚度的研究.机械强度.2020,(01),全文. * |
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