CN120466350B - Quasi-zero stiffness-inertia amplification coupling train floor vibration isolator and design method - Google Patents
Quasi-zero stiffness-inertia amplification coupling train floor vibration isolator and design methodInfo
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- CN120466350B CN120466350B CN202510966653.3A CN202510966653A CN120466350B CN 120466350 B CN120466350 B CN 120466350B CN 202510966653 A CN202510966653 A CN 202510966653A CN 120466350 B CN120466350 B CN 120466350B
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Abstract
The invention discloses a quasi-zero stiffness-inertia amplification coupling train floor vibration isolator and a design method thereof, wherein the vibration isolator comprises one or a plurality of connected unit structures, each unit structure comprises an outer frame, a quasi-zero stiffness subunit and an inertia amplification subunit, the outer frame is used for basic bearing and boundary constraint, the quasi-zero stiffness subunit is used for realizing high static stiffness and low dynamic stiffness characteristics under the no-load-full load working condition, the inertia amplification subunit is used for increasing the effective inertia of an oscillator in the structure under the light condition, the outer frame comprises an upper frame and a lower frame, the lower end of the upper frame is connected with the upper end of the inertia amplification subunit, the lower end of the inertia amplification subunit is connected with the upper end of the quasi-zero stiffness subunit, and the lower end of the quasi-zero stiffness subunit is connected with the lower frame. The invention can improve the low-frequency vibration isolation performance of the train under different operation conditions such as light load, half load, full load, overload and the like, so as to improve the riding comfort of drivers and passengers in the train.
Description
Technical Field
The invention belongs to the technical field of vibration isolator design, and particularly relates to a quasi-zero stiffness-inertia amplification coupling train floor vibration isolator and a design method.
Background
As the high-speed rail network continues to expand and the train running speed continues to rise, the vibration noise suppression control of the high-speed train faces new technical challenges. The floor vibration damping system in the passenger compartment of the high-speed train is mainly used for isolating the vibration transmitted to the floor by the running part at the bottom of the train, and the main forms of domestic application comprise fixed floor vibration damping and floating floor vibration damping. The former has strong durability, but poor riding comfort caused by lack of elastic elements, and the latter adopts elastic elements, such as rubber shock absorbers, has certain elasticity and damping and vibration reduction effects, can better improve the vibration reduction performance of the train floor, and is widely used for CRH series motor train units at present. However, the problem that the feet of passengers feel tingling due to local vibration of a train body still occurs when the domestic motor train unit is operated nowadays. The vibration transmissibility of the steel structure of the car body to the floor is tested by carrying out line operation test on a certain type of high-speed train, and the result shows that the amplification phenomenon can occur when the vibration of the steel structure of the car body in the frequency range of 20-50Hz is transmitted to the floor by the elastic support. Therefore, in order to further improve the riding comfort of passengers, the floor vibration reduction structure needs to be unfolded for optimization design research.
The design of the floor vibration damping block needs to consider the bearing characteristics of the structure, which causes two problems, namely, the design of the elastic supporting element with high rigidity can provide better bearing performance for the vibration damper, but in the traditional linear vibration isolator, only when the excitation frequency is larger than the natural frequency of the systemWhen the vibration isolation effect is doubled, the system can only have the vibration isolation effect, the high rigidity characteristic can influence the low-frequency vibration isolation characteristic of the structure, the quality is improved to be contradicted with the light design requirement of the train, the uniformity of the light-weight, high-bearing and low-frequency vibration isolation performance is difficult to realize, and if the design of the quasi-zero rigidity vibration absorber with high static rigidity and low dynamic rigidity is adopted, the sinking amount of the structure is easy to exceed the design value when the load condition of the floor changes due to the lower dynamic rigidity near the balance position. Therefore, the traditional quasi-zero stiffness structure can be used for bearing and low-frequency vibration isolation, but is not suitable for scenes with load change and limited deformation. In addition, increasing the system mass can also reduce the natural frequency, but is contrary to the lightweight design requirements of trains. Therefore, the design of the train floor damper needs to be improved to a certain extent on the traditional quasi-zero stiffness structure.
Disclosure of Invention
The invention aims to provide a quasi-zero stiffness-inertia amplification coupling train floor vibration isolator and a design method thereof, which are used for solving the problems that a traditional quasi-zero stiffness structure provided in the background art can be used for carrying and low-frequency vibration isolation, but is not suitable for a scene with load change and limited deformation.
In order to achieve the above object, the present invention provides a quasi-zero stiffness-inertia amplifying coupling train floor vibration isolator, comprising one or a plurality of connected unit structures, each unit structure comprising an outer frame, a quasi-zero stiffness subunit and an inertia amplifying subunit;
The inertial amplifier subunit is used for increasing the effective inertia of an oscillator in the structure on the premise of light weight and reducing the initial vibration isolation frequency from the mass level;
The outer frame comprises an upper frame and a lower frame, wherein the upper end of the upper frame is used as a bearing platform to be connected with the floor of the train, the lower end of the upper frame is connected with the upper end of an inertial amplifying subunit, the lower end of the inertial amplifying subunit is connected with the upper end of a quasi-zero stiffness subunit, the lower end of the quasi-zero stiffness subunit is connected with the lower frame, the bottom of the lower frame is connected with a train shock absorber supporting seat, and the upper frame and the lower frame are only pressed to form contact when the train is overloaded.
In a specific embodiment, the upper frame and/or the lower frame is/are provided with a baffle plate structure positioned at two sides;
when the train is in an overload working condition, the upper frame continuously moves downwards, and the upper frame and the lower frame are contacted through the supporting baffle structure, so that the system rigidity of the quasi-zero rigidity-inertia amplification coupling train floor vibration isolator is increased, and the quasi-zero rigidity-inertia amplification coupling train floor vibration isolator is prevented from continuously sinking in large deformation.
In a specific embodiment, a stop plate is arranged on the supporting plate structure at the contact position of the lower frame and the upper frame, the stop plate is used for enabling the contact of the lower frame and the upper frame to be stable, and the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator adjusts the stiffness characteristic under the overload working condition by changing the thickness of the supporting plate structure.
In a specific embodiment, the preparation material of the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator is a high polymer material, a metal material or a micro polymer material, and the preparation mode of the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator comprises 3D printing, metal/nonmetal casting and cutting.
In a specific embodiment, the inertial amplification subunit is a flexible hinge mass block, the shape of the flexible hinge mass block is determined by flexible hinge joint parameters and internal mass distribution modes formed by thin branch connecting beams at two ends and the middle section of the structure, and the inertial amplification function is realized by changing the hinge form and distribution.
In a specific embodiment, the quasi-zero stiffness subunit comprises a T-shaped platform and a curved beam, wherein the upper end of the T-shaped platform is connected with the lower end of the inertia amplifying subunit, and the curved beam is in a sine curve, a parabola curve or a spline curve.
In a specific embodiment, the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator adjusts the empty-to-full load capacity and the high static and low dynamic stiffness range of the train by changing the structural parameters of the curved beam.
In a specific embodiment, the curved beam is in a sine curve, the center of the curved beam is arched upwards, the upper end of the center of the curved beam is connected with the lower end of the T-shaped table, and the lower ends of the two sides of the curved beam are connected with the lower frame.
In a specific embodiment, the expression of the curved beam shape is:
Wherein A is the height of the curved beam, w is the span of the curved beam, and x and y are the corresponding abscissas of each point on the curved beam from the center point.
The invention also provides a design method of the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator, which comprises the following specific steps:
Firstly, planning the array quantity and array distance of unit structures distributed in an array according to the actual installation space and rated load of the vibration isolator;
Then establishing an external frame of a unit structure in the quasi-zero stiffness-inertia amplifying coupling train floor vibration isolator;
And an inertial amplifying subunit and a quasi-zero stiffness subunit are respectively built in the outer frame, the inertial amplifying subunit and the quasi-zero stiffness subunit are connected in series up and down, the upper end of the inertial amplifying subunit is connected with the upper frame, and the lower end of the quasi-zero stiffness subunit is connected with the lower frame.
Compared with the prior art, the invention has the following beneficial effects:
1. The invention relates to a quasi-zero stiffness-inertia amplification coupling floor vibration isolator and a design method thereof, the flexible hinge mass block and the curved beam are adopted to respectively realize an inertia amplification effect and a quasi-zero stiffness effect, and the initial vibration isolation frequency is reduced through the synergistic effect of the mass layer and the stiffness layer.
2. The vibration isolator design under the multi-stage load working condition can realize low-frequency vibration reduction performance by having the characteristics of high static stiffness and low dynamic stiffness under the no-load-half-load-full-load working condition of the train, improves the riding comfort of drivers and passengers in the train, and has high stiffness under the overload working condition to prevent the floor system from sinking too much.
3. According to the variable load vibration isolator, the design of the variable load vibration isolator under different application backgrounds can be realized through the adjustment of parameters such as the curved beam, the external frame, the inertia amplifying structure and the like.
4. The structural coupling mechanism floor vibration isolator can be prepared by adopting different materials, such as high polymer materials, metal materials, micro polymer materials and the like, and can also be prepared by adopting different manufacturing processes, such as 3D printing, metal/nonmetal casting, cutting and the like.
According to the low-frequency vibration damping characteristic of an inertia amplification-quasi-zero stiffness coupling mechanism, the invention designs the elastic vibration damping element applied to the floating floor system of the high-speed train, and the low-frequency vibration damping characteristic of the train in the face of different levels of load working conditions can be optimized.
In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail below.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
figure 1 is a three-dimensional illustration of the overall structure of the vibration isolator of the present invention;
Figure 2 is a schematic illustration of a configuration of a vibration isolator unit designed in accordance with the present invention;
FIG. 3 is a two-dimensional schematic of an inertial amplifying subunit within the isolator of the present invention;
FIG. 4 is a two-dimensional schematic of a quasi-zero stiffness subunit within the vibration isolator of the present invention;
FIG. 5 is a force-displacement curve comparison chart and a partial enlarged view of a vibration isolator and an existing rubber vibration isolator designed according to the present invention, wherein FIG. 5a is a force-displacement curve comparison chart of a vibration isolator and an existing rubber vibration isolator designed according to the present invention, and FIG. 5b is a partial enlarged view of a two-dimensional model of a coupling structure in FIG. 5 a;
Fig. 6 is a cloud chart of structural strength check of the vibration isolator designed by the invention;
figure 7 is a graph comparing force versus displacement curves measured for experiments and simulations of vibration isolators designed in accordance with the present invention;
FIG. 8 is a graph of measured vibration transmissibility for a designed isolator of the present invention simulating an idle condition with an existing rubber isolator;
FIG. 9 is a graph of measured vibration transmissibility for a design isolator of the present invention simulating a half load condition with an existing rubber isolator;
FIG. 10 is a graph of measured vibration transmissibility for a designed isolator of the present invention in a simulated full load condition with an existing rubber isolator;
FIG. 11 is a graph of measured vibration transmissibility for a designed isolator of the present invention simulating an overload condition with an existing rubber isolator;
l, B and H are the length, width and height of the vibration isolator.
In the outer frame, W-cell structure length, t-cell wall thickness, c 2 -upper frame thickness, c 1 -lower frame thickness, t p -stopper thickness, t g -structure gap width.
In the quasi-zero stiffness substructure, the w-curved beam span, the A-curved beam height, the T n -curved beam thickness, and the T-shaped stage width.
In the inertial amplification substructure, t 1 -upper and lower hinge connection width, t 2 -upper and lower hinge joint thickness, t 3 -center mass width, t 3a -connecting rod position starting width, t 3b -connecting rod position ending width, t 4 -center hinge joint thickness, t 5 -center hinge position width, l 1 -hinge connection thickness, l 2 -upper and lower hinge joint length, l 3 -upper and lower hinge and middle hinge distance, l 4 -center hinge joint length, l 5 -center mass length.
Detailed Description
The following detailed description of embodiments of the invention is provided merely to illustrate the invention and is not intended to limit the invention.
The invention relates to a quasi-zero stiffness-inertia amplification coupling train floor vibration isolator which comprises one or a plurality of connected unit structures, wherein each unit structure comprises an external frame, a quasi-zero stiffness subunit and an inertia amplification subunit;
The inertial amplifier subunit is used for increasing the effective inertia of an oscillator in the structure on the premise of light weight and reducing the initial vibration isolation frequency from the mass level;
The outer frame comprises an upper frame and a lower frame, wherein the upper end of the upper frame is used as a bearing platform to be connected with the floor of the train, the lower end of the upper frame is connected with the upper end of an inertial amplifying subunit, the lower end of the inertial amplifying subunit is connected with the upper end of a quasi-zero stiffness subunit, the lower end of the quasi-zero stiffness subunit is connected with the lower frame, the bottom of the lower frame is connected with a train shock absorber supporting seat, and the upper frame and the lower frame are only pressed to form contact when the train is overloaded. And two ends of the vibration isolator are glued and fixed with the train in a threaded connection mode and a gluing mode.
The upper frame and/or the lower frame are/is provided with a baffle plate structure positioned at two sides;
when the train is in an overload working condition, the upper frame moves downwards, and the upper frame and the lower frame are contacted through the supporting baffle plate structure, so that the system rigidity of the quasi-zero rigidity-inertia amplification coupling train floor vibration isolator is increased, and the quasi-zero rigidity-inertia amplification coupling train floor vibration isolator is prevented from continuously sinking in large deformation.
The quasi-zero rigidity-inertia amplification coupling train floor vibration isolator adjusts the rigidity characteristic under the overload working condition by changing the thickness of the supporting baffle structure.
The preparation materials of the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator are high polymer materials, metal materials or micro-polymer materials, and the preparation modes of the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator comprise 3D printing, metal/nonmetal casting and cutting.
The inertial amplification subunit is a flexible hinge mass block, the shape of the flexible hinge mass block is determined by flexible hinge joint parameters and internal mass distribution modes, and the inertial amplification function is realized by changing hinge forms and distribution. The flexible hinge joint consists of two ends of the structure and a thin branch connecting beam in the middle section.
The quasi-zero stiffness subunit comprises a T-shaped platform and a curved beam, wherein the upper end of the T-shaped platform is connected with the lower end of the inertia amplifying subunit, and the curved beam is in a sine curve, a parabola or a spline curve.
The quasi-zero stiffness-inertia amplification coupling train floor vibration isolator adjusts the empty-load to full-load capacity and the high-static low-dynamic stiffness range of the train by changing the structural parameters of the curved beam.
The curved beam is in a sine curve form, the center of the curved beam is arched upwards, the upper end of the center of the curved beam is connected with the lower end of the T-shaped table, and the lower ends of the two sides of the curved beam are connected with the lower frame.
The expression of the curved beam shape is:
Wherein A is the height of the curved beam, w is the span of the curved beam, and x and y are the corresponding abscissas of each point on the curved beam from the center point.
The invention also provides a design method of the quasi-zero stiffness-inertia amplification coupling train floor vibration isolator, which comprises the following specific steps:
Firstly, planning the array quantity and array distance of unit structures distributed in an array according to the actual installation space and rated load of the vibration isolator;
Then establishing an external frame of a unit structure in the quasi-zero stiffness-inertia amplifying coupling train floor vibration isolator;
And an inertial amplifying subunit and a quasi-zero stiffness subunit are respectively built in the outer frame, the inertial amplifying subunit and the quasi-zero stiffness subunit are connected in series up and down, the upper end of the inertial amplifying subunit is connected with the upper frame, and the lower end of the quasi-zero stiffness subunit is connected with the lower frame.
Example 1
As shown in fig. 1, the shock absorber designed by the invention is formed by an array of unit structures along the x direction, the number of the arrays is N, and the array distance is L. The number and the distance of the arrays can be flexibly adjusted according to the actual installation space and the rated load of the vibration isolator. Each unit consists of an external frame, a curved beam structure and a flexible hinge mass block, and is respectively responsible for realizing the multistage load, the quasi-zero stiffness effect and the inertia amplification effect of the structure.
The invention relates to a design method of a quasi-zero stiffness-inertia amplification coupling train floor vibration isolator, which comprises the following steps:
The overall structure is formed by a periodic array of cell structures, the cell structures being as shown in fig. 2. Firstly, an outer frame with the length W of the unit structure and the wall thickness t of the unit is established, in order to enable the unit structure to adapt to different train loads and limit the sinking amount of the unit structure under overload working conditions, the outer frame divides a common rectangular frame into an upper frame and a lower frame, the thicknesses of the upper frame and the lower frame after division are c 2 and c 1 respectively, and a stop plate with the thickness t p is arranged at the cutting position of the original frame so as to ensure contact stability. The clearance between the upper frame and the lower frame after segmentation is t g, when the compression amount is less than t g, the vibration isolator shows high static rigidity low dynamic rigidity characteristic, when the structure bears too big load, the upper frame moves down to contact with the backstop board, and the frame structure directly participates in bearing at this moment, has high rigidity characteristic, prevents that the vibration isolator from further sinking. In general, the external frame can ensure that the vibration isolator has different rigidity characteristics under different load working conditions, and is used for realizing corresponding requirements of different stages.
An inertial amplifying subunit and a quasi-zero stiffness subunit are then built inside the frame, respectively. The upper boundary of the inertial amplifying subunit is connected with the upper frame, and the lower boundary of the quasi-zero stiffness subunit is connected with the lower frame.
The quasi-zero stiffness subunit is composed of a curved beam structure, wherein the expression of the shape of a single curved beam is:
wherein A is the height of the curved beam, w is the span of the curved beam, and x and y are the corresponding abscissas of each point on the curved beam from the center point.
The curved beam height A needs to be selected to have a proper value so as to have a quasi-zero stiffness characteristic, and when the height is too high or too low, the structure is easy to show a negative stiffness characteristic or a positive stiffness characteristic, the structure is easy to be unstable, and the low-frequency vibration damping characteristic cannot be realized. The greater the curved beam thickness t n, the greater the corresponding load at quasi-zero stiffness of the structure. The two curved beams are symmetrical along the T-shaped table, the width of the lower part of the T-shaped table is T, and the upper parameters have little influence on the structure of the T-shaped table and can be adjusted according to the requirement.
The lower part of the inertia amplifying subunit is connected with the T-shaped table, the upper part of the inertia amplifying subunit is connected with the upper frame, and the detailed configuration and the corresponding parameters of the inertia amplifying subunit are shown in figure 3. When the vibration isolator receives compression in the y direction, the flexible hinge in the inertia amplifying subunit rotates and deforms to drive the internal centralized mass block to rotate, so that the effective inertia of the structure is amplified. The deformation degree of the flexible hinge is influenced by the rigidity of the hinge, and the smaller the thicknesses t 2 and t 4 of the hinges at the middle and the two ends are, the shorter the lengths l 2 and l 4 are, the more difficult the hinge is to rotate and deform, so that the inertia amplification effect is facilitated. The central mass block parameters t 3 and l 5 determine the internal mass distribution mode of the inertial amplification subunit, when the product of the central mass block parameters t 3 and the central mass block parameters l 5 is constant, the area of the representative mass block is constant, and the total mass is constant. t 5 determines the stiffness of the inertial amplifying subunit, the smaller t 5, the greater the corresponding stiffness. t 3a and t 3b determine the thickness of the connecting rod component in the inertial amplifying substructure, and the values of the two should be reasonably selected to ensure that the connecting rod has enough rigidity to enable the flexible hinge joint to rotate and deform instead of the central mass block to deform internally when the structure is subjected to external force.
The model according to the embodiment performs statics calculation to obtain a force-displacement curve, and as shown in fig. 5, a two-dimensional plane model and a three-dimensional entity model are selected for calculation to prove accuracy of a result. The vibration isolator has obvious two-stage reaction force change phases in the compression displacement of 0-2.5 mm. The first stage is 0-1.7mm, the force-displacement curve of the structure in the first stage has nonlinearity, the rigidity gradually decreases along with the increase of displacement, and the structure near 1.7mm has the characteristics of high load and low dynamic rigidity. After the displacement is continuously increased to 1.7mm, the restoring force of the structure is increased rapidly and is in a linear mode, and the load capacity and dynamic stiffness of the structure are greatly enhanced. If no second stage exists, the nonlinear stiffness of the structure continues to soften as the compression displacement increases further, as shown by the dashed line of the contactless coupling model, which stiffness approaches and remains within the quasi-zero stiffness range. At this time, the displacement of the shock absorber is greatly increased and the corresponding load is basically unchanged, and if the load is heavy, the structural sinking amount exceeds the design requirement, so that the shock absorber is not suitable for engineering application with variable loads. The vibration isolator is designed from no load to full load of the train, the sinking amount is 1.48mm and is less than 2mm, and the design requirement is met. The conventional rubber vibration isolator has high linear rigidity, and the characteristic can ensure that the structure is suitable for a wide load range under a small deformation amount as shown by a dot-dash line of the linear rubber vibration isolator. However, the structure maintains higher dynamic stiffness characteristics under any load, which is not beneficial to the vibration reduction design requirement of the train floor for further low frequency. By comprehensive comparison, the vibration isolator designed by the invention combines the quasi-zero stiffness characteristic and the high linear stiffness characteristic, and has better low-frequency vibration reduction application potential in different load stages.
The vibration isolator of fig. 1 constructed in this embodiment can be modeled by the parameters of table 1.
Table 1 design parameters for quasi-zero stiffness-inertial amplification coupled variable load train floor vibration isolator
Based on the statics calculation, the maximum stress of the structure in the compression process is calculated, the obtained result is about 10Mpa, and the allowable stress of the TPU material is far smaller than 63.1Mpa, so that the structural strength is basically ensured. Samples were printed using TPU material and a hydrostatic compression experiment was performed with a single sample mass of 196g, less than 240 g/per permit. The static compression experimental result is more consistent with the simulation result, as shown in fig. 5.
And after the static compression test, testing the vibration characteristics of the sample. During testing, two identical vibration isolators are connected with the wood board to bear 20kg-40kg-80kg-120kg loads, and different loads simulate no-load-half-load-full-load-overload working conditions of the vibration isolators respectively. Meanwhile, the existing rubber shock absorber on the train floor is selected as a comparison object for vibration test. The results are shown in FIGS. 8-11. When the system load is increased from no load (20 kg) to overload (120 kg), the initial vibration isolation frequencies of the rubber shock absorber are 40Hz, 38Hz, 35Hz and 33Hz in sequence, and as the load increases, the system mass increases and the vibration isolation frequency decreases. The initial vibration isolation frequency of the vibration isolator is 25Hz, 19Hz, 14Hz and 25Hz in sequence, and the phenomenon that the frequency is reduced and then increased is presented. When the load is increased from no load to full load, the initial vibration isolation frequency is gradually reduced, because as the load is increased, the vibration isolator force-displacement curve shows high static and low dynamic stiffness characteristics, particularly in the full load working condition, the structure almost shows quasi-zero stiffness characteristics, the equivalent dynamic stiffness is the lowest, and the system mass is synchronously increased, so that the initial vibration isolation frequency of the vibration isolator is gradually reduced, and even the vibration isolator is as low as 14Hz under the full load working condition. And continuously increasing the system load to an overload working condition, wherein the coupling shock absorber is contacted internally, and the high linear stiffness characteristic is displayed to adapt to the overload of the system. At this time, even though the system weight increases to lower its natural frequency, the stiffness increases greatly, which ultimately results in a significant increase in the vibration damping frequency of the structure. Therefore, in 4 stage-by-stage loading working conditions, the initial vibration isolation frequency of the system is reduced and increased. In order to ensure that the structure is not deformed beyond the sinking amount under the overload working condition, the cost of the vibration isolation frequency rise is unavoidable. The advantage is that even if the stiffness is greatly increased, the weight change caused by overload can still help the vibration isolation frequency to be maintained in a relatively low frequency state.
Comparing the initial vibration isolation frequencies of the rubber vibration absorber and the coupling vibration absorber under the same working condition, the initial vibration isolation frequencies of the coupling vibration absorber are lower than those of the rubber vibration absorber under 4 working conditions, and the frequencies are respectively reduced by 41.3%, 50%, 60% and 24.2%. It can be seen that the coupled damper has better vibration isolation characteristics under different loads than conventional rubber dampers, especially during the no load to full load phase.
The foregoing is a further detailed description of the invention in connection with specific preferred embodiments, and is not intended to limit the practice of the invention to such description. It will be apparent to those skilled in the art that several simple deductions and substitutions can be made without departing from the spirit of the invention, and these are considered to be within the scope of the invention.
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