Abstract:
A simple self-tuned mass damper is hereby proposed for a broadened frequency band and which can be adapted to large and expensive structures as well as small and inexpensive structures alike. The novel self-tuned mass damper includes an auxiliary mass and a non-linear suspension, which is configured to connect the auxiliary mass to a vibrating structure. The mass of the auxiliary mass and the stiffness of the non-linear suspension are selected such that the natural frequency is at least 6 Hz and that the amplitude of the relative displacement of the auxiliary mass in respect to the vibrating structure is at most 12 mm.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to tuned mass dampers 
       BACKGROUND ART 
       [0002]    Tuned mass dampers are a well known solution to reducing the amplitude of unnecessary or harmful mechanical harmonic vibrations. Tuned mass dampers are used to dampen vibrations of a large scale from microcircuits to tall sky scrapers. The basic idea behind a tuned mass damper is simple: an auxiliary mass is attached to the vibrating structure via a suspension element, which typically consists of a spring and a damper, thus changing the vibrating characteristics of the vibrating structure. Instead of a spring and a damper, the suspension element may be alternatively provided by means of only one element, e.g. a rubber spring which contains both needed properties. 
         [0003]    The mass damper is tuned to the vibrating structure such that the mass of the auxiliary mass and the stiffness of the suspension element are selected to provide an appropriate counterforce to the disturbing excitation force. In particular, the mass ratio, i.e. the relativity of mass between the auxiliary mass and the vibrating structure, and the tuning frequency of the mass damper are calculated according to well known design principles. 
         [0004]    While tuned mass dampers are typically linear, also non-linear mass dampers have been proposed by several publications because non-linear mass dampers work on a wider frequency band. Non-linear tuned mass dampers employ a non-linear spring and/or a non-linear damper and mass. One particular type of non-linear mass dampers is a wire rope spring damper, the principles of which have been disclosed in e.g. ‘Parametric experimental study of wire rope spring tuned mass dampers’ Gerges &amp; Vickery in the Journal of Wind Engineering and Industrial Aerodynamics (91, 2003, 1363-1385). According to Gerges &amp; Vickery, the studied frequency area of the resulting structure is at most 4.5 Hz. 
         [0005]    An issue associated with conventional tuned mass dampers is that they are and can only be tuned to a rather narrow frequency band. The operational window of a conventional tuned mass damper is dictated by the dampening construction in that the width of the frequency band is a trade-off between high dampening efficiency and width of the frequency band. More particularly, an increase in dampening efficiency typically leads to reduced frequency band, whereas widening the frequency band tends to make the dampening less optimal for a specific frequency within the band. There have been many attempts to broaden the frequency band of mass dampers. Many proposals involve the use of active or adaptive mass dampers which employ a controlling unit regulating a series of actuators which adapt the mass damper to dampen a desired frequency. Otherwise, such active mass dampers are designed similarly to passive dampers in terms of providing a counter mass via a suspension to the vibrating structure. Unfortunately, conventional active mass dampers use excessive energy and are rather complex and therefore not feasible to dampen small and inexpensive structures such as microcircuit boards. 
         [0006]    It is therefore an aim of the present invention to provide a simple tuned mass damper which has a broadened frequency band and which can be adapted to large and expensive structures as well as small and inexpensive structures alike. 
       SUMMARY 
       [0007]    The aim of the present invention is achieved with aid of a novel and completely unorthodox manner of providing a self-tuned mass damper including an auxiliary mass and a non-linear suspension, which is configured to connect the auxiliary mass to a vibrating structure. The mass of the auxiliary mass and the stiffness of the non-linear suspension are selected such that the natural frequency is at least 6 Hz and that the amplitude of the relative displacement of the auxiliary mass in respect to the vibrating structure is at most 12 mm. 
         [0008]    Considerable benefits are gained with aid of the present invention. Because the mass damper is dimensioned outside typical specification, a broadened frequency band is achieved with a very simple and capable to be adapted to large and expensive structures as well as small and inexpensive structures alike. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0009]    In the following, exemplary embodiments of the invention are described in greater detail with reference to the accompanying drawings in which: 
           [0010]      FIG. 1  presents an isometric view of a tuned mass damper arrangement according to one embodiment of the invention, 
           [0011]      FIG. 2  presents an isometric view of a tuned mass damper arrangement according to another embodiment of the invention, 
           [0012]      FIG. 3  presents a side elevation view of the arrangement of  FIG. 2 , 
           [0013]      FIG. 4  presents a graph showing the relation between the dynamic amplitude plotted on the horizontal axis, dynamic stiffness plotted on the left vertical axis and loss factor, i.e. damping property, plotted on the right vertical axis, 
           [0014]      FIG. 5  presents a graph showing the frequency response function of a spring-mass system according to  FIG. 1  using 2.5 g as the excitation amplitude level, 
           [0015]      FIG. 6  presents a graph showing the frequency response function of a spring-mass system according to  FIG. 1  using 0.3 g as the excitation amplitude level, 
           [0016]      FIG. 7  presents a graph showing the frequency response function of a spring-mass system according to  FIG. 1  using 0.5 g as the excitation amplitude level, 
           [0017]      FIG. 8  presents a graph showing the frequency response function of a spring-mass system according to  FIG. 1  using 1 g as the excitation amplitude level, 
           [0018]      FIG. 9  presents a graph showing the frequency response function of a spring-mass system according to  FIG. 1  using 4 g as the excitation amplitude level, 
           [0019]      FIG. 10  presents a graph showing the vibration of a structure with modal mass of 200 kg in frequency domain, 
           [0020]      FIG. 11A  presents a graph showing the vibration of a circuit board without a self-tuned mass damper in frequency domain, 
           [0021]      FIG. 11B  presents a graph showing the vibration of a circuit board with a self-tuned mass damper in frequency domain, 
           [0022]      FIG. 12  presents a graph showing the vibration of a structure with modal mass of 900 kg in frequency domain, 
           [0023]      FIG. 13  presents a graph showing the relation between the dynamic amplitude plotted on the horizontal axis, dynamic stiffness plotted on the left vertical axis of the example of  FIG. 12 , and 
           [0024]      FIG. 14  presents a graph showing the relation between dynamic amplitude, which is plotted on the horizontal axis, and dynamic stiffness, which is plotted on the left vertical axis, in an example concerning a wire rope isolator, the height of which is 130 and width 145 mm with a wire diameter of 6 mm and 4 turns. 
       
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0025]    As shown in  FIG. 1 , a tuned mass damper  100  arrangement according to one embodiment features an auxiliary mass  120  which is attached to a vibrating structure  200  via a wire rope isolator  110 . The wire rope isolator  110  includes a wound wire which is attached to the auxiliary mass  120  and to the vibrating structure  200  by means of attachment blocks  113 ,  112 , respectively. In this context, the term wire rope isolator is meant to refer to a structure which are also known in the field by the expression cable mount, cable isolator and/or wire rope spring. Wire rope isolator may be built many ways, e.g. by employing helical, compact, short bar or specially assemblies. All different wire rope isolator types still work in same way as a self-adapting mass damper. 
         [0026]      FIGS. 2 and 3  show a tuned mass damper arrangement according to another embodiment. 
         [0027]    In this second embodiment, the mass damper  110  of  FIG. 1  has been provided with an additional intermediate block  114  between the attachment blocks  112 ,  113 . The attachment blocks  112 ,  113  are in this embodiment joined by a large helical spring wire  112   a,  whereas the intermediate block  114  is coupled to the attachment blocks  112 ,  113  via nested small helical spring wires  111   b,    111   c,  respectively. By using an intermediate block  114  with nesting spring wires  111   b,    111   c  connecting the intermediate block  114  to the attachment blocks  112 ,  113 , the resulting tuned mass damper  110  provides better control for the damping and stiffness. 
         [0028]    Turning now to  FIG. 4  which shows a graph illustrating an exemplary relation between the dynamic amplitude, which is plotted on the horizontal axis, dynamic stiffness, which is plotted on the left vertical axis, and loss factor, which is also known as damping property, which is plotted on the right vertical axis. The illustrated example is the result of a particular mass damper structure, where the wire diameter is 12 mm and height 122 mm and width 144 mm. The structure of the mass damper has an effect on the amplitude-stiffness curve. The most useful non-linear area of wire rope isolator can be estimated using slope of the amplitude-stiffness curve as presented in  FIG. 4 . While the slope approaches value  1 , the wire rope isolator is close to linear spring-damper such as a rubber or helical steel spring for example and the self-tuning property of the mass damper is lost. The rule of thumb is that the self-tuning mass damper works better while the slope of the amplitude-stiffness curve is closer to a second or higher order function than linear equation. This principle is illustrated in  FIG. 4 , where the linear equation is starting from 4 mm and where a closer to second order function is seen with less than 4 mm amplitude. The linear equation in slope of the amplitude-stiffness curve is still non-linear spring, but the effect is lesser compared to second order function in the slope. The dependence of displacement to acceleration amplitude in frequency domain is second order function and often structures vibration acceleration amplitudes are higher with higher frequencies so the non-linear spring needs to be as non-linear as possible to work in wide frequency area. The linear equation of slope in the amplitude-stiffness curve also gives wider operation area in frequency domain compared to conventional tuned mass damper which works only in narrow frequency band. 
         [0029]    It may therefore be concluded that for providing a self-tuned mass damper in the illustrated example, the mass of the auxiliary mass  120  and the stiffness of the non-linear suspension  110  should selected such that the said natural frequency is e.g. at least 6 Hz and that the amplitude of the relative displacement of the auxiliary mass  200  in respect to the vibrating structure is e.g. at most 4 mm. The resulting stiffness to mass ratio would then be at least 1.4 kN/(m·kg) by using static stiffness. 
         [0030]    Another example is depicted here after with reference to  FIG. 14 . 
         [0031]    According to further embodiment, the natural frequency is at least 10 Hz thus yielding stiffness to mass ratio of at least 4 kN/(m·kg) by using static stiffness. According to an even more further embodiment, the natural frequency is at least 14 Hz thus yielding stiffness to mass ratio of at least 7 kN/(m·kg) by using static stiffness. 
         [0032]    Turning now to  FIGS. 5 to 9 , which show graphs depicting the frequency response function of a spring-mass system according to the embodiment shown  FIG. 1 , when using exemplary excitation amplitude levels, namely 2.5 g, 0.3 g, 0.5 g, 1 g and 4 g, respectively. As can be seen from these graphs, response/excitation ratio is above 1 in wide frequency range. 
         [0033]    Next, the design principles of the novel mass damper are described in greater detail by referring to three design examples. 
         [0034]    Turning first to  FIG. 10 , which shows a graph depicting the vibration of a structure with modal mass of 200 kg in frequency domain. The thick line is the original structure without any dampers, thin line is a same structure with conventional tuned mass damper and dashed line is a structure with self-tuned mass damper. In  FIG. 10 , it may be seen a structure with three resonances illustrated by the thick line in frequency domain. The vibration acceleration [g] is presented in vertical axle and frequency [Hz] in horizontal axle. The thin line presents same structure with conventional tuned mass damper which reduces the vibration of two resonances seen in 13 and 14.5 Hz, but it does not have an effect to first resonance near 12 Hz. The dashed line presents same structure with self-tuning mass damper which is able to reduce all resonances. 
         [0035]    Another example of the mass damper is shown in  FIGS. 11A and 11B , wherein the damper is used to dampen vibrations occurring in a much smaller vibrating structure: a circuit board. The circuit board was dynamically tested with an electro-magnetic shaker using wide frequency noise excitation. Many resonances where discovered in the circuit board (see  FIG. 11A ). The self-tuning mass damper was installed in the middle of the circuit board and tested with same excitation (see  FIG. 11B ). The self-tuning mass damper was able to decrease many resonances e.g. near 90, 290 and 460 Hz. 
         [0036]    A third example is shown by reference to  FIGS. 12 and 13 , which presents a graph showing the vibration of a structure with modal mass of 900 kg in frequency domain. A self-tuning mass damper was tested dynamically with resonance table there modal mass was 900 kg (plane table without mass damper thick line in  FIG. 12 ). The self-tuning mass damper was tested using moving auxiliary mass of 40, 60 and 80 Kg (thin lines). From the  FIG. 12  it may be seen that the self-tuning mass damper was able to reduce the vibration levels of the resonance test table in all three resonances (near 29, 44 and 51 Hz). A wire rope isolator that was used in this test was made using 16 mm steel wire rope with 8 turns, length of the frame was 267 mm, the height of the isolator was 109 mm and width 135 mm. 
         [0037]    Amplitude-stiffness curve of the wire rope isolator that was used in resonance table test is presented in  FIG. 13 . From the  FIG. 13  can be calculated the natural frequency of the self-tuning mass damper and compared to results of the resonance table test results presented in  FIG. 12 . The calculation results are presented in Table 1 below. The movement of the self-tuning mass damper was three to four times greater compared to movement of the damped resonance table. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 CALCULATION RESULTS EXAMPLE. 
               
             
          
           
               
                 Structure vibration 
                 Mass damper movement 
                 Self-tuning mass damper 
               
             
          
           
               
                 acc 
                 X 
                 f 
                 acc 
                 X 
                 f 
                 k 
                 m 
                 f 
               
               
                 [g] 
                 [mm] 
                 [Hz] 
                 [g] 
                 [mm] 
                 [Hz] 
                 [N/m] 
                 [kg] 
                 [Hz] 
               
               
                   
               
             
          
           
               
                 0.1 
                 0.010 
                 51 
                 0.4 
                 0.039 
                 51 
                 3500000 
                 40 
                 47 
               
               
                 0.3 
                 0.039 
                 44 
                 0.9 
                 0.118 
                 44 
                 2500000 
                 40 
                 40 
               
               
                 0.3 
                 0.090 
                 29 
                 0.9 
                 0.271 
                 29 
                 1200000 
                 40 
                 28 
               
               
                   
               
             
          
         
       
     
         [0038]    As explained above, the dimensioning values given with reference to the example of  FIG. 4  may vary depending on the structure of the mass damper. Accordingly, another example with a higher amplitude of the relative displacement of the auxiliary mass in respect to the vibrating structure is given here after. 
         [0039]    Turning now to  FIG. 14  which shows a graph illustrating the relation between the dynamic amplitude, which is plotted on the horizontal axis, dynamic stiffness, which is plotted on the left vertical axis. The most useful non-linear area of a wire rope isolator can be estimated using the slope of the amplitude-stiffness curve as presented in  FIG. 14 . While the slope approaches value 1, the wire rope isolator is close to a linear spring damper such as a rubber or helical steel spring for example and the self-tuning property of the mass damper is lost. The rule of thumb is that the self-tuning mass damper works better while the slope of the amplitude-stiffness curve is closer to a second or higher order function than linear equation. This principle is illustrated in  FIG. 14 , where the linear equation is starting from 12 mm and where a closer to second order function is seen with less than 12 mm amplitude. The linear equation in the slope of the amplitude stiffness curve is still a non-linear spring, but the effect is lesser compared to second order function in the slope. The dependence of displacement to acceleration amplitude in frequency domain is a second order function. The vibration acceleration amplitude of a structure is often higher with higher frequencies, whereby a non-linear spring needs to be as non-linear as possible to work in a wide frequency area. The linear equation of slope in the amplitude-stiffness curve also gives a wider operation area in frequency domain compared to a conventional tuned mass damper, which works only in narrow frequency band. 
         [0040]    The difference between the examples of  FIG. 4  and  FIG. 14  is the wire diameter compared to height and width of the wire rope isolator. There therefore exists a particular amplitude value, where non-linear stiffness increases, while the wire diameter versus height and width of the wire rope isolators is decreased. This means that with a small wire diameter compared to a relatively large height and width of the wire rope isolator the non-linear stiffness part is relatively high in amplitude: e.g. 12 mm with  FIG. 14  example, where the wire diameter is 6 mm, height 130 mm and width 145 mm, but only 4 mm with  FIG. 4  example, where the wire diameter is 12 mm and height 122 mm and width 144 mm. 
         [0000]    
       
         
               
             
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 LIST OF REFERENCE NUMBERS. 
               
             
          
           
               
                 Number 
                 Part 
               
               
                   
               
               
                 100 
                 tuned mass damper 
               
               
                 110 
                 wire rope isolator 
               
               
                 111 
                 wire 
               
               
                 112 
                 attachment block 
               
               
                 113 
                 attachment block 
               
               
                 114 
                 intermediate block 
               
               
                 120 
                 auxiliary mass