Patent ID: 11946524
Assignee: DALIAN UNIVERSITY OF TECHNOLOGY
Field: Mechanical elements (Mechanical engineering)
Classification: CPC E  F  G | IPC E  F  G

Claim 1:
2. A design method of a double-ring shaped strong magnet array nonlinear dynamic vibration absorber for vibration mitigation of suspender cables, comprising steps of:
step 1, obtaining characteristics of a suspender cable to be controlled by field survey, the characteristics including outer diameter of sheath for the suspender cable, and natural frequencies;
step 2, determining design parameters of the double-ring shaped strong magnet array nonlinear dynamic vibration absorber, the design parameters including:
1) a mass ratio of an outer magnet ring array and additional weights to modal mass of the suspender cable: 1% to 5%, and within which the larger the mass ratio, the better the vibration mitigation effect, and the mass ratio determined according to demand of vibration mitigation for the suspender cable;
2) a damping ratio of the vibration absorber is equal to an optimal damping ratio of a tuned mass damper (TMD) under the same mass ratio;
3) designed values for linear and cubic stiffness of the vibration absorber: numerical model of cable-absorber system is established as shown in equation (1):, {
     
      
       
        
         
          
           M
           ⁢
           
            
             w
             ¨
            
            (
            t
            )
           
          
          +
          
           C
           ⁢
           
            
             w
             .
            
            (
            t
            )
           
          
          +
          
           Kw
           ⁡
           (
           t
           )
          
         
         =
         
          F
          ⁡
          (
          t
          )
         
        
       
      
      
       
        
         
          
           m
           ⁢
           
            v
            ¨
           
          
          +
          
           c
           [
           
            
             v
             .
            
            -
            
             
              w
              .
             
             ⁢
             
              δ
              ⁡
              (
              
               x
               -
               d
              
              )
             
            
           
           ]
          
          +
          
           
            k
            1
           
           [
           
            v
            -
            
             w
             ⁢
             
              δ
              ⁡
              (
              
               x
               -
               d
              
              )
             
            
           
           ]
          
          +
          
           
            
             k
             2
            
            [
            
             v
             -
             
              w
              ⁢
              
               δ
               ⁡
               (
               
                x
                -
                d
               
               )
              
             
            
            ]
           
           3
          
         
         =
         0
        
       
      
     
    
   
   
    
     (
     1
     )
    
   
  
 

where, w(t) denotes vector of displacements corresponding to each degree of freedom of the suspender cable, {dot over (w)}(t) and {dot over (w)}(t) denote velocity and acceleration of the suspender cable, respectively; M denotes mass matrix of the suspender cable; C denotes damping matrix of the suspender cable employing Rayleigh damping; K denotes stiffness matrix of the suspender cable; F(t) denotes sum of external loads on the suspender cable and reaction of the vibration absorber to the suspender cable; m, c, k1, k2 denote mass, damping, linear stiffness and nonlinear stiffness of the vibration absorber, respectively; ν denotes displacement of the vibration absorber, {dot over (ν)} and {umlaut over (ν)} denote velocity and acceleration of the vibration absorber, respectively; one end of the suspender cable is starting point of x-axis, x is x-axis coordinate of point on the suspender cable, d denotes installation location of the vibration absorber along x-axis, and δ(x−d) is Dirac function;
an objective function for parameter optimization as shown in equation (2), J
     =
     
      min
      ⁡
      (
      
       
        Δ
        control
       
       Δ
      
      )
     
    
   
   
    
     (
     2
     )
    
   
  
 

where Δ denotes a root-mean-square value, variance of time-history responses of displacement or velocity at a specific location along the suspender cable under an influence of white noise load, Δcontrol denotes the root-mean-square value, variance of time-history responses of displacement or velocity at the specific location along the suspender cable under the influence of white noise load when the vibration absorber is deployed, and Δ and Δcontrol are selected or established according to the demand of vibration mitigation;

dynamic responses of the suspender cable are calculated by using the numerical model of the cable-absorber system under the white noise loads at multiple points, and the optimal linear stiffness and the optimal nonlinear stiffness are obtained by automatic optimization;
4) geometric parameters of the inner magnet ring and the outer magnet ring array: with overall consideration of cost of the vibration absorber and section size of the suspender cable to be controlled, number, radius angle and inner diameter of magnet shoes in the inner magnet ring array and the outer magnet ring array are determined; a parametric electromagnetic field numerical model of the double-ring shaped strong magnet array nonlinear dynamic vibration absorber system is established, and by adjusting thickness and height of the magnet shoes of the inner magnet ring array and the outer magnet ring array, combination of the inner magnet ring array and the outer magnet ring array achieves designed linear stiffness and designed cubic stiffness;
5) geometric parameters of additional weights for the vibration absorber: total mass of the vibration absorber minus mass of the outer magnet ring array is the mass of additional weights, and then length, width and height of the additional weights are designed according to density of the additional weight;

step 3, machining and fabricating the double-ring shaped strong magnet array nonlinear dynamic vibration absorber according to the design parameters obtained from step 2; and, step 4, installing the manufactured double-ring shaped strong magnet array nonlinear dynamic vibration absorber on the suspender cable in the laboratory, and measuring the force-displacement relationship of the double-ring shaped strong magnet array nonlinear dynamic vibration absorber with a dynamometer and a ruler to ensure the linear and cubic stiffness of the vibration absorber to be the design values; letting the vibration absorber move freely, then measuring the displacement signal of the outer magnet ring array, and determining the damping ratio by free-vibration decay method etc., and then adjusting the damping ratio by adjusting the friction force between universal wheels and a base.