These factors are used to represent friction in the bushing material and also other
                effects such as viscoelasticity.
            The overall scale factor is defined on the left for stiffness and on the right for
                damping as follows:
            
                 
             
            
            The following plot shows the behavior of the scaling function 
                        
                            
                                
                                    
                                        S 
                                        y 
                                     
                                 
                                MathType@MTEF@5@5@+=
                                    feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                    hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                    4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                    vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                    fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa
                                    aaleaacaWG5baabeaaaaa@37F8@  
                             
                         
                       for various values of 
                        
                            
                                
                                    
                                        | 
                                        y 
                                        | 
                                     
                                 
                                MathType@MTEF@5@5@+=
                                    feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                    hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                    4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                    vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                    fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaaca
                                    WG5baacaGLhWUaayjcSdaaaa@3A16@  
                             
                         
                       and 
                        
                            
                                
                                    p 
                                    2 
                                 
                             
                            MathType@MTEF@5@5@+=
                                feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaaBa
                                aaleaacaaIYaaabeaaaaa@37D3@
                             
                         
                     
                     .
                Note that the y-axis is plotted on a log scale to make the effects more obvious.
            Figure 1 .    
                
                 
             
            The functional form of 
                        
                            
                                
                                    
                                        S 
                                        y 
                                     
                                 
                                MathType@MTEF@5@5@+=
                                    feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                    hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                    4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                    vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                    fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa
                                    aaleaacaWG5baabeaaaaa@37F8@  
                             
                         
                      is selected as it easily represents a variety of
                shapes with very few parameters. 
Note:  
                            
                                
                                    
                                        
                                            S 
                                            y 
                                         
                                     
                                    MathType@MTEF@5@5@+=
                                        feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa
                                        aaleaacaWG5baabeaaaaa@37F8@  
                                 
                             
                          and 
                            
                                
                                    
                                        
                                            S 
                                            w 
                                         
                                     
                                    MathType@MTEF@5@5@+=
                                        feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa
                                        aaleaacaWG3baabeaaaaa@37F6@  
                                 
                             
                          are primarily responsible for capturing the
                    dependency of the dynamic stiffness and loss angle on the amplitude of the
                    input.
 
            The next figure shows the same data as the figure above, except 
                        
                            
                                
                                    
                                        | 
                                        y 
                                        | 
                                     
                                 
                                MathType@MTEF@5@5@+=
                                    feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                    hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                    4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                    vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                    fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaaca
                                    WG5baacaGLhWUaayjcSdaaaa@3A16@  
                             
                         
                       is the x-axis and 
                        
                            
                                
                                    
                                        p 
                                        2 
                                     
                                 
                                MathType@MTEF@5@5@+=
                                    feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                    hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                    4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                    vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                    fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCamaaBa
                                    aaleaacaaIYaaabeaaaaa@37D3@  
                             
                         
                       the curve parameter:
            Figure 2 .