symbols

definitions

L

length of the cable

C

damping coefficient of the damper

K

stiffness coefficient of the damper

m

mass of the cable per unit length

T

cable tension

a, a'

distances between the installation point of the damper and the left and right anchor ends

x, x'

axial coordinate of the cable

α

nonlinear coefficient of damping

β

nonlinear coefficient of stiffness

v(x,t)

cable vibration amplitude

ωn

natural frequency of the n order

Fk

force caused by the spring

Fc

force caused by the dashpot

η

dimensionless damping coefficient

μ

dimensionless stiffness coefficient

ξn,max

Maximum damping ratio

ηopt

Optimal damping coefficient