Moreover, [B.sub.eq] is the equivalent viscous damping
coefficient, [K.sub.s] is the return spring shifftness, [[theta].sub.L] is the angular position of the throttle plate, [T.sub.PL] is the spring preload torque, [T.sub.f] is the frictional torque generated by the movement of the throttle plate, and [K.sub.m] is the motor torque constant.
Among the main forms of energy dissipation in an oscillatory system, viscous damping
is most frequently used.
Li, "Dynamic analyses of viscoelastic dielectric elastomers incorporating viscous damping
effect," Smart Materials & Structures, vol.
force calculation formula of the particle is based on the Stokes drag law of fluid mechanics , which can be expressed as
Lin and Chang  improved ICSM by using the real absolute acceleration response spectrum instead of the pseudo-acceleration response spectrum, especially for them system with equivalent viscous damping
ratio [[beta].sub.eq] > 10% and period T > 0.15 s.
(i) The classical one-dimensional (1D) vibrational system with viscous damping
consists of a mass m, an elastic element with an elastic constant k, and a damper characterized by a constant c (Figure 1).
Though the uncertainty in viscous damping
itself does not affect much of the calculation accuracy, in order to investigate the influence of damping magnitude on the overestimation effect, several cases are chosen where different damping is considered when the disk mass is uncertain given its high sensitivity.
The phenomenon can be described by a viscous damping
where c is called a dashpot or viscous damping
Among the various transmitting boundaries developed and implemented in SSI analysis, the most widely used one is the viscous boundary  which replaces the far field with viscous damping
. Also widely used is the viscoelastic boundary  which employs springs to the viscous boundary to improve the accuracy.
In the past, most of the studies on Duffing system have been performed by considering the linear viscous damping
. Several researches have been reported on the chaotic motion of forced Duffing equations [8-10].
ElGawady, "Appropriate viscous damping
for nonlinear time-history analysis of base-isolated reinforced concrete buildings," Earthquake Engineering & Structural Dynamics, vol.