Abstract: The viscous damping force in the mixed form as f_d \left(
\dot {x} \right) = c_1 \dot {x} + c_2 \left| \dot {x} \right|\dot {x}
can well describe damping characteristics of isolators and dampers in many
cases. In this paper, performance characteristics of single-degree-of-freedom
(SDOF) linear-stiffness isolators with mixed and piecewise mixed viscous
damping are analytically examined under harmonic base excitation. Based on the
first-order harmonic balance method (HBM), both relative and absolute
displacement transmissibility expressions with the equivalent linear damping
coefficient (ELDC) are given. And the analytical calculations show good
agreement with the numerical results. Also, the influence of nonlinear damping
on the response characteristics is investigated by comparing the
transmissibility of linear and nonlinear systems. The resonant frequency always
shifts to a lower value as the nonlinear damping component of the force
f_d \left( \dot {x} \right) = c_1 \dot {x} + c_2 \left| \dot {x}
\right|\dot {x} becomes stronger, and when the damping ratio in the
corresponding linear model is relatively high, the relative transmissibility
decreases at frequencies higher than the resonance frequency of the
corresponding linear damping system and the absolute one increases for the
frequency ratios above \sqrt 2 . Finally, the displacement
transmissibility of a nonlinear isolator with piecewise mixed viscous damping
is discussed and the process shows research similarity with the non-piecewise
case.
