Viscous Heating of Fluid Dampers. I: Small-Amplitude Motions

Abstract

The problem of viscous heating of fluid dampers is examined in this paper at the limit of small-amplitude motions where the heat transfer equation becomes linear. At this limit, a one-dimensional energy equation expressed at a cross section of the damper is proposed to approximate the three-dimensional heat transfer equation. The power input into the damper is represented by a distributed heat source located at the piston head. Solutions under different forcing functions are derived for the temperature rise within the damper as a function of time and position. Of particular interest are the solutions for the temperature rise adjacent to the piston head where most of the input energy is dissipated. The derived closed-form expressions can be directly used to estimate the steady-state temperature of fluid dampers subjected to long-duration, small-amplitude motions.