Viscous heating of fluid dampers. II: Large-amplitude motions

In this paper, the problem of viscous heating of passive and controllable fluid dampers is analyzed at the limit of long-stroke motions, where most of the fluid travels through the damper orifice(s) or valve(s). This study is of interest in the case of strong earthquake motions where dampers are subjected to long-stroke motions. It is shown that under long-stroke motions the temperature rise of the entire fluid within the damper is nearly uniform. The one-dimensional energy equation presented in the companion paper is further contracted to a macroscopic energy balance equation over the entire fluid within the damper. Closed-form expressions for the temperature rise in viscous, nonlinear, viscoelastic, and controllable fluid dampers are developed under harmonic and triangular wave motions; and it is shown that under long-stroke motions the temperature rise is proportional to the pressure drop and independent of the piston velocity.