The Earthquake Engineering Online Archive

Viscous heating of fluid dampers during seismic and wind excitations: analytical solutions and design formulae

Makris, Nicos; Roussos, Yiannis; Whittaker, Andrew S.; Kelly, James M.

UCB/EERC-97/11, Earthquake Engineering Research Center, University of California, Berkeley, 1997-11, 55 pages (530/V57/1997)

The problem of viscous heating is examined, and closed-form expressions are developed to compute the temperature rise within fluid dampers as they dissipate the earthquake or wind-induced energy in structures. First, the problem of viscous heating is analyzed at the limit of very small piston motions. The range of validity of the linearized heat transfer equation is investigated, and analytical solutions for the temperature rise on the piston head are derived. Solutions for different forcing functions are derived by considering an approximate one-dimensional energy equation expressed at a cross section of the damper, which was obtained after replacing the power input in the damper with a distributed heat source located at the piston head. Subsequently, the problem of viscous heating is analyzed at the limit of long-stroke motions where most of the fluid travels through the damper valve(s). This study is of interest in the case of strong earthquake motions where dampers are subjected to large displacements. The one-dimensional energy equation 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, viscoelastic and nonlinear dampers are developed; and it is shown that, in some cases, the temperature of the fluid within the dampers might reach critical values. Recommendations on the damper design are offered to keep the damper temperatures within acceptable values.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-97-11.pdf (4 MB)