Approach for Selection of Rayleigh Damping Parameters Used for Time History Analysis

Abstract

Nonlinearities, whether geometric or material, need to be addressed in seismic analysis. One good analysis method that can address these nonlinearities is direct time integration with Rayleigh damping. Modal damping is the damping typically specified in seismic analysis Codes and Standards [1,2]. Modal damping is constant for all frequencies where Rayleigh damping varies with frequency. An approach is proposed here for selection of Rayleigh damping coefficients to be used in seismic analyses that are consistent with given Modal damping. The approach uses the difference between the modal damping response and the Rayleigh damping response along with effective mass properties of the model being evaluated to match overall system response levels. This paper provides a simple example problem to demonstrate the approach. It also provides results for a finite element model representing an existing piping system. Displacement, acceleration, and stress results are compared from model runs using modal damping and model runs using Rayleigh damping with coefficients selected using the proposed method.

Rayleigh coefficients for series infrastructure systems with multiple damping properties

“…This ambiguity is again primarily due to the velocity dependence of the Kelvin-Voigt approximation: methods for the determination of and inherently incorporate multiple system-level natural frequencies that do not have a one-to-one correspondence to multiple material properties, requiring the user to exercise judgment in what range of frequencies is to be examined for each material (e.g. Spears and Jensen, 2009). Many previous researchers (e.g.…”

“…While several recommendations exist for the determination of and for materials based upon prior to global matrix assembly (e.g. Chopra, 2001;Spears and Jensen, 2009), these recommendations rely heavily upon user judgment and can result in the selection of many possible, equally justifiable and values. This ambiguity is again primarily due to the velocity dependence of the Kelvin-Voigt approximation: methods for the determination of and inherently incorporate multiple system-level natural frequencies that do not have a one-to-one correspondence to multiple material properties, requiring the user to exercise judgment in what range of frequencies is to be examined for each material (e.g.…”

Seismic response analysis of a piping system subjected to multiple support excitations in a base isolated NPP building

“…It is also recommended that the cumulative effective mass ratio should reach at least 5% and 50% of the total modal mass at the minimum and maximum frequencies, respectively (Spears and Jensen, 2012). The modal analysis is performed by using the Block Lanczos method to obtain the natural frequencies.…”

Seismic Design of Subsea Jumper per ISO: Part I- Preliminaries

“…An "effective damping" can be introduced using some combination of all damping, but the effective damping depends on soil structure dynamic properties. In a non-linear time-domain analysis Rayleigh approach is used to implement damping (Spears and Jensen [29]). The problem with the Raleigh method is that its parameters are calibrated using natural frequencies of the system in the linear range; as the natural frequencies change due to complex nonlinearity in soil-spool iteration, the Rayleigh effect is unknown.…”