Rayleigh's damping method

You can use Rayleigh's damping method to define modal viscous damping ratios. Rayleigh's damping method forms a damping matrix, [C], which is proportional to the stiffness and mass matrices, and such that

	Equation 1

By transforming the damping into the modal-degree of freedom space, the damping ratio (factors) can be calculated by

	Equation 2

The mass and stiffness damping constants, and , are determined by choosing the fractions of critical damping at two different frequencies and solving simultaneous equations for the constants. Thus

	Equation 3

	Equation 4

where

	= the design frequency range (represented by A in the figure)
	= damping factors at ω1 and ω2, respectively

The following figure shows the relationship between the fraction of critical damping (y) versus frequency (x), where A represents the frequency range of the design spectrum, B is the contribution made by stiffness-proportional damping, and C is mass-proportional damping.

Look up more details

Modal hysteretic and viscous damping ratios

Equivalent viscous damping ratio

Reference

Quick links

Command reference

Pre/Post video examples

Bulk Entry Descriptions

Simcenter 3D tutorials

Browse Simcenter 3D help by product area

Rayleigh's damping method , Simcenter 3D 2021.1 Series

© 2020 Siemens

window.mainLanguage="en_US"

window.delivId=""

window.projectId=""

MathJax.Hub.Config({ TeX: { extensions: ["autoload-all.js"] }, tex2jax: { displayMath: [ ] }, "SVG": { scale: 125 } });