Select Newmark method and click Parameters in the Time history analysis dialog to define the parameters of the Newmark method.
The parameters of the Newmark method include the alpha and beta damping parameters.
In the dialog there is a calculator that enables definition of the damping coefficient from the following formula.
ξ = (α + β * ω*ω) / ( 2 * ω)
After preparing a system of equations, the following formulas for alpha and beta are obtained (ω1 and ω2 are roots of the above quadratic equation).
if
then
where:
ω - Pulsation (circular frequency)
ξ - Relative damping, i.e. a part of critical damping.
The damping matrix C is calculated as a combination of the stiffness matrix K and mass matrix M with the enumerated parameters taken into account:
C = beta * K + alpha * M
See also: