Task $2$

Rayleigh damping

$C=K+M$

${}^{T}C={}^T(K+M)$

tilde$(C)={}^2+I$

where

tilde$(C)=\left[\begin{array}{ccc}2{}_1{}_1& 0& 2{}_2{}_2\end{array}\right]$

$0$

$\left[\begin{array}{c}2{}_1{}_1\end{array}\right]$

$2{}_2{}_2=\left[\begin{array}{ccc}{}_1^2& 1& 1\end{array}\right]$

${}_2^2\left[\begin{array}{c}\end{array}\right]$

$\left[\begin{array}{c}\end{array}\right]$

$=\left[\begin{array}{ccc}{}_1^2& 1& 1\end{array}\right]$

${}_2^2{?}^{-1}\left[\begin{array}{c}2{}_1{}_1\end{array}\right]$

$2{}_2{}_2$

Institute of Structural Engineering

Method of Finite Elements II

$7$

Case study B

A vertical load is applied to all nodes of the free end

The material behavior is assumed to be elastic perfectly plastic

The first two natural frequencies of the system are ${}_1=0\mathrm{.}4703ra\frac{d}{s}$ and ${}_2=1\mathrm{.}9118ra\frac{d}{s}$