Typora测试
2018-04-07 本文已影响0人
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Abstract
格式ctrl+B,I,U
typora typora typora <u>typora</u>
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<center>图1. 测试图片</center>
插入表格ctrl+T
| 1 | 2 | 3 |
|---|---|---|
| a | 1 | 4 |
| b | 3 | 1 |
| c | 2 | 1 |
一段matlab代码
%find the Linear system's response by state-space method
function Xt = findResponse(K,M,C,dt,U,X0)
nd = size(M,1); N = max(size(U));
B = eye(nd); %外荷载作用的位置
Ac = [zeros(nd),eye(nd); -inv(M)*K, -inv(M)*C];
Bc = [zeros(nd);inv(M)*B];
1. Introduction
2. Conventional SOD method
2.1 sod theory
数学证明：
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证：取（1）的逆 $\Psi^{-1} (XXT）{-1} \Psi^{-T} = \Sigma_q^{-1}$
并右乘（2）得$\Psi^{-1} (XXT）{-1} （VV^T）\Psi = Sigma_q^{-1}\Sigma_\dot{q}=\Lambda_{xv}$
移项得$（VV^T）\Psi =XX^T \Psi\Lambda_{xv}$
两边除以$N-1$即$R_{v}\Psi =R_{x} \Psi\Lambda_{xv}$,证毕。
2.2 sod for damped and noise contaminated signals
2.3 sod for $m\lt n$
由于SOD倾向于提取出能量较大模态坐标振动，假设前m阶响应能量较大, 设$\Sigma_q$的前m行m列为$\hat{\Sigma}q$, 后n-m行n-m列为$\check{\Sigma}q$
$XX^T = \Phi{m \times m} \hat{\Sigma}q \Phi{m \times m}^T+\Phi{m \times (n-m)} \check{\Sigma}q \Phi{m \times (n-m)}^T$
