Altair随机振动资料

6
6
正态分布的置信水平 1σ~3σ
安全区域
危险区域0.135%
99.73%
危险区域0.135%
6 5σ
4
3
2
1
1
σ
2
3
4 5 6
F ( x)
1 2


x
e
( x )2 2 2
P(|x|σ) 68.27% 95.45% 98.76% 99.73% 99.953% 99.9937%
PSD计算公式 PSD Function Calculation
双边谱
1 S xx ( ) 2



Rxx ( )e
i
d
2 S xx PSD使用单边谱 Gxx 0
0 0
2 1 S xx FFT x(t ) T
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Copyright © 2013 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.
13
13
典型PSD载荷谱(2/2)
Example 2 of random loading:
Freq(Hz) 10 20 50 600 1500 2000 g2/Hz 0.1 0.1 0.3 0.3 0.12 0.12
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3
各态历经随机信号，N(µ,σ) Ergodic Random signal
acce acce
µ
0
Time
Pdf
F ( x)
Square of Transfer Function
H 2 r / x ( )
Pa 2 Hz
160 140 120 100 80 60 40 20
Response PSD
0
S rr ( ) H r / i Si ( )
0 20 40 60 80 100 120 140 160 180 200
• Stationary: For every t, PDF (Probability Density Function), x and x2 of every record are constant. 对每个采样数据，概率密度函数， x和x2 是恒定的。 • Ergodic: If the random process is stationary , and the characters of any single record are the same as the ensemble of records.对所有 的采样数据，任意时间段内都是稳态的
10
10
如何生成PSD载荷 Convert time records to PSD
不同路面的时域数据
Zero mean
PSD (g2)/Hz 取包络线 log
A
Input PSD = Envelope curve包络线
包络线下的面积为A
f1
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.001 10 100 1000
12
log10(f)
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典型PSD载荷谱(1/2)
Jaap Wijker，Random Vibrations in Spacecraft Structures Design， Page163
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5
随机振动响应的两个基本假设
随机振动分析方法有两个基本假设：
‒ 载荷和响应 满足正态分布假设
‒ 载荷和响应 满足零平均值假设
Copyright © 2013 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.
2 1 2 1
lg 2
0.30103
-6 dB/oct (- slope) xxx grms
十倍频decade lg
f f
2 1
.1 .01
log10(a)
g2/Hz
Gxx
+5 dB/oct (+ slope)
-6 dB/oct (- slope)
Gx f 2 dB 10 log10 G x f1
随机振动结果的常用置信水平
Common confidence level for random vibration
acce
+g
acce
µ =0
σ
2σ
3σ
Pdf
-g Time
F ( x)
1 2

e
x

x2 2 2
dx
σ 2.5σ
安全率 98.76%
失效率 1.24%
3σ
3.5σ
99.73%
0.1000
+3dB/oct (pos) (10,0.02519)
-9dB/oct (neg)
频率点(Hz) 10 100 600 2000 RMS(g)
谱密度(g2/) 0.02519 0.25 0.25 0.00683 14.3497
0.0100
(2000,0.00683)
0.0010 10.00
T /2
自功率谱密度函数定义 (Auto)PSD
1 S xx ( ) 2



Rxx ( )e
i
d
PSD
Rxx ( ) S xx ( )e d A


i
RMS A
f1
9
A
f2
Copyright © 2013 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.
P(|x|>σ) 31.7% 4.55% 1.24% 0.27% 0.047% 0.0063%
Per Million/每百万 317,300 45,500 12,400 2,700 470 63
dx
1σ 2σ 2.5σ 3σ 3.5σ 4σ
1 n 2 RMS a i n i 1
随机振动采用双边置信水平
5σ
6σ
99.999943%
99.9999998%
7
0.000057%
0.0000002%
0.57
0.002
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自相关函数： (Auto)correction
1 Rxx ( ) E x (t )x t dt x t x t lim t T T /2
x 2 x 2 Rxx ( ) x 2 x 2 , Rxx ( ) Rxx (0)
1 2

e
x
( x )2 2 2
dx
1 n 2 a RMS i n i 1
工程上常见的随机信号，可以用高斯分布，即正态分布来表示。 均方根(标准差Standard deviation)：每个样本点到平均值的平均距离。 x，x 只能反映载荷的幅值或者强度变化，但是完全不能反映频谱特性
g Hz
2
0.06 0.05 0.04 0.03 0.02 0.01 0.00 3500 0 A B
Input PSD
S xx ( )
C 100 200 300
Pa 2 g2
3000 2500 2000 1500 1000 500
4% 5% 6% 8% 0 0 20 40 60 80 100 120 140 160 180 200
log
11
f2 11
PSD输入谱的典型定义
二倍频octave log 2
2 1
Example 1 of random loading: 20-160 Hz 160-800 Hz 800-2000 Hz Overall +5 dB/oct (+ slope) 0.06 g2/Hz
f f lg f f lg f f
典型的PSD谱及换算
Example 3 of random loading:
频率范围(Hz)
谱密度(g2/Hz)
1.0000
10-100 100-600 600-2000
RMS(g)
+3dB/oct
(100,0.25) (600,0.25)
0.25 -9dB/oct
14.3497 换算
Acce PSD g2/Hz
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