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10
频响函数的时域含义
m
x1 H11

x2 x3

=

H
21
H 31

Inverse FRF: F(orce)/R
Dynamic Stiffness动刚度 Mechanical Impedance机械阻抗
Apparent Mass
(Source: “Modal Testing: Theory, Practice and Application,” by D. J. Ewins)
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3
时域到频域的转换
⚫ 载荷用谐波表示
Mx(t) + Cx(t) + Kx(t) = f (t)
取某一特定激励频率
20
模态阻尼OptiStruct数值计算案例
99.875298 14.83414 102.96423 21.093685 106.05316 15.001724
输入阻尼 g=0.06
536.28412 552.87024 569.45636
4.6593304 6.6819339 4.8037124
模态法 Modal approach
18
频率激励/输出设置
⚫ FREQ定义离散频率点
‒ 以下例子定义20,100,200,500,1000Hz共5个输出频率
1
2
3
4
5
6
7
8
9
10
FREQ SID
F1
F2
F3
F4
F5
-etc.-
FREQ 1
20.
100.
200.
500.
1000.
⚫ FREQ1线性平均离散频率点
time
11
频响函数的时域含义
|H31 |
f =1
m
f =1
time 1
自动正弦扫描激励(Auto-Swept Sine Excitation)
Tr
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12
frequency
frequency 2
Time
频响函数的试验获取方式
⚫ 对于中小型结构可以用振动台或者激振器作为激励源
⚫ 大型结构使用力锤
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7
传递函数/频响函数的重要意义
⚫ 线性系统单位激励下的频率响应
⚫ 代表线性系统的力/能量传递路径
f1
xp
⚫ 通过频响函数可以得到频率和阻尼
fi
system
xr
⚫ 复杂激励可以通过单位频响函数来叠加得到
fj
xq
fm
Test Model
Frequency Response Function
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17
直接法 Vs模态法频响分析
⚫ 模态法计算速度快 more faster ⚫ 模态法比直接法更精确地捕捉响应峰值 more accurate
直接法 Direct approach
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2
频响分析 Frequency Response Analysis
⚫ 想象给结构一系列的不同频率的正弦波激励，每个激励都可以进行瞬 态分析。当系统达到稳定状态时，取其振动幅值。
⚫ 因此，频响分析也称为谐波分析，或者实验称为正弦扫频分析。
=
f
--------------
t
谐波激励 Sinusoidal excitations:
a1, f1, 1 a2, f2, 2 a3, f3, 3
= a4, f4, 4
.
ai, fi, i
.
a40, f40, 40
16
幅值
相位
This curve is actually a histogram
确定性的 (频域)
时延与相位 Delay vs Phase
t1
+ t1
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Out
15
freq
TF/FRF
frequency
Out = In FRF
freq
时延与相位 Delay vs Phase
随机的 (时域)
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Displacement
Velocity Acceleration
Standard FRF: R/F(orce)
Receptance响应率
Admittance导纳 Dynamic Compliance动柔度
Dynamic Flexibility动柔度
Mobility
Accelerance Inertance
‒ 以下例子定义从20Hz开始，每隔20Hz输出一个结果，共输出100个频点 ，即频率范围20Hz~2000Hz
1
2
3
4
5
6
7
8
9
10
FREQ1 SID
F1
DF
NDF
FREQ1 1
20.0
20.0
99
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‒ 所有的外力在每一个指定的频率上都是已知的。 ‒ 激励可以是外力也可以是强迫运动（位移、速度、加速度）。
⚫ 频响分析的典型应用：
‒ NVH ‒ 转子系统的载荷 ‒ 直升机叶片等
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x(t) = u()eit

f
(t)
=
F
()eit
(−2M + iC + K )u() = F ()
⚫ 可以采用2种算法：
‒ 直接法 ‒ 模态法
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g f1
= f f1
= 106.05 − 99.88 = 5.99% 102.96
f 569.46 − 536.28
g f2 = f2 =
552.87
= 6.001%
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( ) j () =
f j () −2m j + ic j + k j
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6
什么是传递函数
⚫ 一般把单位载荷下的频响称为传递函数(Transfer Function)

xn H n1
H12 H 22 H 32
Hn2
H13 H 23 H 33
Hn3
H1n f1
H2n H 3n


f2 f3



H nn fn
x3
time
f =1
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19
输出频点的自动加密FREQ4
⚫ FREQ4可以自动在共振频点进行加密计算，提高计算精度。
A
在每个自然频率附近加密输出频点；
A
默认为共振频率+/- 10% (经常使用是
2
+/- )
f=gfn=2fn
fn
frequency
OptiStruct使用freq4卡片
5
5 5
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