第10课 试验模态分析

Copyright© 2003 Brüel & Kjæ r Sound & Vibration Measurement A/S All Rights Reserved

Experimental Modal Analysis

Modal Analysis 1

f(t) m c k x(t)

SDOF and MDOF ModelsDifferent Modal Analysis Techniques Exciting a Structure Measuring Data Correctly

=

+

+

+ + Modal Analysis Post Processing

Modal Analysis 2

Simplest Form of Vibrating SystemDisplacement

d = D sin nt DTime

Displacement

T m k

1 T

Frequency

Period, Tn in [sec] Frequency, fn= n= 2 fn =1 Tn

in [Hz = 1/sec]

k m

Modal Analysis 3

Mass and Spring

time

n 2 f n

k m m1

m1

m

Increasing mass reduces frequency

Modal Analysis 4

Mass, Spring and Damper

time

Increasing damping reduces the amplitude k

mc1 + c2

Modal Analysis 5

Basic SDOF Modelf(t)

mc k

x(t)

M (t ) Cx(t ) Kx(t ) f (t ) xM = mass (force/acc.) C = damping (force/vel.) K = stiffness (force/disp.)

(t ) x x( t ) x( t ) f (t )

Acceleration Vector Velocity Vector Displacement Vector Applied force Vector

Modal Analysis 6

SDOF Models — Time and Frequency DomainF( ) H( ) X( )

|H( )|

f(t)m x(t)

1 k

1 2m

1 c

c

k

H( ) 0º – 90º – 180º

0 = k/m

f (t ) m (t ) cx(t ) kx(t ) x

H ( )

X ( ) 1 F ( ) 2m j c k

Modal Analysis 7

Modal MatrixModal Model (Freq. Domain) X 1 X H11 H 21 2 H 22 X 3 H 23 H n1 X n

H1n F3 H nn

X2X1

X3 H22

X4

H21

F3

Modal Analysis 8

MDOF ModelMagnitude

1+2 d1 + d 2 m

2

1Frequency

d1Phase

dF

Frequency 0°

1-90°

2 1+2

-180°

Modal Analysis 9

Why Bother with Modal Models?Physical Coordinates = CHAOS Modal Space = 1

Simplicity

Rotor2 1

1

q12 01

Bearing

Bearing1

2q22 02

Foundation

2 2

3 1q32 03

2 3

Modal Analysis 10

Definition of Frequency Response FunctionF(f) FH

H(f) X

X(f)

f

H

f

f

H(f ) X(f ) F(f )H(f) is the system Frequency Response Function F(f) is the Fourier Transform of the Input f(t) X(f) is the Fourier Transform of the Output x(t)

Modal Analysis 11

Benefits of Frequency Response FunctionF(f) H(f) X(f)

Frequency Response Functions are properties of linear dynamic systems They are independent of the Excitation Function

Excitation can be a Periodic, Random or Transient function of timeThe test result obtained with one type of excitation can be used for predicting the response of the system to any other type of excitation

Modal Analysis 12

Different Forms of an F

RF

Compliance (displacement / force)Mobility (velocity / force) Inertance or Receptance (acceleration / force)

Dynamic stiffness (force / displacement)Impedance (force / velocity) Dynamic mass (force /acceleration)

Modal Analysis 13

Alternative EstimatorsF(f)

H(f)

X(f)

H( f ) X ( f ) F( f )

H1( f ) GFX ( f ) GFF ( f ) H 2 ( f ) GXX ( f ) GXF ( f )H3( f ) G XX GFX H1 H 2 GFF GFX2

GFX G G* H 2 ( f ) FX FX 1 GFF GXX GFF GXX H 2Modal Analysis 14

Which FRF Estimator Should You Use?AccuracyDefinitions:H1( f ) GFX ( f ) GFF ( f ) H 2 ( f ) GXX ( f ) GXF ( f )G XX GFX H3( f ) GFF GFX

Accuracy for systems with:

H1

H2

H3

Input noiseOutput noise Input + output noise

Best -

Best-

Best

Peaks (leakage)Valleys (leakage)

Best

Best-

-

User can choose H1, H2 or H3 after measurementModal Analysis 15

f(t) m c k x(t)

SDOF and MDOF ModelsDifferent Modal Analysis Techniques Exciting a Structure Measuring Data Correctly

=

+

+

+ + Modal Analysis Post Processing

Modal Analysis 16