Transcript Document

MODULE 10
EXPERIMENTAL MODAL ANALYSIS
Most vibration problems are related to resonance phenomena where
operational forces excite one or more mode of vibration.
Modes of vibration which lie within the frequency range of the operations
dynamic forces, always represent potential problems.
An important property of modes is that any dynamic response (forced or free)
of a structure can be reduced to a response of discrete set of modes.
DISCRETE SYSTEMS
2DOF.SLDASM
DISCRETE SYSTEMS
multi pendulum.SLDASM
DISTRIBUTED SYSTEMS
1st mode
2nd mode
3rd mode
4th mode
5th mode
Experimental analysis to follow
LEGO.SLDASM
Experiment 4 Shaker LEGO
Experiment 4 Shaker LEGO
Detailed geometry
Simplified geometry
Experiment 4 Shaker LEGO
2.323g
1.261g
Modulus of elasticity as for the ABS plastic
Material density has been adjusted so that the simplified block have the same mass as real blocks
Experiment 4 Shaker LEGO
lego cantilever.SLDASM
Note that there are gaps between blocks
indicated by red arrows.
The first vibration mode in
the direction of excitation
DISTRIBUTED SYSTEMS
1st mode
pan.SLDPRT
4th mode
2nd mode
5th mode
3rd mode
6th mode
EXPERIMENTAL MODAL ANALYSIS
The modal parameters are:
Modal frequency
Modal shape
Modal damping
Modal parameters represent the inherent properties of a structure which are independent of
any excitation.
Modal analysis is the process of determining all the modal parameters which is sufficient for
formulating a mathematical model of a dynamic response.
Modal analysis may be accomplished either through analytical, numerical or experimental
techniques.
EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES
Impact testing
EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES
Impact testing
EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES
Impact testing
EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES
Shaker testing
EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES
Shaker testing
EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES
Shaker testing
EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES
Shaker testing
SHAKERS
Note:
sine excitation is NOT the only
one available
Shaker can provide both force and base excitation
SHAKERS
shaker.sldprt
SHAKERS
Shakers
Mode 1
Mode 2
pan.SLDPRT
CANTILEVER BEAM EXPERIMENT
Mode 1
3.5Hz
Mode 2
23Hz
Mode 3
63Hz
Mode 4
127Hz
Experimental kit to demonstrate modes of vibration of a cantilever beam
CANTILEVER BEAM ANALYTICAL SOLUTION
CANTILEVER BEAM NUMERICAL SOLUTION
cantilever beam MME9500.SLDPRT
This model should give the same results as the experiment in previous slide.
CANTILEVER BEAM NUMERICAL SOLUTION
Mode 1
Mode 2
Where is Mode 4 ?
Mode 3
Mode 5
EXPERIMENTAL MODAL ANALYSIS
Most common means of Implementing the excitation
Non-attached exciters
Hammers
Pendulum impactors
Attached exciters
Shakers
Eccentric rotating devices
Hammers
The excitation is transient
The duration and thus the shape of the spectrum of the impact is determined by the mass and
stiffness of both the hammer and the structure. For a relatively small hammer used on a hard
structure, the stiffness of the hammer determines the spectrum.
Fixed
geometry
1000N
base 010.sldprt
Force excitation time history
Fixed
geometry
500N
500N
base 010.sldprt
Uz
Force excitation time history
Uy
Fourier beam.sldprt
1
2
1.5
Transformation from the time
to the frequency domain
1
0.5
0
0
0.05
0.1
0.15
0.2
0.25
(Fourier transformation)
0.75
0.5
-0.5
0.25
-1
-1.5
0
-2
0
20
40
60
80
100
Response time history
Response spectrum
It is not immediately obvious
what frequencies are present in
the response
In the frequency domain it is
clear that two frequencies have
been excited: 8Hz and 53Hz
FOURIER TRANSFORM
The Fourier transform is a mathematical operation that decomposes a signal into its constituent frequencies. Thus the
Fourier transform of a musical chord is a mathematical representation of the amplitudes of the individual notes that make
it up. The original signal depends on time, and therefore is called the time domain representation of the signal, whereas
the Fourier transform depends on frequency and is called the frequency domain representation of the signal. The term
Fourier transform refers both to the frequency domain representation of the signal and the process that transforms the
signal to its frequency domain representation.
FOURIER TRANSFORM
What is a Fourier Transform?
A Fourier Transform is a mathematical operation that transforms a signal from the time domain to the frequency
domain. We are accustomed to time-domain signals in the real world. In the time domain, the signal is expressed
with respect to time. In the frequency domain, a signal is expressed with respect to frequency.
What is a DFT? What is an FFT? What's the difference?
A DFT (Discrete Fourier Transform) is simply the name given to the Fourier Transform when it is applied to digital
(discrete) rather than an analog (continuous) signal. An FFT (Fast Fourier Transform) is a faster version of the DFT
that can be applied when the number of samples in the signal is a power of two. An FFT computation takes
approximately N * log2(N) operations, whereas a DFT takes approximately N2 operations, so the FFT is significantly
faster.
http://www.ni.com/support/labview/toolkits/analysis/analy3.htm
FOURIER TRANSFORM
Continuous function
Discrete function
30
20
10
0
0
0.2
0.4
0.6
0.8
1
-10
Fourier beam.sldprt
-20
-30
16.00
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00
0.00
10.00
20.00
30.00
40.00
50.00
60.00
Mode 1
4.5Hz
Mode 1
0.22s
Mode 3
42Hz
0.023s
26Hz
0.038s
Mode 4
75Hz
0.013s
Fourier beam.SLDPRT
Study 01dt
impulse duration 0.0075
Response time history
FFT of response time history
Only mode 1 and mode 2 are excited. Larger impulse (longer duration) caused larger displacement amplitude
response
Study 01dt
Fourier beam.SLDPRT
Study 02dt
impulse duration 0.05
Response time history
FFT of response time history
Only mode 1 is excited. Larger impulse (longer duration) caused larger displacement amplitude response
Study 02dt
Study 03dt
impulse duration 0.0075
Response time history
FFT of response time history
Mode 1 and mode 2 are excited.
Study 03dt
Study 04dt
impulse duration 0.0075
Response time history
FFT of response time history
Mode 1 and mode 2 are excited.
Study 04dt
Fourier beam.SLDPRT
Study 05dt
impulse duration 0.05
Based on one mode only
1% damping
How to excite mode 3
- side hit
How to excite mode 4?
Hit here!
and here!
The format is:
freq(Hz) real amplitude (units)
imaginary amplitude (units)
fft_half.out
double sided half amplitude magnitude
fft_full.out
single-sided full amplitude output
fft_full_mp
full amplitude magnitude & phase output
fourier.exe or fft.exe can be used
PREPARATION FOR LAB
elipse.sldprt in /vibration experiments
PREPARATION FOR LAB
hex.sldprt in /vibration experiments
PREPARATION FOR LAB
tree.sldprt in /vibration experiments