MODULE 10 EXPERIMENTAL MODAL ANALYSIS Most vibration problems are related to resonance phenomena...
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Transcript of MODULE 10 EXPERIMENTAL MODAL ANALYSIS Most vibration problems are related to resonance phenomena...
MODULE 10EXPERIMENTAL 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.
1st mode
2nd mode
3rd mode
4th mode
5th mode
LEGO.SLDASM
DISTRIBUTED SYSTEMS
Experimental analysis to follow
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
2.323g 1.261g
Experiment 4 Shaker LEGO
The first vibration mode in the direction of excitation
lego cantilever.SLDASM
Note that there are gaps between blocks indicated by red arrows.
Experiment 4 Shaker LEGO
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
Note:
sine excitation is NOT the only one available
SHAKERS
Shaker can provide both force and base excitation
Experimental kit to demonstrate modes of vibration of a cantilever beam
Mode 1 3.5Hz
Mode 2 23Hz
Mode 3 63Hz
Mode 4 127Hz
CANTILEVER BEAM EXPERIMENT
cantilever beam MME9500.SLDPRT
This model should give the same results as the experiment in previous slide.
CANTILEVER BEAM NUMERICAL SOLUTION
Most common means of Implementing the excitation
Non-attached exciters
Hammers
Pendulum impactors
Attached exciters
Shakers
Eccentric rotating devices
EXPERIMENTAL MODAL ANALYSIS
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.
Fourier beam.sldprt
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2 0.25
0
0.25
0.5
0.75
1
0 20 40 60 80 100
Response time history
It is not immediately obvious what frequencies are present in the response
Transformation from the time to the frequency domain
(Fourier transformation)
Response spectrum
In the frequency domain it is clear that two frequencies have been excited: 8Hz and 53Hz
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
-30
-20
-10
0
10
20
30
0 0.2 0.4 0.6 0.8 1
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0.00 10.00 20.00 30.00 40.00 50.00 60.00
Fourier beam.sldprt
Study 01dt
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 02dt
Response time history FFT of response time history
Only mode 1 is excited. Larger impulse (longer duration) caused larger displacement amplitude response
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