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.

2DOF.SLDASM

DISCRETE SYSTEMS

multi pendulum.SLDASM

DISCRETE SYSTEMS

1st mode

2nd mode

3rd mode

4th mode

5th mode

LEGO.SLDASM

DISTRIBUTED SYSTEMS

Experimental analysis to follow

Experiment 4 Shaker LEGO

Detailed geometry Simplified geometry

Experiment 4 Shaker LEGO

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

pan.SLDPRT

1st mode

2nd mode

3rd mode

4th mode

5th mode

6th mode

DISTRIBUTED SYSTEMS

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

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

Note:

sine excitation is NOT the only one available

SHAKERS

Shaker can provide both force and base excitation

shaker.sldprt

SHAKERS

SHAKERS

pan.SLDPRT

Mode 1

Mode 2

Shakers

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

CA

NT

ILE

VE

R B

EA

M A

NA

LY

TIC

AL

SO

LU

TIO

N

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 Mode 3 Mode 5

Where is Mode 4 ?

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.

Force excitation time historybase 010.sldprt

Fixed geometry

1000N

Force excitation time historybase 010.sldprt

Fixed geometry

500N

500N

Uz Uy

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

FOURIER TRANSFORM

Continuous function

Discrete function

-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

Mode 1 4.5Hz

0.22s

Mode 1 26Hz

0.038s

Mode 3 42Hz

0.023s

Mode 4 75Hz

0.013s

Fourier beam.SLDPRT

Study 01dt impulse duration 0.0075

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

Fourier beam.SLDPRT

Study 02dt impulse duration 0.05

Study 02dt

Response time history FFT of response time history

Only mode 1 is excited. Larger impulse (longer duration) caused larger displacement amplitude response

Study 03dt impulse duration 0.0075

Study 03dt

Response time history FFT of response time history

Mode 1 and mode 2 are excited.

Study 04dt impulse duration 0.0075

Study 04dt

Response time history FFT of response time history

Mode 1 and mode 2 are excited.

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

elipse.sldprt in /vibration experiments

PREPARATION FOR LAB

hex.sldprt in /vibration experiments

PREPARATION FOR LAB

PREPARATION FOR LAB

tree.sldprt in /vibration experiments