Lab 1 Instructions
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Date
Dec 6, 2023
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ENME 599, Winter 2023
Lab 1 Instructions
1 |
P a g e
Free Vibration (Transient Response) of Single Degree of Freedom Mechanical Systems
Objectives
1.
Working with a function generator and oscilloscope
2.
Experimental analysis of the dynamics of a single-degree-of-freedom (SDOF) mechanical system
3.
Quantitative characterization of the dynamics of an SDOF system
•
Data acquisition using accelerometer and NI (National Instruments) DAQ in LabVIEW
•
Identification of the natural frequency and the damping ratio using the logarithmic decrement method
4.
Comparison of the experimental and analytical results
Safety and Instrument Protection
The accelerometers used in this experiment are
very delicate
and
expensive
(up to $1000 per piece). They can
be easily damaged by shock (
e.g
., dropping or hitting a hard object). Please handle them with care. Also, take
care not to tangle the cords of the accelerometers, as they can be damaged. Check that all the signal cables
from/to the accelerometer, DAQ, BNC cables and oscilloscope are
disconnected
at the end of the lab.
Agenda
1.
A brief introduction to the free vibration of SDOF systems by the TA
2.
Demonstration of procedures by the technician (or TA) that needs to be followed by each group
•
Measurement of signals from a function generator and output of a potentiometer using an oscilloscope
•
Building a data acquisition block diagram in LabVIEW
•
Data acquisition of a slender beam without and with end-mass using accelerometer and DAQ in LabVIEW
Experiments
1.
Measurement using a function generator and oscilloscope:
The circuit shown in
Figure 1
is built and then
connected to a function generator. The input and output signals of the circuit are measured using the
oscilloscope. The connections must be as follows:
Figure 1:
Measurement setup consists of a function generator, potentiometer and oscilloscope
•
Connect the function generator to the input of the circuit.
•
Connect the function generator to
channel 1
and the output of the circuit to
channel 2
of the oscilloscope.
•
Measure the signals from the function generator and the potentiometer using cursors on the oscilloscope.
Function
generator
Oscilloscope
Ch1
Ch2
Ch3
Ch4
POT
(10 kΩ)
Ground
Input
Output
Input
Capacitor (10 μF)
Ground
BNC cables
ENME 599, Winter 2023
Lab 1 Instructions
2 |
P a g e
2.
Free vibration of SDOF system:
A LabVIEW program is used to acquire the signals with an appropriate
sampling rate. Figure 2 shows the experimental setup and the test procedure for the beam without and with
the end mass.
•
Measure the length, width and thickness of the beam and weight of the additional mass and fill out Table 1 on
the worksheet (already filled).
•
Attach the accelerometer by pressing and gently twisting it onto the beam.
•
Tape down the cables to avoid picking up additional noise during your measurements.
•
Connect the accelerometer to the DAQ 9234.
•
Turn on the accelerometer using NI-MAX according to the instruction. Use
m/s
2
as the unit for acceleration.
•
Apply a
10 mm
initial displacement at the end of the beam and then release it.
•
Acquire and save data in text format (1
st
column: time and 2
nd
column: acceleration) and use them to complete
the lab assignments.
Figure 2:
Single-degree-of-freedom experimental setup
Note 1:
When the experiment is performed with the end mass, the accelerometer must be attached to the top of the
mass.
Note 2:
Do not hit on the table or shake the cables when acquiring data.
Note 3:
The data files can be read using MATLAB, Excel or Notepad. The first column of the data files is the time (sec)
signal and the second column is the acceleration (m/s
2
) signal.
Lab Assignment:
1.
Use the data file of the beam without the end-mass (
Beam_Without_Mass.lvm
) and do the following calculations:
a.
Plot the acquired waveform and calculate the experimental period of oscillation
T
nE
, from the plotted data.
Consider at least ten oscillations and disregard the first three oscillations.
b.
Estimate the damping ratio
ξ
, using the logarithmic decrement method. Consider at least five oscillations.
c.
Calculate the analytical period of oscillations
T
nA
, by following the procedure presented in Table 2 of the
worksheet.
d.
Compute the error between the measured and calculated periods of oscillation.
e.
Explain possible causes of discrepancies between the measured and calculated periods of oscillation.
2.
Use the data file of the beam with the end-mass (
Beam_With_Mass.lvm
) and do the following calculations.
a.
Repeat sections
a to d
from question 1 for the beam with end mass.
b.
Formulate the equation of motion (EOM) and find the displacement of the beam
analytically
. Consider an initial
displacement of
X
0
= 0.01
m
and an initial velocity of
V
0
= 0 m/s as the initial condition of the problem. Except for
the damping ratio, which is identified experimentally, all other parameters (natural frequency,
etc
.) must be
calculated using analytical expressions (refer to the worksheet).
c.
Calculate the experimental displacement of the beam by dividing the experimental accelerations by
–
ω
n
2
(experimental).
d.
Plot the analytical displacement, from section b, and experimental displacement, from section c, in a single figure.
Only show twenty oscillations. Compare the results and discuss the deviations.
Note 4:
The worksheet should also be completed and provided with the lab report.
L
h
m
b
Accelerometer
Beam
NI 9234
AI0
AI1
AI2
AI4
y
0
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