SEGi University FACULTY OF ENGINEERING & BUILT ENVIRONMENT

SUBJECT: EME3431 LAB. INVESTIGATION 4

Experiment: Forced Vibration of an Undamped Simply Supported Beam

1.0 Objective:

To determine the amplitude of vibration for an undamped simply supported beam subjected to a rotating unbalanced mass, variable mass and fixed motor speed.

2.0 Procedure

Setting up the apparatus1. Check the position of the pinned supports to make sure that they are at the same

level.2. Take the beam and mount it on the two supports. Make sure that the beam is held

in position at one support, by slightly turning the screw such that it touches the beam. Ensure that the other end of the beam is free to slide over the support

3. Locate the centre of the beam and fixed the motor with the out-of-balanced mass at this location.

4. Fixed the vertical guide to the horizontal member of the frame directly below this position.

5. Decide on the mass to be used for loading the beam.6. Anchor the weight stopper tightly to the loading rod.7. Insert the loading rod through the hole at the centre of the mass.8. Insert another weight stopper at the bottom of the mass and tightened it so that the

mass is between the two weight stoppers.9. Insert the lower end of the loading rod through the hole in the vertical guide.10.Screw the top end of the loading rod to the hole at the bottom of the motor

mounting.11.Adjust the position of the vertical guide so that the the loading rod is vertical and

free to oscillates.12.Fixed the LVDT to the LVDT stand13.Adjust the position of the stand so that the LVDT's probe is resting on top of the

motor and clear of all objects.14.Anchor the stand to the frame by turning the knob at the top of the stand.15.Adjust the height of the LVDT such that the probe is approximately at its centre

position. Anchor theLVDT to the stand.16. .Connect the LVDT to one of the channel at the data acquisition terminal block.

Setting the motor speed

17.Decide on the motor speed in rpm.

18.Switch on the motor. Adjust the speed control button until the desired speed is displayed on the LED monitor.

19.Switch off the motor and let the oscillation dies down.

Setting the software

20.From the Window Start menu, go the to program menu. Choose Data translation Inc, then click on the quickDAQ button. This will run the data acquisition program.

21.Refer to the quickDAQ manual to setup the data acquisition system

22.Click the 'Run' button to record the initial position of the displacement transducer.23.After a few seconds click the 'Stop' button

24.Save data using the 'Save As' command in the 'File' menu. Save data in the CSV format so that it can be read by EXCEL spreadsheet.

25.Switch on the motor and click the 'Run' button to record the oscillation of the beam.26.After a few seconds click the 'stop' button and switch off the motor. Let the

oscillation dies down.27.Save data using the 'Save As' command in the 'File' menu. Save data in the CSV

format so that it can be read by EXCEL spreadsheet28.Unscrew the loading rod and the weight stopper and increase the load on the rod.29.Tightened the weight stopper and screw the top end of the loading rod to the hole

at the bottom of the motor mounting.30.Repeat step 22 to 29 for a few more load increaments.31.Measure the width and thickness of the beam

3.0 ResultDiameter of out-of-balance mass 150 mm (please check)Mass of out-of-balance mass gm eachMass of motor assembly gmMass of loading rod gmThickness of beam mmWidth of beam mmMoment of inertia, I, of beam mm4

Length between supports mmMotor speed from speed indicator rpmLVDT conversion factor mV/V/mm

Experiment al Frequency and Period Of Oscillation For Each Mass

1. Run the Excel spread sheet program.

2. Open the 'initial position of the LVDT' data file for the first mass. Caculate the average voltage output from the transduce before the experiment (initial reading)

3. Open the data file that records the experimental results of the first mass. Subtract the initial reading from all the data (the beam is now oscillating approximately about the 0 volt axis)

4. Add column to the left of the data.5. In the new column insert the data number for each data6. Plot the graph of LVDT readings Vs time for approximately 10 cycles.7. From the graph determine the frequency of vibration by filling in the Table 1 below .

The frequency of vibration coincide with the speed of rotation of the out of balance mass. The speed meter only indicates the approximate speed of rotation of the motor. Therefore all calculations should be based on the frequency obtained from the graph.

8. From the graph obtain the double amplitude of vibration and record it in Table 2 below. Convert the double amplitude readings from voltage to meter using the conversion factor given for the transducer. Refer to Manual

9. Repeat the above procedures for other masses

Table 1: Mass No.1Data No. For each

CycleCycle No. Start End Time per cycle millisec

%

Note : * Time / cycle, (period) = No. of (Data / Cycle) x (Time to scan 1 sample) ** Frequency = 1/(period)

Repeat the above procedures until the frequencies and double amplitude of all the masses are obtained and fill the results in Table 2 below.

Table 2 Experimental ResultsMass (kg) Average Angular Freq =

Frequency of rotating Mass

(rad/sec)

Double Amplitude YT m

\

Calculate the amplitude for all the masses and fill the results in the Table 3 below

* Table 3

Oscillating Mass.m kg

Experimental Theoretical Frequency Of The

System u>rad/sec

Double Amplitude YT m

Average Single Amplitude,Y=Yt/2

m

Plot the graph of maximum amplitude versus oscillating mass. Draw conclusions from the results obtain

LVDT to measure displacement

Motor

Vertical Guide

Beam Specimen

Rotating Unbalanced Mass

Mass undergoing oscillation

Motor Controller

Experimental Setup

The equipment comprises of:(a) A beam that is tightly anchored to the pinned supports.(b) The loading rod to mount the oscillating mass to the beam.(c) Weight stopper to hold weight in position during oscillation.(d) A motor to drive the out-of-balanced mass(e) A motor speed controller to set the speed of the rotating unbalanced

mass(f) LVDT to measure the displacement during oscillation.(g) 6 volt battery pack to energise the displacement transducer.(h) A simple data acquisition system to logged the output from the displacement

transducer.

The LVDT

The LVDT is of the inductive type. Its connection to the power supply and data acquisition system is as follows:

Red connected to positive excitation terminal Blue connected to the negative excitation terminal White connected to the positive signal terminal Green connected to the negative signal terminal

The output from the LVDT is dependent on the battery voltage. Each transducer has its own conversion factor and is shown on the paper attached to

the lead wire. The conversion factor is given in the form of xxx mV/V/mm output. Thus if the

conversion factor is 15.5 mV/V/mm and the battery voltage is 6.34 volts, then 1 mm displacement will generate 15.5 x 6.34 mv of signal. This signal will be digitised by the data acquisition system.

To convert the digitised signal back to mm simply divide the digitised voltage by the conversion factor and the battery voltage.

Displacement (mm) = digitised voltage / (conversion factor x battery voltage)

Mass Of Critical ComponentsMass of semicircular disk & attachment (each) = 193 gms Total motor attachment + guide = 1658 gmLoading rod = 195 gm

Units of measurement for calculation purposes Mass kilogram

Displacement meter Stiffness Newton per meter

Time Second