APPLIED MECHANICS LAB (MEC424) – DYNAMICS OF MACHINES LAB TITLE Forced Vibration Experiment – Resonance of Spring-Dashpot System with Damping
ABSTRACT The experiment is study the for the spring-dashpot system where we to study the effect of damping on the system. Through the experiment, we are to study the damped frequency and relate it to the natural frequency as well study the occurrence of resonance and its effect on the system.
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APPLIED MECHANICS LAB (MEC424) – DYNAMICS OF MACHINES LAB
TABLE OF CONTENTS 1.0 List of Table........................................................................................................................... 3 2.0 List of Figures........................................................................................................................ 3 3.0 Introduction............................................................................................................................ 4 3.1 Objective.................................................................................................................... 4 4.0 Theory ................................................................................................................................... 5 5.0 Apparatus .............................................................................................................................. 6 6.0 Experimental Procedure ........................................................................................................ 7 7.0 Discussion, Results and Conclusion 8.0 References
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APPLIED MECHANICS LAB (MEC424) – DYNAMICS OF MACHINES LAB 1.0
LIST OF TABLES Table: Experimental data
2.0
LIST OF FIGURES Set up of apparatus
page 6
Dimension of the beam
page 6
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APPLIED MECHANICS LAB (MEC424) – DYNAMICS OF MACHINES LAB 3.0
INTRODUCTION Forced vibration is vibration that takes place under the excitation of external forces. The system will vibrate at the excitation frequency when the excitation is oscillatory. Resonance will occur if the frequency of excitation coincides with one of the natural frequencies of the system and dangerously large oscillations may result. The failure of major structures such as buildings, bridges, or airplane wings is an awesome possibility under resonance.
3.1
OBJECTIVE OF THE EXPERIMENT
The objective of the experiment is to determine the resonance of spring-dashpot system in different damping.
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APPLIED MECHANICS LAB (MEC424) – DYNAMICS OF MACHINES LAB 4.0 THEORY As stated in Introduction section, resonance will occur if the frequency of excitation coincides with one of the natural frequencies of the system and dangerously large oscillations may result. The large oscillations may reach the maximum amplitude of the oscillation for a certain body thus may result in failure of member of the system. This is because, the member may reach the maximum deformation it can attain and soon will fracture. The relation of rotational frequency during resonance is,
Where,
is the damped frequency and
is the natural frequency of the system. Both are in
(rad/s) in unit. As they are equal, the resonance will occurs and result in maximum amplitude for the oscillation. As for the damper, it resists motion via viscous friction. The resulting force is proportional to the velocity, but acts in the opposite direction, slowing the motion and absorbing energy. It is commonly used in conjunction with a spring.
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APPLIED MECHANICS LAB (MEC424) – DYNAMICS OF MACHINES LAB 5.0
APPARATUS
Frame
Spring (k=3.0 N.mm)
Beam
Mechanical recorder Unbalance exciter
Damper
Control Unit (TM150)
The dimensions of the beam are as follows: Width
Length Thickness
Thickness, h = 12 mm
Width, w = 25 mm Length, L = 700 mm
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APPLIED MECHANICS LAB (MEC424) – DYNAMICS OF MACHINES LAB 6.0
EXPRIMENTAL PROCEDURE
1. First, the apparatus is set up. The graph paper (which attached in roll on the mechanical recorder) is slotted into the holder. 2. As the graph paper is ensured in grip, a pen is fixed in the graph pointer slot. (It is advisable to use blunt-tip pen or a gel pen). 3. The mechanical recorder is then tested, to ensure if the graph is being recorded clearly and properly. 4. The control unit is turned on. 5. With no damper, the unbalance exciter is controlled its frequency by the control unit. 6. Before any reading is taken, the maximum amplitude at what frequency is first predicted as the beam is forced oscillation by the exciter. 7. Once we roughly know at what frequency the amplitude is at maximum, range of reading needed to be taken is tabulated. ± of 2 Hz is taken from the predicted natural frequency, fn of reading is set. Data for each 0.5 Hz is taken. 8. The excited oscillation of each set frequency is plotted on the graph paper by the mechanical recorder each. 9. Steps 6-8 is repeated with damper (needle open) is positioned at 150 mm of the beam, damper (needle closed) is positioned at 150 mm of the beam, and damper (needle closed) is positioned at 550 mm of the beam. Precaution: Each graph plotted needs to be labeled every time before plotting the next graph, so that, later on will not be confused or mistakenly taken.
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