M2_1 - CONTENTS Topics Page 1. OBJECTIVE 1 2. INTRODUCTION...

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Unformatted text preview: CONTENTS Topics Page 1. OBJECTIVE 1 2. INTRODUCTION 1 2.1 Theory 2.2 The mass-spring-damper system 2.3 Transient Solution 3. EQUIPMENT 7 4. PROCEDURE 9 5. RESULTS 11 5.1 Log Sheet 6. DISCUSSION 19 6.1 Effectiveness and difficulties involved in using a digital storage oscilloscope to measure vibrations. 6.2 Effect of damping on the damped free vibration of the system. 6.3 Discussion of experimental results. 6.4 Comparison of theoretical and experimental results. 7. CONCLUSION 23 8. REFERENCES 23 1. OBJECTIVE The objective of this experiment is to learn how to use a digital storage oscilloscope to measure the followings : (a) The undamped and damped natural frequencies of a cantilever beam using the free vibration method. (b) The amplitude and phase relationships of the system using sinusoidal excitation method. 2. INTRODUCTION 2.1 THEORY Vibrations are forces that are usually caused by unbalance in a rotating machinery itself or in the bearings of the machine. And the subject of vibration deals with the behaviour of bodies under the influence of such oscillating force. Generally, there are two cases of vibrations - free and forced. Free vibration occurs when a system oscillates under the action of forces inherent in the system itself, and when external impressed forces are not present. System under such vibration will vibrate at one or more of its natural frequencies, which are properties of the dynamic system established by its mass and stiffness distribution. Vibration that occurs under the excitation of an external force is called forced vibration. When the excitation is oscillating, the system is forced to vibrate at the excitation frequency. If the frequency of excitation coincides with one of the natural frequencies, resonance may occur and results in large oscillations. This behaviour is unacceptable in rotating machineries and also may lead to fatigue and failure of major structure such as bridges, buildings and airplane- wings. However, the concept of resonance is exploited in the manufacturing industries. For example, the vibratory bowl feeder operates close to or at resonant frequency. This allows energy conservation as only a little amount of excitation force is needed to vibrate the feeding bowl. All machineries are subjected to damping to certain degree. If the damping is small, it is considered to have negligible effect on the resonance and hence calculations for natural frequencies are made on the basis of the damping. On the other hand, damping is important in reducing the amplitude of vibration at resonance. 2 2.2 THE MASS-SPRING-DAMPER SYSTEM Consider the one-dimensional motion of the system shown in Fig. 2.2(a). The body of mass m can be treated as a particle since the motion consists of pure translation in which all points in the body have the same velocity and acceleration, and undergo identical displacements from their initial positions. The forces acting on the body are shown on Fig. 2.2(b). The force cx , which is always opposite to...
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This note was uploaded on 10/18/2009 for the course ECONS 111 taught by Professor Yo during the Spring '09 term at Nassau CC.

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M2_1 - CONTENTS Topics Page 1. OBJECTIVE 1 2. INTRODUCTION...

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