Development of Experimental Set-up for Study of Vibrations in Academia

Study of the subject of ‘vibrations’ is becoming increasingly important as most human activities involve vibration in one form or the other. In a world driven by prime movers which have an inherent imbalance, vibration related problems are encountered in everyday industrial and domestic use. Modelling a system for characterization of its vibration properties for several input conditions and initial configurations involves set of complex equations and hence, the theory of vibrations remains one of the most abstract field in the study of physics and engineering. Numerical simulations, animations and experimental setups for different vibration systems can thus be a very useful tool in making students understand the subject better. This report is based on a semi-portable and low-cost vibration demonstration equipment which covers two discrete systems and a continuous system in the classical vibrations textbooks. A simple pendulum and a double pendulum is accommodated in a single modular pendulum set- up. A string fixed at both ends under a specified tension is chose as a continuous degree of freedom system. The experimental setup for a single, two degree of freedom system and a continuous system is explained in detail. Derivations for the equations of motions in both polar and Cartesian coordinates for the pendula is covered. It is limited to Cartesian coordinates in case of the chosen continuous degree of freedom system. Study of motion governed by these equations is carried out with the help of a commonly available web camera and video processing software. Results obtained from the motion analysis are compared against the theoretical solution available for the system to establish accuracy of the vision based approach. This set-up is intended for use in classroom demonstrations and laboratories. The technique may be extended to other experimental studies which could be advantageous to underdeveloped and developing countries in setting up various laboratories; a process which otherwise would be highly cost and technology intensive. A multi-parameter condition monitoring setup is also proposed, with primary input being a vision based sensor.

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