frequency - University of Texas at Arlington MAE 3183,...

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University of Texas at Arlington MAE 3183, Measurements II Laboratory Frequency Response of a Physical System 1 Experiment #3 Frequency Response of a Physical System
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University of Texas at Arlington MAE 3183, Measurements II Laboratory Frequency Response of a Physical System 2 Introduction A simple physical system can be made of a spring, mass, and damper (SMD). This system can exhibit various responses depending upon the parameters of the components and the input provided. Considering a step input, the response can be very slow and show very little signs of changing. It can also go to equilibrium very quickly and show no signs of resonance. Or, the system can seemingly oscillate forever. These various responses depend entirely upon the systems components. With only three components involved, two of the values of the system can be fixed while the third can be changed to give all the responses mentioned above. A large complex indeterminate structure can be divided into many smaller SMD systems. This allows the characterization of smaller-defined regions when subjected to loading. When analyzed simultaneously, the smaller SMD systems give results similar to that seen in the actual system. This concept forms some of the elementary tools in Finite Element Analysis (FEA). Considering a periodic input, the response will typically act in one of two different ways. (1) The system will possibly resonate uncontrollable until something breaks or (2) resonate but within a limit. These two responses can be achieved by knowing the frequency of the periodic wave and tailoring the system. It's obvious that in some situations such as earthquake zones a building must be constructed so that it's natural frequency will not match that of the ground movements. In this case the response is desired to be less than that of the input. In an entirely different example, the case of a guitar, the body must be built so as to not dampen the sound created by the resonating strings thus creating a harmonious and in some cases pleasant sound from the guitar. Even with only slight knowledge of buildings (or guitars) it becomes evident that the basic SMD system is a crucial element in determination of physical response of structures. This experiment looks at the SMD system and allows the student to change a few variables and examine the change on the system's response. As an added real-world benefit, the experiment requires that a relationship for damping ratio to number of turns be found for a fluid damper in the system. Theory System Components The components that form the SMD system relate force to displacement, velocity, and acceleration. The component that relates force to displacement is typically called a spring. Springs are usually constructed of an elastic material. In most applications springs are expected to operate in a linear region. Out of this linear region the spring will be overloaded and experience plastic deformation and even failure if the loading is excessive. The spring force always acts along the line joining two ends of the spring. The linear
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This note was uploaded on 06/15/2009 for the course MAE 3183 taught by Professor Staff during the Spring '08 term at UT Arlington.

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frequency - University of Texas at Arlington MAE 3183,...

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