Effective Use Of Experimentation And Finite Element Analysis In A Vibrations Course

It is a challenge for many students to firmly grasp the relationships between calculated results from textbook equations for multi degree of freedom structural vibration and actual behavior of a structure. While students can easily perform the calculations, they often do not fully understand how the theoretical results relate to behavior of an actual system. Experimentation is often included in courses to help bridge the gap between theory and actual system behavior. This paper outlines an approach that seems to be effective which combines experimentation, including use of smart materials, with the high-level graphics and animation capabilities available in a commercial finite element (FE) code, ANSYS. Initial experimentation involves a simple structure, then structures with increasing levels of complexity are considered. The first system involves flexible springs and standard laboratory masses. Students set initial conditions by displacing masses by hand to produce motion dominated by one of two modes. Natural frequencies are determined using a stopwatch and counting oscillations. The results agree well with calculations based on theory for the lumped mass system. The simple system is also modeled in ANSYS, the natural frequencies are calculated, and the mode shapes are animated. The second experiment involves cantilevered beams. One thin, flexible beam includes piezoelectric patches, mounted such that an applied voltage produces a moment. Natural frequencies are determined experimentally from impact tests. Natural frequencies are also calculated from partial differential equation solutions and FE analysis. The mode shapes are animated in ANSYS. The beam is then excited with a sinusoidal voltage. The displacement pattern for vibration response due to excitation at either of the first two natural frequencies can be easily detected visually, and clearly agrees with theory and animated mode shapes from ANSYS. By varying the excitation frequency, the concept of large amplitude response for excitation near resonance is clearly demonstrated. A final experiment involves test and analysis of a compressor stator vane, for which a theoretical solution is not available. The overall approach seems to provide the students with a good foundation in theory, basic modal testing techniques, practical application of a widely used commercial finite element code, and also a brief introduction to smart materials (PZT). P ge 10511.1 “Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright  2005, American Society for Engineering Education”