Experimental Modal Analysis of Rectangular and Circular Beams

Abstract

Analytical and experimental methods are used to determine the natural frequencies and mode shapes of Aluminum 6061-T651 beams with rectangular and circular cross-sections. A unique test stand is developed to provide the rectangular beam with
different boundary conditions including clamped-free, clampedclamped, clamped-pinned, and pinned-pinned. The first 10 bending natural frequencies and mode shapes for each set of boundary conditions are measured. The effect of the bolt torque on the measured natural frequencies is examined. A new technique is used to mount an accelerometer on the circular beam to measure its torsional modes; its first 20 natural frequencies and first 10 mode shapes are measured. The measured natural frequencies and mode shapes of both beams are compared with their theoretical predictions. The Timoshenko
beam theory is shown to provide better predictions of the higher bending natural frequencies of the circular beam than the Bernoulli-Euler beam theory. The material properties of the circular beam, including the elastic modulus, shear modulus, and Poisson?s ratio, are determined accurately. The use of the rectangular and circular
beam test stands as a teaching tool for undergraduate and graduate students is discussed. The laboratory demonstration using the test stands was well received by students in the undergraduate vibrations class.