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, clamped-clamped, clamped-pinned, and pinned-pinned. The first 10 bending frequencies and mode shapes for each set of boundary conditions are measured. The effects of the bolt torque on the measured frequencies of the rectangular beam are examined. The material properties of the circular beam, including the elastic modulus, shear modulus, and Poisson’s ratio, are determined by measuring its first 20 natural frequencies. A new technique is used to mount an accelerometer to measure the torsional modes of the circular beam. A roving hammer test is conducted to measure the first 10 mode shapes. The measured mode shapes of the circular and rectangular beams are compared with their thoretical predictions using the modal assurance criterion. The Timoshenko beam theory is shown to provide better predictions of the natural frequencies for the higher modes of the circular beam than the Bernoulli-Euler beam theory. The use of the rectangular and circular beam test stands as a teaching tool for undergraduate and graduate students is discussed.