Analysis of Elastic Flexural Waves in Non-Uniform Beams Based on Measurement of Strains and Accelerations

Abstract

Elastic flexural waves in an unloaded and unsupported segment of a non-uniform beam were considered. A method based on Timoshenko’s model was established for evaluation of shear force, transverse velocity, bending moment and angular velocity at an arbitrary section from four independent measurements of such quantities at one to four sections. From the evaluated quantities, shear stress, power transmission, etc. can be obtained. Experimental tests were carried out with an aluminium beam which had an abrupt change in height from 15 to 20 mm and was equipped with strain gauges and accelerometers at four uniformly distributed measurement sections and at three evaluation sections. The distance between the two outermost measurement sections was 600 mm, corresponding to 1.12 wave lengths at the upper end of the frequency interval 2500 Hz considered. Bending moments and transverse velocities evaluated from four measurements of any one of these quantities agreed well with those measured at evaluation sections located (i) centrally among the measurement sections and (ii) at a distance of 100 mm, or 0.17 wave lengths, outside. When it was located (iii) at a distance of 500 mm, or 0.83 wave lengths, outside, there was relatively large disagreement as expected from error analysis.