Experimental Measurement of the Flexural Spectrum of a Vibrating Beam Above the Critical Frequency

Abstract

Abstract In this paper, we report the bending spectrum measured experimentally on oscillating beams with free extremes in a frequency range below and above the cutoff or critical frequency. The experimental setup used to obtain the bending spectrum consisted of a novel and selective method to excite mainly bending modes, as well as an identification process in which oscillation modes other than bending were discarded. For the first time, we identified bending modes above the cutoff frequency for square and circular cross-sectional beams and a good agreement is obtained when the measured frequencies are compared with the predictions of the Timoshenko beam theory (TBT) and those numerically obtained from the elasticity theory by using a three-dimensional finite element method (FEM) calculation. Higher frequency values at which TBT should cease to be valid were not achieved in the experiments. Instead, our experimental results show that TBT remains valid above the cutoff frequency, with an error smaller than 6%.