Estimation of complex modulus using wave coefficients

Abstract

The paper presents a new, efficient and accurate method for experimentally determining structural damping properties of stiff materials in flexural vibration. The estimation method seeks a wavenumber that forces data at all measurement points to conform with the general forced-vibration solution for a beam, and, thus, to have the same wave coefficients. The method does not depend on beam boundary conditions, making it relatively simple to implement in any laboratory setting. The paper shows results of using the method to estimate the complex modulus of aluminum and of polymethyl methacrylate (PMMA) beams in the frequency range from 30 to 800 Hz.Results compare very well with those obtained by more conventional methods and with those previously published over most of the frequencies of interest. Discrepancies in results for frequencies less than 80 Hz are attributed to the difficulty in measuring differences of velocity between points that are near each other at low frequency, and a technique for avoiding such discrepancies is outlined. Evidence shows that the error in the results near 350 Hz is due to a resonance in the scanning laser vibrometer that was used to take the experimental measurements.