Using sound in the very near field of vibrating plates for determination of their mechanical properties

Abstract

During the evaluation of Young’s modulus by vibroacoustic methods, it is usually assumed that the Poisson's ratio is known. This assumption is based on a reasonable tolerance of the vibroacoustic methods to an inadequate estimate of Poisson's ratio. However, most studies do not consider the influence of the Poisson's ratio error in the estimation of the Young's modulus error. Moreover, the evaluation of the total error typically does not include any parametric analysis at all. Therefore, a new vibroacoustic method is proposed that provides a simple and reciprocal determination of the Young's modulus and Poisson's ratio. The method is based on measurements of the natural vibration modes of elongated plates using a scanning microphone in the very near field. The results of the sound pressure scanning are interpolated with a quadratic harmonic function to improve the spatial resolution in locating the vibration nodes. The advantage of this method is that the Poisson's ratio can be calculated directly by measuring the wavelength of the bending wave. Poisson's ratio is otherwise much more difficult to measure than Young's modulus. Therefore, this method can be used to determine the Poisson's ratio of various polymers, wood, and composites. The parametric analysis of the proposed method is compared with the parametric analysis of the standardised ASTM 1875 method “Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance”. The results show that the accuracy of the Poisson's ratio determination is mainly influenced by the accuracy of the material density and the accuracy of the measured sample thickness. The accuracy of these two parameters also has a dominant influence on the accuracy of the determination of the Young's modulus. The proposed method and its accuracy are demonstrated on three different plates: aluminium, steel and soft plexiglass. The results of the proposed method for aluminium were compared with those obtained by the standardised ASTM method. The proposed method provides smaller error for given experimental conditions.