Elsevier

Ultrasonics

Volume 38, Issues 1–8, March 2000, Pages 206-211
Ultrasonics

Resonant frequency method for the measurement and uncertainty analysis of acoustic and elastic properties

https://doi.org/10.1016/S0041-624X(99)00038-4Get rights and content

Abstract

A resonant frequency method is proposed to determine the bar speed and the Poisson’s ratio of a rod several meters long of the kind often used for manufacturing power sonic transducers and mechanical horns in mass production. This method is shown to be robust in a field test and with high resolution for estimation of the bar speed. The uncertainty (standard deviation/average) for the bar speed and the Poisson’s ratio can be reduced by appropriately selecting the mode number pairs and increasing the mode number. In this study, the uncertainties of the bar speed and Poisson’s ratio are less than 0.043% and 2.9%, respectively. The resonant frequency method is verified by comparing the dilatational wave speeds calculated by elastic theory with those from experiments, the difference between them being less than 0.17%.

Introduction

Knowledge of material properties such as the bar speed and Poisson’s ratio is important in the design of acoustic transducers. In a power sonic system, one needs a good acoustic impedance match or the same resonant frequencies between transducers and mechanical horns in order to increase the efficiency of energy transmission. When simultaneously exciting multiple ultrasonic transducers in an ultrasonic cleaning water tank, one needs to use transducers with similar resonant frequencies to increase the driving efficiency of the electrical power system. Because the composition of raw materials for manufacturing ultrasonic transducers and mechanical horns may vary between batches and manufacturers, it is more costly and inefficient to screen the manufactured products than the raw materials in mass production. Therefore, one needs a fast and accurate method with a high resolution to screen the elastic properties of the raw materials in order to tighten the resonant frequencies of ultrasonic transducers and mechanical horns.

Several methods [1], [2], [3], [4] have been studied to determine the acoustic velocity either in the time domain or in the frequency domain. With a predetermined liquid speed, some methods [1], [2], [4] can determine the acoustic speed by the time-of-flight method without knowledge of the thickness of a sample. However, in these methods, the thickness of a sample must be a reasonable value in order to avoid overlapping of consecutive reflecting waves. When the thickness of a sample is small, the amplitude spectrum [3] can be applied to determine the phase velocity, and this is also valid for a dispersive material. A complex modulus can be determined by two response points from a one-dimensional wave equation [5], [6], [7]. However, the Poisson’s ratio was not determined in these methods [1], [2], [3], [4], [5], [6], [7]. A rod several meters long is quite often used for power sonic transducers and mechanical horns, especially in mass production lines. In addition, one needs a robust method that can determine the acoustic and elastic properties of materials in the field for such a long rod. In this paper, a resonant frequency method with high resolution is proposed to measure the bar speed and Poisson ratio’s for a long rod from a two-dimensional wave equation. The measurement uncertainty and the minimization of this uncertainty of this method are also included in this paper.

Section snippets

Theory

In the high-frequency range, vibration motion in the longitudinal direction of an isotropic bar will induce lateral vibration due to the Poisson’ ratio effect. Including the effect of the lateral vibration of a bar, the longitudinal wave equation or Love’s theory can be written as [8]:2u∂x2+ν2k2C204u∂x2∂t2=1C202u∂t2,where u is the particle displacement, t is the time, x is a coordinate, ν is the Poisson’s ratio, k is the radius of the gyration of the cross-sectional area of the bar, C0 is

Experiments and results

Two aluminum cylinders were selected in this study. Sample L1 had a diameter of 41.35 mm and a length of 895 mm, and sample L5 had a diameter of 45 mm and a length of 1891 mm. The experimental set-up is illustrated in Fig. 1. A non-contacting microphone sensor was used in this test to avoid any mass loading influence on the resonant frequencies of the test samples. The frequency response functions for longitudinal modes of the bar were obtained between the impact hammer and the microphone, and the

Validation and applications

Once bar speed and Poisson's ratio are obtained from , , the dilatational wave speed, Cb, can be calculated as follows [5]Cb=C01−ν(1+ν)(1−2ν)1/2.

The experimental dilatational wave speeds are 6406.2 m/s and 6452.9 m/s for cylinder L1 and L5, respectively. The experimental dilatational wave speed is measured for a small sample by the time of flight method with a 5 MHz transducer and a pulser/receiver Panametric 5055PR. The experimental dilatational wave speeds are averaged from two small samples cut

Conclusions

It has been shown that the resonant frequency method can accurately measure the bar speed and Poisson ratio of a rod that is several meters long and quite often used for manufacturing power sonic transducers and mechanical horns in a mass production. This method is shown to be robust in the field test and with a high resolution for the estimation of bar speed that is an essential factor influencing on the resonant frequencies of power sonic transducers and mechanical horns. In this study, the

References (9)

  • T. Pialucha et al.

    Ultrasonics

    (1989)
  • B. Lundberg et al.

    Journal of Sound and Vibration

    (1988)
  • S. Odeen et al.

    Journal of Sound and Vibration

    (1993)
  • I.Y. Kuo et al.

    J. Acoust. Soc. Am

    (1990)
There are more references available in the full text version of this article.

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