measuring the resulting acoustic emissions. The time histories of the measured acoustic response were used to estimate the power spectral density (PSD) of the response. The peaks in the PSD were used to identify the approximate frequencies of the modes of the sample. Three frequencies were identified from the data. The test and model frequencies were correlated through comparisons between mode shapes calculated with approximate values for Young’s modulus and Poisson’s ratio as well as three dimensional laser based visualization of the measured mode shapes [4]. The identified frequencies and damping ratios for each sample are given in Table 1. Figure 1 Geometry of Test Sample Table 1 Experimental Frequencies Determined from Acoustic Emissions Mode 7 Mode 9 Mode 16 Sample modal freq Damping modal freq damping modal freq damping density # (Hz) (%) (Hz) (%) (Hz) (%) (lbf/in^3) A 11,514 0.24 16,335 0.28 27,928 0.29 1.0995E-02 B 11,159 0.39 15,858 0.30 27,344 0.28 1.0885E-02 C 11,308 0.34 16,041 0.27 27,656 0.26 1.0931E-02 D 10,819 0.65 15,313 0.29 26,566 0.37 1.0595E-02 E 11,365 0.29 16,134 0.27 27,774 0.32 1.0994E-02 F 11,056 0.34 15,669 0.29 27,110 0.27 1.0812E-02 G 10,953 0.39 15,541 0.31 26,743 0.30 1.0809E-02 H 11,027 0.35 15,660 0.31 27,122 0.28 1.0828E-02 I 11,142 0.35 15,767 0.29 27,239 0.25 1.0799E-02 Mean 11,149 0.37 15,813 0.29 27,276 0.29 1.0850E-02 The model used for calculating the natural frequencies of the sample given a density, elastic modulus, and Poisson’s ratio was developed using a finite element model and an empirical model mapping the parameters to the frequencies. Since the sample and consequently the model consist of only one material, the functional form of the natural frequencies can be given as Q U i i g E f (1) where ݂ is the ith natural frequency, E and ρ are the Young’s modulus and density, and gi describes the functional variation of the natural frequency with Poisson’s ratio. The specific form of gi will be dependent on the geometry and boundary conditions of the sample. For the data used here, the geometry and boundary conditions were essentially unchanged between samples and therefore assumed constant. Small variations in the as-built dimensions of the sample were ignored in the frequency analysis. To determine the function gi, the geometry in Figure 1 was meshed using solid elements. The model was then run using an elastic modulus of 1 psi, a density of 1 lb/in3, and for Poisson’s ratios ranging from 0 to 0.45. The frequencies of interest were extracted from each run and tabulated. Some effort is required to insure that the same mode shape is tracked throughout the variation of Poisson’s ratio. Many times the modes switch order so tracking modes by order was not successful. A plot of the resulting data is given in Figure 2. 0.5 inches 1.5 inches 220
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