Volume 115, Issue 4, April 2004
Index of content:
- STRUCTURAL ACOUSTICS AND VIBRATION 
115(2004); http://dx.doi.org/10.1121/1.1687424View Description Hide Description
We study waves in elastic waveguides, with a view toward the nondestructive evaluation of slender structures by means of imposed vibrations. Envisioned applications demand an accurate understanding of both propagating and evanescent guided waves in waveguides of arbitrary cross section. Accordingly, we develop a theoretical framework in which energy principles and finite element discretization lead to a discrete set of solutions representing both wave types. We examine the solutions in great detail, with a particular emphasis on the accuracy of the finite element discretization. Results are compared with analytic solutions of the Pochhammer–Chree equations for the special case of a circular cross section, determining the combination of mesh parameters and frequency regimes for which the code yields accurate results. Convergence studies are conducted for the case of a more complex cross section, that of a typical railroad rail.
115(2004); http://dx.doi.org/10.1121/1.1675818View Description Hide Description
The steady state response of a cylindrical elastic waveguide of arbitrary cross section to a harmonic load is considered. The inverse problem of wavenumber extraction is simulated using finite element discretization of the cross section. The case of a concentrated lateral point load on a railroad rail is used for illustration, at a frequency of 202 Hz, corresponding to a frequency well below the first cutoff, but above the regime where simple strength of materials concepts are accurate. The work is conceived with a view towards applications in the nondestructive characterization of such beams by means of scanned laser vibrometry for measurement of lateral bending wavenumbers dependent on a contained static axial load. Simulations of such measurements are generated, and subjected to noise and to a variety of potential systematic errors. Linear and nonlinear least squares minimization of the residual between simulated measurements and fits show that the lateral bending wavenumber can be recovered accurately, with remarkable robustness, even in the presence of noise and systematic errors.
115(2004); http://dx.doi.org/10.1121/1.1645609View Description Hide Description
In near-field acoustic holography, when measurements are made over a limited surface, there has been recent interest in numerically enlarging the measurement surface tangentially. Current algorithms use iterative methods to extrapolate the field tangentially outward. An algorithm based on the method of superposition is applied here which may be used to either extrapolate the field to enlarge the measurement surface or to interpolate in case there is a “hole” in the measurement surface where data are not available.