Index of content:
Volume 134, Issue 2, August 2013
- STRUCTURAL ACOUSTICS AND VIBRATION 
134(2013); http://dx.doi.org/10.1121/1.4812261View Description Hide Description
The free vibration behavior of completely unrestrained elastic circular plates with trigonal and isotropic material symmetry is studied with an approach involving approximate continuum solutions to the three-dimensional theory of linear elasticity. Of primary interest are (1) the influence of trigonal material symmetry on the modes of free vibration and (2) the accuracy of thin plate theory relative to the more exact three-dimensional theory. Resonant frequencies are calculated from the weak form of the equations of motion for the plate through the use of approximation functions and the Ritz method formulated in cylindrical coordinates. This approach enables the resulting eigenvalue problem to be split through group-theoretical symmetry analysis. Representative examples are given and quantitative limits are discussed.
134(2013); http://dx.doi.org/10.1121/1.4812260View Description Hide Description
Acoustic focusing experiments usually require large arrays of transducers. It has been shown by Etaix et al. [J. Acoust. Soc. Am. 131, 395–399 (2012)] that the use of a cavity allows reducing this number of transducers. This paper presents experiments with Duralumin plates (the cavities) containing scatterers to improve the contrast of focusing. The use of a scatterer array in the plate allows increasing the modal density at given frequencies. The scatterers used are membranes and buttons that are manufactured in Duralumin plates. Their resonances are studied both experimentally and numerically. Such scatterers present the advantage of having a tunable frequency resonance, which allows controlling the frequencies at which the modal density increases. The dispersion relations of plates with scatterer array show high modal density at given frequencies. Finally acoustic focusing experiments in air, using these plates, are compared to the ones of simple duralumin plates demonstrating the improvement of contrast. Acoustic source localization is also realized using these plates.
134(2013); http://dx.doi.org/10.1121/1.4812262View Description Hide Description
Previously unknown spatial convolution formulas for a variant of the active normal intensity in planar coordinates have been derived that use measured pressure or normal velocity near-field holograms to construct a positive-only (outward) intensity distribution in the plane, quantifying the areas of the vibrating structure that produce radiation to the far-field. This is an extension of the outgoing-only (unipolar) intensity technique recently developed for arbitrary geometries by Steffen Marburg. The method is applied independently to pressure and velocity data measured in a plane close to the surface of a point-driven, unbaffled rectangular plate in the laboratory. It is demonstrated that the sound producing regions of the structure are clearly revealed using the derived formulas and that the spatial resolution is limited to a half-wavelength. A second set of formulas called the hybrid-intensity formulas are also derived which yield a bipolar intensity using a different spatial convolution operator, again using either the measured pressure or velocity. It is demonstrated from the experiment results that the velocity formula yields the classical active intensity and the pressure formula an interesting hybrid intensity that may be useful for source localization. Computations are fast and carried out in real space without Fourier transforms into wavenumber space.
134(2013); http://dx.doi.org/10.1121/1.4812777View Description Hide Description
The transient response of a resonant structure can be altered by the attachment of one or more substantially smaller resonators. Considered here is a coupled array of damped harmonic oscillators whose resonant frequencies are distributed across a frequency band that encompasses the natural frequency of the primary structure. Vibration energy introduced to the primary structure, which has little to no intrinsic damping, is transferred into and trapped by the attached array. It is shown that, when the properties of the array are optimized to reduce the settling time of the primary structure's transient response, the apparent damping is approximately proportional to the bandwidth of the array (the span of resonant frequencies of the attached oscillators). Numerical simulations were conducted using an unconstrained nonlinear minimization algorithm to find system parameters that result in the fastest settling time. This minimization was conducted for a range of system characteristics including the overall bandwidth of the array, the ratio of the total array mass to that of the primary structure, and the distributions of mass, stiffness, and damping among the array elements. This paper reports optimal values of these parameters and demonstrates that the resulting minimum settling time decreases with increasing bandwidth.