Acoustical interaural differences were computed for a succession of idealized shapes approximating the human head-related anatomy: sphere, ellipsoid, and ellipsoid with neck and torso. Calculations were done as a function of frequency (100–2500 Hz) and for source azimuths from 10 to 90 degrees using finite element models. The computations were compared to free-field measurements made with a manikin. Compared to a spherical head, the ellipsoid produced greater large-scale variation with frequency in both interaural time differences and interaural level differences, resulting in better agreement with the measurements. Adding a torso, represented either as a large plate or as a rectangular box below the neck, further improved the agreement by adding smaller-scale frequency variation. The comparisons permitted conjectures about the relationship between details of interaural differences and gross features of the human anatomy, such as the height of the head, and length of the neck.
The spherical model of the human head, attributable to Lord Rayleigh, accounts for important features of observed interaural time differences (ITD) and interaural level differences (ILD), but it also fails to capture many details. To gain an intuitive understanding of the failures, we computed ITDs and ILDs for a succession of idealized shapes approximating the human head: sphere, ellipsoid, ellipsoid plus cylindrical neck, ellipsoid plus cylindrical neck plus disk torso. Calculations were done as a function of frequency (100–2500 Hz) and for source azimuths from 10 to 90 degrees using finite-element models. The computations were compared to free-field measurements on a KEMAR manikin. The spherical head model approximated many measured interaural features, but the frequency dependence tended to be too flat in both ITD and ILD. The ellipsoidal head produced greater variation with frequency and therefore agreed better with the measurements, reducing the RMS discrepancies in both ITD and ILD by 35%. Adding a neck further increased the frequency variation. Adding the disk torso further improved the agreement, especially below 1000 Hz, decreasing the ITD discrepancy by another 21\%. The evolution of models enabled us to associate details of interaural differences with overall anatomical features. [Work supported by the AFOSR grant 11NL002.]
We propose a new method for vibration suppression in a flexible structure using a frictionless sliding constraint. The constraint force applied by the slider is assumed known from measurements and the slider motion is prescribed to do negative work on the structure. The structure is modeled as a two-dimensional nonlinear rod with pinned-pinned boundary conditions and the slider is assumed to constrain the position of one point on the rod but not its slope. The problem is formulated using variable-length finite elements in the framework of Arbitrary Lagrange-Euler (ALE) description. The governing equations of motion are derived using the principle of virtual displacements and D’Alembert’s principle. Numerical simulation results are presented to demonstrate the effectiveness of the control strategy based on the idea of negative work. To meet the bandwidth requirement of the actuator, a nonlinear filter is placed in the feedback loop and asymptotic stability of the equilibrium configuration is established using Lyapunov stability theory.
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