Brody Dylan Johnson

A broadband passive–active sound absorption system

In recent years, hybrid absorption systems have been implemented which achieve high sound absorption over a broad frequency range. This work is an experimental study of a broadband hybrid absorption system which is comprised of a layer of sound-absorbing material (the passive component) positioned at a distance from a movable wall (the active component) inside an impedance tube. The movable wall is used to impose desired boundary conditions in the cavity behind the passive layer, thereby increasing the absorption of the system at frequencies where the passive material is not independently effective. Both pressure-release (i.e., minimizing the pressure at the back surface of the layer) and impedance-matching (i.e., minimizing the reflected wave from the layer) boundary conditions are studied. The performance of the hybrid system for these two boundary conditions is compared for broadband disturbances over a frequency range of 100–1000 Hz. The unmodified passive system showed absorption coefficients greater...

The Nonholonomy of the Rolling Sphere

An old problem in the field of holonomy asks: Given a pair of orientations for a sphere resting on a plane, is there a closed path along which one can roll the sphere (without slipping or twisting), starting with the first orientation, and return to the origin with the sphere in the second orientation? (See Figure 1.) The answer is yes, and the goal of this article is to provide an elementary proof of this fact.

Broadband control of plate radiation using a piezoelectric, double-amplifier active-skin and structural acoustic sensing

The potential of a piezoelectric, double-amplifier active-skin with structural acoustic sensing (SAS) is demonstrated for the reduction of broadband acoustic radiation from a clamped, aluminum plate. The active-skin is a continuous covering of the vibrating portions of the plate with active, independently controllable piezoelectric, double-amplifier elements and is designed to affect control by altering the continuous structural radiation impedance rather than structural vibration. In simulation, acoustic models are sought for the primary and secondary sources that incorporate finite element methods. Simulation indicates that a total radiated power attenuation in excess of 10 dB may be achieved between 250 and 750 Hz with microphone error sensing, while under SAS the radiated power is reduced by nearly 8 dB in the same frequency range. In experiment, the adaptive feed forward filtered-x LMS (least mean square) algorithm, implemented on a Texas Instruments C40 DSP, was used in conjunction with the 6I6O control system. With microphone error sensing, 11.8-dB attenuation was achieved in the overall radiated power between 175 and 600 Hz, while inclusion of SAS resulted in a 7.3-dB overall power reduction in this frequency band.

On the Oversampling of Affine Wavelet Frames

The properties of oversampled affine frames are considered here with two main goals in mind. The first goal is to generalize the approach of Chui and Shi [Proc. Amer. Math. Soc., 121 (1994), pp. 511--517], [SIAM J. Math. Anal., 28 (1997), pp. 213--232] to the matrix oversampling setting for expanding, lattice-preserving dilations, whereby we obtain a new proof of the second oversampling theorem for affine frames. The second oversampling theorem, proven originally by Ron and Shen [J. Funct. Anal., 148 (1997), pp. 408--447] via Gramian analysis, states that oversampling an affine frame with dilation M by a matrix P will result in a frame with the same bounds (after renormalization), provided that P and M satisfy a certain relative primality condition. In this case, the matrix P is said to be admissible for M. The second goal of this work is to examine the compatibility of admissible oversampling with the refinable affine frames arising from a certain class of scaling functions. In this setting we show that ...

Quincunx Wavelets on \({\mathbb{T}}^{2}\)

This article examines a notion of finite-dimensional wavelet systems on \({\mathbb{T}}^{2}\), which employ a dilation operation induced by the Quincunx matrix. A theory of multiresolution analysis (MRA) is presented which includes the characterization and construction of MRA scaling functions in terms of low-pass filters. Orthonormal wavelet systems are constructed for any given MRA. Two general examples, based upon the classical Shannon and Haar wavelets, are presented and the approximation properties of the associated systems are studied.

The use of a piezoelectric double amplifier active‐skin in the control of panel radiation

The potential of a piezoelectric active‐skin is analytically demonstrated for the reduction of broadband acoustic radiation from a vibrating panel in the frequency range from 0 to 750 Hz. The active‐skin is comprised of a number of independently controllable piezoelectric double amplifier elements arranged in a contingent surface over the vibrating panel. Both the finite‐element method (FEM) and the boundary element method (BEM) are employed in the development of numerical models for relation of the piezoelectric voltage excitation to vibrational and acoustic responses of these active‐skin elements. The adaptive feedforward filtered‐x least‐mean‐squares (LMS) algorithm is employed in the time domain simulation of control with the active‐skin. Both FIR and IIR compensator types are investigated. ANC and ASAC perspectives are examined for the realization of the active‐skin. Control performance is quantified using both sound power level (Lw) and sound pressure level (SPL) data. Simulation shows that an atten...