Charles E. Bradley

Dispersive pulse propagation and group velocity

The propagation of pulses in a dissipative medium is investigated both theoretically and experimentally. The theoretical work is based on the dissipative dispersion integral, and the measurements are made in an air‐filled periodic waveguide (i.e., the dispersion is Bloch wave dispersion). The dispersion integral is considered in the context of a sequence of characteristic pulse duration distances. The pulse propagates without distortion up to the smallest characteristic distance, and thereafter undergoes a new variety of distortion as it encounters each subsequent characteristic distance. Several new solutions of the dispersion integral that exhibit a variety of novel propagation properties are found. Pulses that shift in frequency as they propagate, accelerate as they propagate, and propagate at near‐infinite group velocity are found analytically and verified experimentally. [Work supported by ONR.]

Nonlinear acoustic streaming: Field theory and experiment

The theory of nonlinear acoustic streaming is presented with emphasis on physical interpretation and general statements regarding the structure of the flow field. In addition, measurements are shown in which the flow is driven by the evanescent acoustic field near a micromachined thin plate with flexural waves traversing it. A fundamental acoustic field drives dc flow in four ways: (1) via a force field, (2) via an effective mass source distribution in the body of the fluid, (3) via a mass sink distribution at the acoustic projector, and (4), via Stokes pumping. The decomposition of the system of equations into irrotational and solenoidal components results in a number of findings. For instance, it is found that the irrotational flow that arises from the mass sources and sinks exactly cancels the irrotational component of the Stokes flow. Likewise, the solenoidal component of the force source distribution drives purely solenoidal flow while the irrotational component drives a dc pressure field. Several ex...

Linear and nonlinear acoustic Bloch wave propagation in periodic waveguides

Abstract : Propagation of acoustic waves (linear arid nonlinear, time harmonic and pulsed) in a broad class of periodically nonuniform wave guides is investigated theoretically and experimentally. It is shown that the linear, time harmonic solution wave functions are Bloch wave functions. Expressions for parameters characterizing Bloch waves (such as the Bloch wave number) are derived and the features of their band structure determined. Propagation of linear Bloch wave pulses is investigated using the standard dispersion integral. Several new dispersive pulse solutions exhibiting highly unusual behavior (such as acceleration, carrier frequency shifting, and near infinite group velocity) are found. In the case of nonlinear time harmonic Bloch wave propagation, a forward traveling fundamental Bloch wave generates both forward and backward traveling second harmonic Bloch waves, the amplitudes of which oscillate with distance. An effective coefficient of nonlinearity for Bloch waves is identified and found to be, dependent upon frequency, either larger or smaller than that of the host fluid. The dispersion associated with Bloch waves provides an effective means of suppressing the waveform distorting effect of nonlinearity. These findings are verified with measurements made in an air filled, rectangular aluminum duct loaded with a periodic array of scattering side branches.

Acoustic Bloch wave energy transport and group velocity

The relationship between the steady‐state rate of energy transport and the group velocity is investigated for acoustic Bloch waves in a periodic waveguide. A time‐average energy flux relation is derived and used to find the energy transport velocity for an arbitrary periodic waveguide. An apparent disparity between the energy transport velocity and the power delivery is discussed. The group velocity is derived using a Bloch wave generalization of the usual Fourier transform method and is shown to be equal to the rate of energy transport. The integral transform method works well for the boundary value problem as the associated Bloch wave transform is relatively straightforward. The initial value problem, however, involves the inverse Bloch wave transform, the problems associated with which are discussed. [Work supported by the Office of Naval Research.]

Linear and nonlinear acoustic propagation in a periodic waveguide

The effect of periodic nonuniformity of a waveguide on the propagation of both infinitesimal and finite‐amplitude waves is investigated theoretically and experimentally. Analytic expressions for a dispersion relation, the impedance function, and the Bloch wavefunction are derived for the case of linear, plane wave mode propagation in a rectangular wave‐guide that is periodically loaded with rigidly terminated side branches. Experiments have been done in a 25.4‐mm × 38.1‐mm × 6‐m air‐filled aluminum waveguide with 38.l‐mm‐deep side branches at 0.l‐m intervals. Measurements verify the predicted passband/stopband structure of the dispersion relation and the forward and backward traveling wave composition of the Bloch wavefunction. In the case of finite‐amplitude excitation, the compound wave composition of the fundamental Bloch wave results in a bidirectional excitation of the second harmonic. Preliminary measurements show that second harmonic behavior is qualitatively similar to that for an ordinary dispers...

Finite amplitude acoustic propagation in a periodic structure

Linear wave propagation in periodically inhomogeneous media is characterized by the division of the frequency spectrum into regions known as passbands and stop bands, the waves (called Bloch waves) associated with which are propagated and attenuated, respectively. A dispersion relation is derived for zeroth‐order propagation in a rectangular waveguide, which is periodically loaded with rigidly terminated side branches. This dispersion relation exhibits both the characteristic band structure and, in the low‐frequency limit, Korteveg‐DeVries dispersion. For the case of finite amplitude pure tone excitation, a quasilinear analysis shows that parametric upconversion is effectively blocked regardless of whether the second harmonic frequency resides in a passband or a stop band, though the blocking mechanisms are fundamentally different. A 25.4‐mm×38.1‐mm×6‐m waveguide was built with 38.1‐mm‐deep side‐branches at 0.1 m intervals. Early measurements show dispersion, band structure, and second harmonic behavior q...