Low-Frequency Acoustic Propagation Through Crossing Internal Waves in Shallow Water

Crossing internal wave trains are commonly observed in continental shelf shallow water. In this paper, we study the effects of crossing internal wave structures on three-dimensional acoustic ducts with both theoretical and numerical approaches. We show that, depending on the crossing angle, acoustic energy, which is trapped laterally between internal waves of one train, can be either scattered, cross-ducted or reflected by the internal waves in the crossing train. We describe the governing physics of these effects and illustrate them for selected internal wave scenarios using full-field numerical simulations.

Component Mode Synthesis Method Applied to Two-Dimensional Acoustic Analysis in Ducts

This paper presents a modal approach to calculate the acoustic normal modes in complex ducts. In this study, the component modal synthesis (CMS) method in two dimensions for application in large duct with acoustic propagation in order to obtain a reduced acoustic model will be developed. The proposed technique is based on division of the acoustic system in well-known modal model subdomains and uses a CMS procedure to obtain a reduced acoustic modal model of the large system. In this paper, the applicability of the CMS Craig-Chang's method was adapted for acoustics CMS, considering only acoustic fluid interaction. In the modal synthesis technique developed originally for structural purpose, displacements and forces were coupled at the boundary of the substructures by dynamic constraint equations. The methodology developed here is based on residual flexibility, using residual inertia relief attachment modes in place of simply residual attachment modes to couple sound pressure and flow rates at the substructures interfaces. The approach leads to a versatile method with a low computational cost. To validate the proposed CMS approach, comparison with acoustic ducts models using finite element methodology (FEM) and analytical solutions were made. The differences between the analytical and numerical results as well as the limitations and advantages of each method were discussed.

TRANSVERSE RESONANT OSCILLATIONS IN ACOUSTIC DUCTS

A theoretical study is made of the flow induced by a piston, performing rotational sinusoidal vibrations in a uniform two-dimensional planar duct. A frequency of the forced vibrations is close to a cut-off frequency. It is shown that exactly at a cut-off frequency the steady-state response represents a transverse periodic shock wave, propagating between duct walls and decaying algebraically in the far field.

Modeling and Control of Acoustic Ducts

This paper presents closed-form mathematical models for an acoustic duct with general boundary conditions. These infinite-dimensional models are derived using symbolic computations. A new method to obtain finite dimensional approximations of infinite-dimensional models using quartic functions is presented. The theoretical models are compared with the experimental data obtained for the KSU duct. The experimental results of a new robust broadband feedback controller, designed using passivity-based techniques, are presented. The controller design is shown to be robust to the unmodeled dynamics and parametric uncertainty.