Structural elements with mathematically defined surfaces for enhanced structural and acoustic performance

Abstract

Two design methods are explored to reduce vibration, minimize unwanted acoustic noise, and increase stiffness in structures. The first design approach is to create nearly isotropic panels with increased stiffness using two-dimensional curvature. These quasi-isotropic designs can be used in lieu of typical panel reinforcements, and can provide an inexpensive alternative to honeycomb sandwich designs. The second approach is to design panels formed into the shape of a mode shape to reduce detrimental modal dynamics. The effects of combining the two-dimensionally curved designs with constrained layer damping is also investigated. Further, it is also the goal of this research that these panels can be inexpensively manufactured with current manufacturing methods (e.g. stamping, rolling, thermoforming, etc.), resulting in a more effective structural element that does not require significant extra cost or weight. Initial analysis was performed using geometric modeling and finite element analysis. Experimental analysis involved both static and dynamic system identification. The experimental results indicate that quasi-isotropic designs can be accomplished with two-dimensional curvature.

(cont.) These quasi-isotropic designs increase the stiffness of a panel and raise the natural frequency by a factor of 2 (compared to a flat panel of the same mass). Although the quasi-isotropic designs have no acoustic benefit, they were shown to be effective replacements as honeycomb cores. The mode-shaped designs demonstrated the unique quality of simultaneously reducing vibration and acoustic noise over a broad frequency range (50-10,000 Hz). The mode-shaped panels demonstrated a factor of 3 increase in the natural frequency, a ten-fold reduction in dynamic deflection displacements, and a 3 to 4 dB RMS reduction in the radiation index over a broad frequency range.