Sound and Vibration in Composite Tubes of Variable Cross Section

Abstract

Abstract To investigate the coupling between sound production and wall vibration in composite tubes of variable cross section, a set of composite cones with varying wall material and thickness was manufactured and tested experimentally. The approach undertaken was to optimize the relationship between cross sectional radial vibrations and structural stiffness. Employing Webster’s variation of the wave equation as a basis for a theoretical analysis, a second generalized equation was derived to include the effects of surface vibrations onto the standing wave pattern in the composite tube. Methods for solving this differential equation analytically are discussed, as are assumptions to arrive at a general solution for the natural frequency mode and shapes. The focus of the experimental research was to produce such composite cones, excite standing waves in the cones at particular frequencies, and record the acoustic radiation and the corresponding wall oscillations for each. Carbon, Kevlar and wood veneer were chosen as materials for the composite. To reduce the influence of other factors that effect acoustical properties, each cone was laid up over a single mold. In addition, pre-impregnated fabrics were used to insure a consistent volume fraction, and the sinusoidal source and mechanical procedures were held constant. The results suggest that composite tubes of variable cross section can be designed to obtain a coupling between the standing wave and wall vibrations to produce a specific sound quality.