Sound Radiation of Cylindrical Shells

Abstract

The acoustic signature of submarines is very critical in such high performance structure. Submarines are not only required to sustain very high dynamic loadings at all time, but also being able maneuver and perform their functions under sea without being detected by sonar systems. Submarines rely on low acoustic signature level to remain undetected.

Reduction of sound radiation is most efficiently achieved at the design stage. Acoustic signatures may be determined by considering operational scenarios, and modal characteristics. The acoustic signature of submarines is generally of two categories; broadband which has a continuous spectrum; and a tonal noise which has discrete frequencies.

The nature of sound radiation of submarine is fiction of its speed. At low speed the acoustic signature is dominated by tonal noise, while at high speed, the acoustic signature is mainly dominated by broadband noise. Submarine hulls are mainly constructed of circular cylindrical shells.

Unlike that of simpler structures such as beams and plates, the modal spectrum of cylindrical shell exhibits very unique characteristics. Mode crossing, the uniqueness of modal spectrum, and the redundancy of modal constraints are just to name a few.

In cylindrical shells, the lowest natural frequency is not necessarily associated with the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index either. Solution of the vibration problem of cylindrical shells also indicates repeated natural frequencies. These modes are referred to as double peak frequencies. Mode shapes associated with each one of the natural frequencies are usually a combination of Radial (flexural), Longitudinal (axial), and Circumferential (torsional) modes.

In this paper, the wave equation will be set up in terms of the pressure fluctuations, p(x, t). It will be demonstrated that the noise radiation is a fluctuating pressure wave.