Modal Vibration Control Of Submarine Hulls

Abstract

Cylindrical shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. Most of these structures are required to operate in a dynamic environment. The acoustic signature of submarines is very critical in such a high performance structure. Submarines are not only required to sustain very high dynamic loadings at all times, but must also be able to maneuver and perform their functions under the sea without being detected by sonar systems. Reduction of sound radiation is most efficiently achieved at the design stage, and the 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. Therefore, investigating the dynamic characteristics of a submarine hull is very critical in developing a strategy for modal vibration control for specific operating conditions. During the design optimization of a submarine hull, one is faced with some unique challenges. Unlike that of simpler structures such as beams and plates, the modal spectrum of a cylindrical shell exhibits very unique modal characteristics. The interrelationship between modes usually results in mode crossing, uniqueness of the modal spectrum, and the redundancy of modal constraints. Design optimization due to modal frequency constraints also results in nonunique solutions. Those designs must be examined for their modal frequency response to determine the best suitable design. In this paper, a strategy for modal vibration control is investigated. First, the modal characteristics of a submarine hull are examined. Second, the optimum design for modal frequency constraints is established. The frequency responses of the resulting optimum designs are compared. Third, a frequency response optimization is presented and compared with other models. High Performance Structures and Materials II, C.A. Brebbia & W.P. De Wilde (Editors) © 2004 WIT Press, www.witpress.com, ISBN 1-85312-717-5 1 Modal characteristics of submarine hull The modal spectrum of cylindrical shell exhibits very unique characteristics. Unlike that of simpler structures such as beams and plates, the lowest natural frequency in cylindrical shells does not necessarily correspond to the lowest wave index shown in Figure 1. In fact, the natural frequencies do not fall in ascending order of the wave index either, as indicated in Table 1. The eigen solutions also indicate multiple eigenvalues, i.e. repeated natural frequencies with similar mode shapes. These are referred to as double peak frequencies [1]. Shell displacements of each mode shape are defined in three orthogonal directions that are associated with radial (flexural), longitudinal (axial), and circumferential (torsional) components.