Analytical and Experimental Modal Characteristics of Cylindrical Shells

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 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. 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 cylindrical shells is very critical first step in developing a strategy for modal vibration control for specific operating conditions. Unlike those of beam structure, the lowest natural frequency does not necessarily correspond to the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index in cylindrical shells. Mode shapes associated with each natural frequency are combination of Radial, Longitudinal, and Circumferential modes. In this paper, a scaled model of submarine hull segment under shear diaphragm boundary conditions is analyzed analytically and numerically. Then experimental modal analysis of the scaled model utilizing a fixed response approach was performed to obtain the modal characteristics of the cylindrical shell between 0 and 800 Hz. The cylinder was excited at predetermined points with an impact hammer, while the response was measured using an accelerometer at specified fixed point. Designing a boundary condition that simulate a shear diaphragm is very challenging task by itself. A total of ten natural frequencies were found within that range with their corresponding mode shapes. The experimental data were correlated with those results obtained analytically and numerically using the finite element methods using MSC.NASTRAN software. The results were found to be in excellent agreement.