Abstract
Based on the fact that beam-type modes play the main role in determining the sound radiation from an underwater thin slender (length-to-radius ratio L/a>20) elastic cylindrical shell, an equivalent-beam method is proposed for calculating the low-frequency radiated sound power of underwater thin slender unstiffened and stiffened cylindrical shells. The natural bending frequencies of the cylindrical shell are calculated by analytical and numerical methods and used to solve equivalent Young’s modulus of the equivalent beam. This approach simplifies the vibration problem of the three-dimensional cylindrical shell into that of a two-dimensional beam, which can be used to simplify the calculation process of radiated sound power. Added mass is used to approximate the fluid-structure coupling, further simplifying the calculation process. Calculation examples of underwater simply supported unstiffened and stiffened cylindrical shells verify the proposed method by comparison with analytical and numerical results. Finally, the effects of the size and spacing of the stiffeners on the sound radiation characteristics of underwater free-free stiffened cylindrical shells are discussed. The proposed method can be extended to the rapid calculation of the sound radiation characteristics of underwater slender complex cylindrical shells in the low-frequency range.
Highlights
IntroductionErefore, studying the low-frequency vibroacoustic responses of cylindrical shells is important for reducing the sound radiation from submarine structures, and a suitable metric for quantifying the sound field is the radiated sound power
Cylindrical shells are regarded as typical models of submarine structures whose radiated noise in the low-frequency range plays an important role in the overall mechanical noise. erefore, studying the low-frequency vibroacoustic responses of cylindrical shells is important for reducing the sound radiation from submarine structures, and a suitable metric for quantifying the sound field is the radiated sound power
With supported boundary conditions, the analytical method is used, but with other boundary conditions, numerical methods such as the finiteelement method (FEM) or the boundary-element method (BEM) are used. (2) e equivalent beam is established with structural parameters that are the same as those of the cylindrical shell. (3) e natural bending frequencies of the cylindrical shell in air obtained in step 1 are substituted into equation (13) to calculate the equivalent coefficients of Young’s modulus. (4) e equivalent coefficients of Young’s modulus and the added mass are used to calculate the equivalent natural bending frequencies of the underwater cylindrical shell by equations (12)–(15). (5)
Summary
Erefore, studying the low-frequency vibroacoustic responses of cylindrical shells is important for reducing the sound radiation from submarine structures, and a suitable metric for quantifying the sound field is the radiated sound power. For the sound radiation characteristics of unstiffened cylindrical shells, Junger [1, 2] developed the velocity distribution and pressure field of an infinite fluid-loaded shell excited by a line force. Using Green’s functions and Fourier integrals, Stepanishen [4, 5] evaluated the radiation impedance of, and radiated power from, the nonuniform harmonically vibrating surface of an infinite cylindrical shell. He evaluated the pressure field and vibratory response of a finite fluid-loaded
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