Buckling and vibro-acoustic behavior analysis of laminated immersed cylindrical shells with hydrostatic pressure based on Chebyshev-Fourier spectral approach

The buckling and vibroacoustic behaviour of laminated cylindrical shell structures is vital for the safety and operational efficiency of underwater vehicles. This paper introduces a Chebyshev-Fourier spectral approach for the comprehensive analysis of buckling and vibro-acoustic behaviour in water-immersed laminated cylindrical shells under external hydrostatic pressure. The approach combines Chebyshev polynomials and Fourier series to approximate the displacement of shell and acoustic pressure of the fluid-structure-interaction (FSI) surface in cylindrical coordinates. An approximate solution is used in the axial direction, while an analytical solution is used in the circumferential direction, allowing for the analysis of different circumferential wave numbers n. The influence of external fluid pressure is characterized through the Helmholtz boundary integral equation, while the effect of hydrostatic pressure is deduced using linear elastic theory. From a theoretical derivation standpoint, hydrostatic pressure leads to a reduction in equivalent stiffness, while the external fluid contributes to an increase in the effective mass matrix. Validated against established literature analysis, the study finds that hydrostatic pressure decreases the natural frequencies, though the impact is less significant for lower circumferential wave numbers. For these lower wave numbers, the overall radiated sound power remains largely independent of external hydrostatic pressure, regardless of being in air or water. However, at higher circumferential wave numbers, the effect is more pronounced. This study not only advances the theoretical framework for analysing submerged cylindrical shells but also provides crucial insights into designing more robust structures for underwater applications.