Vibration and critical pressure analyses of functionally graded combined shells submerged in water with external hydrostatic pressure

This paper describes a unified nondestructive semi-analytical formulation for the critical pressure of underwater functionally graded combined shells subjected to external hydro-static pressure. The structural model of combined shells is constructed from the first-order shear deformation theory, Voigt mixing law, and virtual spring technology. The admissi-ble displacement functions are uniformly expressed with Legendre polynomials along the generatrix direction and Fourier series along the circumferential direction. The Kirchhoff-Helmholtz boundary integral equation is discretized by using the Legendre-Gauss spectral boundary element method, and the external acoustic field model is derived by expand-ing the Green's function, sound pressure, and displacement of combined shells with one-dimensional Fourier transformation. The linear elastic material theory is applied to deduce the work done by the hydrostatic pressure. The key technology to predict the critical pres-sure is to create an accurate equivalent model of the hydrostatic pressure. Through solv -ing the final coupled governing equation, the critical pressure is obtained from the linear relationship between the hydrostatic pressure and the square of natural frequency. The convergence and correctness are verified by comparison with the results from published papers and numerical methods. The effects of different hydrostatic pressures, power-law exponents, geometric parameters, and boundary conditions on the critical pressure are in-vestigated in several examples. Computed results can provide security guidance for the nondestructive prediction of underwater functionally graded combined shells at the be-ginning of engineering application design.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper presents a unified nondestructive semi-analytical formulation for predicting the critical pressure of underwater functionally graded combined shells subjected to external hydrostatic pressure. The structural model is based on the first-order shear deformation theory, Voigt mixing law, and virtual spring technology, with admissible displacement functions expressed using Legendre polynomials and Fourier series. The critical pressure is obtained by solving the coupled governing equation and establishing a linear relationship between hydrostatic pressure and the square of the natural frequency. The accuracy and convergence of the method are verified through comparisons with published results and numerical methods, and various factors such as hydrostatic pressure, power-law exponents, geometric parameters, and boundary conditions are investigated.