A semi-analytical model for nonlinear vibration analysis of clamped, submerged, and fluid-filled cylindrical shells

Abstract

This work introduces a semi-analytical approach to examining the forced and nonlinear oscillations of a cylindrical shell clamped with clamped-free boundary conditions. The structural model considers the fluid–structure interaction provoked by an external and internal fluid. The effects of the free surface motion are also considered in the fluid–structure interaction. The Sanders–Koiter nonlinear theory is employed to characterize deformation fields and changes in curvature. Displacement fields are described through modal expansions obtained from Chebyshev polynomials. Using the Rayleigh–Ritz method, the set of nonlinear equilibrium equations are derived and subsequently solved to determine natural frequencies, vibration modes, and the forced response. The results of the derived semi-analytical model are compared with the numerical results, obtained through a finite element analysis, to check the convergence. The inclusion of external and internal fluid in dynamic analysis is crucial as it introduces additional mass and reduces natural frequency values, influencing the forced response of the investigated clamped-free cylindrical shell. This work also investigates the nonlinear vibrations induced by static uniform pressure or a time-dependent uniform harmonic pressure, evaluating the time responses and phase planes. The obtained forced response presents good agreement with the results came from finite element analysis, demonstrating the efficiency of the derived semi-analytical model to obtain the free and the forced nonlinear response of the proposed fluid–structure interaction problem.