On the non-linear vibrations of fluid-filled clamped-free cylindrical shells subjected to harmonic loads.

Resumo

This study addresses the nonlinear vibrations of fluid filled and partially fluid filled clamped-free cylindrical shells and subjected to harmonic external load. The fluid is considered incompressible and inviscid, and the internal filling level is varied to evaluate its influence on the structural response. In such configurations, fluid-structure interaction becomes a critical aspect in the design and performance of these structural systems. The shell is modeled using the nonlinear Sanders-Koiter theory, with discretization based on the shell's natural modes and the derivation of the governing equations through the Lagrangian energy approach and to obtain the nonlinear dynamic equations, the Hamiltn principle is applied, which are in turn, solved by the fourth order Runge-Kutta method. The displacement fields are expanded using two complementary functional bases trigonometric functions and Chebyshev polynomials, ensuring the exact satisfaction of boundary conditions and promoting rapid modal convergence. Different modal expansions are employed, ranging from 15 to 48 generalized coordinates, to investigate the convergence of the solution. The lowest natural frequency of the system is computed and compared against analytical solutions reported in the literature. The results reveal that, depending on the shell's geometric parameters and internal fluid level, different patterns of natural frequencies emerge and complex nonlinear dynamic behavior.