Keywords: cantilevered tank, nonlinear vibration, geometric imperfection, hydrostatic pressure, harmonic excitation.

In this paper, the influence of liquid height and initial geometric imperfections on the large-amplitude vibrations of upright, liquid-filled cantilevered tanks are studied theoretically. The system is formulated using the extended Hamilton's principle; a nonlinear model based on Flügge's thin shell theory is utilized to describe the tank motions, and the fluid perturbations are described by linearized potential flow theory. Equations of motion are discretized by expanding the solution with trigonometric functions and the cantilevered beam eigenfunctions in the circumferential and axial direction, respectively. The essential boundary conditions are satisfied exactly, while the natural ones are satisfied in the mean. The system of coupled nonlinear ODEs are integrated numerically by using the pseudo-arclength continuation method implemented in the AUTO software. The vibrational response of the system is demonstrated in the form of frequency-response curves, computed in the neighbourhood of the fundamental frequency. Both softening and hardening nonlinear responses are observed, and it is understood that the degree and type of nonlinearity depend on the imperfection amplitude and the liquid height.

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