Nonlinear vibrations of a fluid-filled, soft circular shell: experiments and system identification

Vibration experiments are carried out on a slightly corrugated circular cylindrical shell made of polyethylene terephthalate fabric. The shell is liquid-filled, it is pressurized by a liquid column that applies a pressure of 100 mmHg, and the two edges are clamped to fix supports. Forced vibrations of the shell are experimentally studied in the linear (small amplitude) and in the geometrically nonlinear (large amplitude) regime. The large-amplitude vibrations of the liquid-filled shell are characterized by a strong softening behavior that cannot be captured by any quadratic nonlinear stiffness. Since compressed fibers do not carry load, a piecewise linear stiffness with viscous damping is thus introduced in a reduced-order model, resulting in a very good agreement between experimental and simulated responses. The stiffness parameters and the damping ratios are identified from the experimental results. The damping ratio grows linearly with the excitation amplitude, indicating a predominant hydrodynamic damping. In particular, the damping ratio increases 2.75 times from the small-amplitude vibrations to a maximum amplitude of 1.26 mm. This is a very significant increase that highlights the necessity to introduce nonlinear damping to model shell structures.