Nonlinear vibrations of a fluid-filled, soft circular shell: experiments and system identification
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ORIGINAL PAPER
Nonlinear vibrations of a fluid-filled, soft circular shell: experiments and system identification Prabakaran Balasubramanian . Giovanni Ferrari . Marco Amabili
Received: 5 June 2020 / Accepted: 7 October 2020 Springer Nature B.V. 2020
Abstract Vibration experiments are carried out on a slightly corrugated circular cylindrical shell made of polyethylene terephthalate fabric. The shell is liquidfilled, 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 liquidfilled 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 smallamplitude 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.
P. Balasubramanian G. Ferrari M. Amabili (&) Department of Mechanical Engineering, McGill University, Macdonald Engineering Building, 817 Sherbrooke Street West, Montreal, QC H3A 0C3, Canada e-mail: [email protected]
Keywords Soft shell Vibrations Nonlinear vibrations Identification
1 Introduction Nonlinear vibrations of circular cylindrical shells made of linearly elastic materials received large attention in the literature. Reviews were written by Amabili and Paı¨doussis [1] and Alijani and Amabili [2]. Particularly relevant are the studies of Chen and Babcock [3], Batista and Goncalves [4], Amabili, Pellicano and Paı¨doussis [5], Amabili [6–8], Pellicano [9], Jansen [10], Ribeiro [11], Amabili, Balasubramanian and Ferrari [12]. They studied the presence of a second mode, identical to the one directly excited by an external force but orthogonal to it, in a narrow frequency range close to the resonance due to a one-toone internal resonance. The effect of a contained liquid, giving additional inertia through the so-called virtual mass, was also investigated in references [4–8]. Experimental results were reported in [4, 7, 12] together with the corresponding numerical simulations. The mechanics and dynamics of hyperelastic shells have received much less attention in the literature. Nonlinear vibrations of a hyperelastic anisotropic circular cylindrical shell were addressed by Breslavsky, Amabili and Legrand [13]. Amabili [14] and
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