Parametric Excitation of an Inextensible, Air-Inflated, Cylindrical Membrane

摘要

Two-dimensional non-linear oscillations of a long cylindrical membrane areexamined. The membrane is anchored along two generators to a horizontal base, and its material is inextensible. The internal pressure has a static part and a small dynamic part containing multiple harmonic components with frequencies lambda sub m. A one-term Galerkin approximation is applied to the equation of motion, and weakly non-linear motions are determined using the method of multiple scale. The following resonances are investigated, where omega is the linear vibration frequency of the system: (i) lambda sub 1 approx = 2 omega; (ii) lambda sub 1 approx = omega; (iii) lamdba sub 1 approx = 3 omega; (iv) lambda sub 2 + lambda