Abstract
A finite element solution procedure is proposed, and the nonlinear vibrations of a flexible membrane under periodic load are investigated numerically. First, a simplified model is proposed for the flow-induced vibration of a membrane wing at higher angles of attack and the corresponding governing equation is derived briefly. Then, a solution procedure based on the Galerkin finite element method, Generalized- $$\upalpha $$ method and Newton–Raphson method is developed to solve the governing equation and its accuracy and stability are examined by a steady problem with exact solution. Finally, using the numerical method proposed, the forced vibration of a flexible membrane under periodic load is simulated, and the effects of the membrane density, elastic modulus and pre-strain are investigated in detail. In addition, the change in the vibration state along the membrane is also analysed to examine whether the centre point can reflect correctly the vibration state of the whole structure.
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