In communities such as the sailing design,civil engineering,Micro Aerial Vehicle(MAV)design,bionics and hemodynamics,flow-induced vibrations(FIV)of the membrane structures such as the heart valves,insect wings,MAV wings,parachutes,sails and cable-membrane structures in many buildings,have attracted a great attention of both engineers and scientists.In the past two decades,many studies have been carried out on experimenting,modeling and simulating the FIVs of the flexible membranes,and more and more details of the corresponding fluid-structure interaction process have been observed and revealed recently.Unfortunately,the mechanism of such FIV problems is still poorly understood by far due to their characteristics of strong unsteadiness and nonlinearity.To investigate the mechanism of the fluid-membrane interaction,establishing suitable models for the membrane structures in nature and engineering and investigate thoroughly the intrinsic characteristics as well as the dynamic behaviors of the flexible membranes are very important.However,little work has been carried out on this subject.In this paper,the dynamic response and bifurcation behaviors of the flexible membrane under different structure parameters and period loads are analyzed by numerical method.First,a structure model proposed by Gordnier is introduced to describe the vibration of a very flexible membrane when external loads are imposed.Then,the finite element method for spatial discretization and the generalized-αmethod for temporal integration are presented for solving numerically the governing equations,and the involved nonlinear theories for analysis are introduced briefly.Finally,using the proposed numerical method and nonlinear analysis techniques,the natural frequency and main vibration mode of the flexible membrane are solved to reveal the intrinsic characteristics of the flexible membrane,and the influence of the parameters,such as the density,damping,modulus of elasticity and the amplitude and frequency of the period loads,on the dynamic response of the forced vibration of a flexible membrane is investigated in detail.