Two-dimensional vibrations of air-filled geomembrane tubes resting on rigid or deformable foundations

Geomembrane tubes may be used as an alternative to sandbags for flood protection. The static and dynamic behavior of such tubes is considered, in the absence of external water. A two-dimensional analysis of a cross section of the tube is conducted. The tube is inflated with air, and the weight of the tube causes the equilibrium shape to be noncircular. The material is assumed to be inextensible and to have no bending resistance. Equilibrium configurations and small vibrations about equilibrium are investigated for tubes on rigid, Winkler, and Pasternak foundations. The mode shape corresponding to the lowest frequency is symmetric with two nodes. The effects of the internal pressure, foundation stiffness, and foundation shear modulus on the first four frequencies and modes are determined numerically using a shooting method.