Free Vibrational Characteristics of Pretensioned Cable Roofs

Cable roofs are analyzed using nonlinear membrane theory. The cable network is simulated by an equivalent thin elastic prestressed membrane without shear rigidity. The equations of motion for the vibrating membrane are formulated by considering the static equilibrium position of the membrane as the position of the membrane after it undergoes nonlinear deformation due to uniform transverse load over the projected area of the membrane. The equations of motion are then solved for natural frequencies and associated mode shapes by restricting the analysis to small amplitude vibrations about the static equilibrium position. Two special cases are considered: a flat rectangular membrane, and a membrane that has the shape of a hyperbolic paraboloid surface that is rectangular in plan. Comparisons between linear and nonlinear membrane theory solutions are presented.