Nonlinear vibration of cable-stiffened pantographic deployable structures

Cable-stiffened deployable pantographic structures are fully prestressed at the end of deployment. Indirect effects of this state of prestress are increased stiffness and friction at the end joints of the pantograph rods, and increased cable damping. Both effects are a function of the prestress level in each particular component, are amplitude dependent and frequency dependent, and can be characterized using the restoring force identification method after carrying out component level tests. For a particular model structure it is shown that the resonant frequencies of its first 4 modes tend to decrease when the excitation amplitude is increased, whereas the variation in the modal damping is non-monotonic. A nonlinear dynamic model of this structure is set-up, which accounts for the effects of joint preload and passive cable pretension via equivalent stiffness and damping coefficients. This model predicts accurately the resonant frequencies of the first 4 modes. It also predicts modal damping to good accuracy, provided that unmodelled degrees-of-freedom, such as joint rocking, are not excited.