On the analytical modeling of the nonlinear vibrations of pretensioned space structures

Abstract

Linear, quasi-linear and nonlinear analyses have been used to investigate a relatively simple two-dimensional cable-stiffened structure under sinusoidal excitation. For linear vibrations, both an exact and a simplified analysis in which each cable is modeled as a spring with its mass lumped at the ends have been compared. The exact analysis, which accounts for distributed cable inertia, indicates a mass lumping procedure which is valid for both low and high ratios of cable to joint mass and represents an improvement to using a consistent mass lumping. The quasi-linear analysis extends the simplified linear model to account for cable slackening by removing a cable when its axial load vanishes. The nonlinear analysis accounts for distributed cable mass which permits large cable deformations and the natural collapse of a cable when it slackens. Appropriate dimensionless quantities are derived from the nonlinear differential equations and results are presented in terms of these quantities. The nonlinear analysis predicts softening of the overall structural mode due to cable slackening and hardening of strongly coupled cable-structural modes due to raised tension levels during large cable deformations. Quasi-linear analysis predicts the softening mode provided motions are not very large, but it cannot predict hardening modes. Hardening modes can involve structural motions of the same magnitude as the overall structural mode and can be the fundamental mode of the cable-stiffened structure. Prediction of the hardening mode amplitude requires nonlinear analysis, however, the amplitude of the softening mode can be predicted by linear analysis even through it fails to predict the downward change in frequency.