Nonlinear Dynamic Response of MDOF Cable Nets Estimated by Equivalent SDOF Models

In this work the geometric nonlinear dynamic response of saddle-shaped cable nets subjected to uniform harmonic loads is investigated. The detection of nonlinear phenomena can be realised by numerous numerical nonlinear dynamic analyses leading to diagrams of response curves. This procedure demands much computational effort for different loading amplitudes, changing the frequencies by very small steps and taking into consideration initial conditions by means of nodal initial displacements and velocities. The number of such analyses can be significantly reduced by means of an analytical solution that can provide the necessary information about the conditions for which nonlinear resonances occur. To that effect, an equivalent SDOF model is set up, and its equation of motion is found to be similar to the one of the Duffing oscillator, for which analytical solutions under primary or secondary resonances can be found in the literature. The transformation of the MDOF cable net to the SDOF one is obtained by similarity relations. The comparison between the two models by means of the steady-state amplitude of the central node demonstrates that the behaviour of the SDOF model describes satisfactorily the one of the MDOF model, predicting the dominant nonlinear phenomena.