Nonlinear Dynamic Behaviour of a Saddle Form Cable Net Modeled by An Equivalent Sdof Cable Net

Abstract eng:
The purpose of this paper is to estimate the geometrically nonlinear dynamic behavior of a saddle form cable net, using an equivalent single-degree-of-freedom model. First, a symmetric simple cable net is assumed, consisting of two crossing cables, considering the vertical displacement of the central node as the only degree of freedom. The equation of motion is found to be similar to the one of the Duffing oscillator with a hardening cubic term. Next, a MDOF symmetric cable net model is considered, with fixed cable ends, having a circular plan view and forming a surface of a hyperbolic paraboloid. Harmonic external loads act vertically on every node of the net, with the same amplitude and time variation. Modal analyses are conducted in order to calculate the linear eigenfrequencies and the corresponding eigenmodes of the network. The nonlinear dynamic response of the cable net is obtained by performing time history analysis. Detecting nonlinear phenomena, such as bending of the response curve, jump phenomena, different response amplitudes according to the initial conditions, superharmonic or subharmonic resonances, demands much computational effort for different load amplitudes and ratios of loading frequency. Based on a method of approximate analysis for prediction of the response of cable nets, the MDOF model is transformed to an equivalent SDOF one, using similarity relations. The analytical solution of the single-degree-of-freedom model can provide, with minimum computational time, the basic information needed for nonlinear dynamic response, i.e. secondary resonances, jump phenomena, dependence on the initial conditions and the exact loading frequency for which the maximum steady state oscillation amplitude is obtained. The comparison between the two models by means of the steady state amplitude of the central node, demonstrates that the behavior of the SDOF model describes satisfactorily the one of the MDOF model, predicting the dominant nonlinear phenomena.

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