Nonlinear dynamic phenomena in a SDOF model of cable net

摘要

The dynamic behavior of the simplest possible cable net is studied in this paper, consisting of two crossing cables in perpendicular vertical planes, having the same span and opposite sags. A concentrated mass is attached at the central node, and only the vertical translational degree of freedom is assumed as active. First, the static behavior is explored up to the load level that causes tensile cable failure. Then, the dynamic response is investigated for different resonant conditions and is found to give significantly larger amplitudes with respect to the static ones, even for loading frequencies away from the eigenfrequency of the system. In order to derive analytical solutions, the equation of motion is simplified and the cable net is proved to be a Duffing oscillator. For the simplified problem, the occurrence of nonlinear phenomena is verified analytically, such as bending of the response curve, jump phenomena, instability regions, dependence on the initial conditions, and superharmonic and subharmonic resonances. These phenomena are also detected by means of numerical analyses. A comparison between the exact model and the simplified one shows that the analytical solution of the Duffing equation describes the dynamic behavior of the cable net with satisfactory accuracy.