The Study of the Stochastic Jump Phenomenon in a Nonlinear Cantilever Beam Immersed in Water Under Narrow-Band Random Excitation

For the modelling of marine structures, such as the oil columns and structures, the terminal and base of oil platforms and the towers surrounded by water usually a cantilever beam or rod is used. These models are subjected to random excitation and the response amplitude of these structures is of particular importance during design. In this paper, a nonlinear cantilever beam immersed in a fluid with a concentrated mass under a narrow band random excitation has been studied and its response has been analyzed. With the development of the harmonic balance method, the variance of the random system response has been determined and the phenomenon of jumping and random jumping has been investigated. The analytical solution and the numerical simulations show that in comparison with the deterministic response, the random excitation increases the amplitude of the random response between the bifurcation points of the beam. As the intensity of the random excitation increases, the steady response changes from a circular to a cyclic state. The results also show that the random jump phenomenon occurs in the area where there are three states for the system. Finally, the results of analytical and numerical modeling indicate that there is a very good agreement between the data and the results of these two methods.