Dynamic analysis of preload nonlinearity in nonlinear beam vibration

The objective of this paper is to propose a novel exact equivalent function (EF) for preload nonlinearity. The nonlinear preloaded spring force, which is exerted on the cantilever beam has been rewritten with a definite force-displacement relationship using new EF. This approach permits us to overcome severe computational issues that are encountered in the analytical investigations of nonlinear problems. Highly nonlinear equation of beam vibration under the influence of preloaded spring at its end with cubic nonlinearity is considered and the related analytical solution is obtained through Parameter-expansion Method (PEM). Finally, the soundness of the introduced EF would be verified by comparison of the results with the obtained solutions using numerical method.