No abstract

This study intends to introduce the novel and efficient exact equivalent function (EF) for well-known deadzone nonlinearity. To indicate the effectiveness of this EF, the nonlinear vibration of cantilever beam in presence of deadzone nonlinear boundary condition is studied. The powerful analytical method, called He's Parameter Expanding Method (HPEM) is used to obtain the exact solution of dynamic behavior of mentioned system. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution. Comparison of the obtained solutions using numerical method shows the soundness of this analytical EF.

This article attempts to investigate the dynamical analysis of beam vibrations in the presence of preload discontinuity and proposes an innovative accurate equivalent function for this well-known nonlinearity. This approach enables us to overcome the inherent computational difficulty of the preload nonlinearity in the analytical investigations. At first, the nonlinear equation of beam vibration with preload boundary condition is considered and analytical solution is obtained using He’s parameter expanding method. The precision of the proposed equivalent function has been elucidated by comparison of our results with the obtained solutions using numerical method. Finally, the accuracy of the obtained results in the vibration analysis of suspension bridges as a realistic problem, verifies the strength of the presented modeling.

No abstract

No abstract