Novel equivalent function for deadzone nonlinearity: applied to analytical solution of beam vibration using He's Parameter Expanding Method

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.