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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.

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This paper presents the application of novel and reliable exact equivalent function (EF) for deadzone nonlinearity in an analytical investigation of nonlinear differential equations. A highly nonlinear equation of cantilever beam vibration with a deadzone nonlinear boundary condition is used to indicate the effectiveness of this EF. To obtain the analytical solution of dynamic behavior of the mentioned system, a powerful method, called He’s parameter expanding method (HPEM) is used. Comparison of the obtained solutions using a numerical method reveals the accuracy of this analytical EF.