Abstract

New analytical work on the well-known preload nonlinearity using the innovative equivalent function (EF) is presented in this paper. The nonlinear vibration of cantilever beam with nonlinear boundary condition in the presence of preload spring with cubic nonlinearity is studied. The powerful analytical method, called He’s Parameter Expanding Method (HPEM) is used to obtain the exact solution of dynamic behavior of the mentioned system. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution. Finally, we successfully compare our analysis with numerical solutions.

Key words: He’s parameter expanding method, preload nonlinearity, exact equivalent function, nonlinear vibration of beam.