Abstract: This paper gives the direct formulas of stiffness matrixes of two-kinds of Kirchhoff nonlinear elements under total-Lagrange coordinate. For the first one, it includes not only the quadric terms of increments of strain and displacement but also-the influence of rotations. For the second one, it is simplified and its nonlinear is considered by taking into account the influence of axial force on the equilibrium equation in the linear beam theory.The nonlinear equation obtained from both of the above-Said elements is solved by mixed Newton-Raphson method, and by comparing the results obtained from two kinds of nonlinear beam some important conclusions that we can know how to use them right are given in our paper.

Key words: single-degree-of-freedom linear vibroimpact system, subharmonic response, Zhuravlev transformation method, random averaging method