Abstract: By combining the Newton method with the method of harmonic balance (HB), we have established improved analytical approximations to the period and the corresponding periodic solution to the non-linear Jerk equations. This method is established by successively linearizing the rewritten governing equation and, subsequently, appropriately imposing the HB method in order to obtain linear algebraic equations. Therefore, the complexity of the HB method has been greatly simplified. The improved solutions are in excellent agreement with the numerically exact solution, and are valid for small and large allowable values of initial velocity amplitude.

Key words: nonlinear Jerk equations, Newtonharmonic balance method, analytical approximation