Two Harmonics Method for Unsymmetrically Dynamic Systems with Strong Nonlinearity

Frequency is one of the essential factors to describe the dynamical property of the periodic oscillation systems.The strongly nonlinear problems are difficult to solve by the classical procedures such as perturbation methods. Two har-monics method is presented for strongly nonlinear dynamic-system. in a periodic oscillation, the periodic solutions canbe expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described asa second order ordinary differential equation, can be expressed as a set of non-linear algebraic equations with a frequency,amplitudes and central-offset as the independent variables using Ritz-Galerkin's method. Considering binding equationof initial conditions, they constitutes a complete set of non-linear algebraic equations with a frequency, amplitudes andcentral-offset as the independent variables. For examples, a unsymmetrical Hamilton's systems of strong nonlinearitywith a parameter are solved by two harmonics method. The results are compared with analytic method, and the agreementsare very good too. Two harmonics method combine together the method of harmonic balance and the method of equivalentlinearization. It overcoming two weakness and absorbed two advantages. Two harmonics method has excellence that themethod is briefness. we can attain the higher accuracy using a number of harmonics that takes the less.