The Polynomial Nonlinearities Analysis based on the Second-order Normal Form Method

The second order normal form method shows its intelligence in handing the weak nonlinear vibration problems. With the sinusoid excitation, it is easy to obtain the steady state response with higher harmonics. Usually the nonlinearities in the system can be expressed as a polynomial form. The function of each term with different power indexes in the polynomial expression is analyzed. The result concludes that the summation of power index of each nonlinear term decides the final form of the frequency response function of the system. The general form of the frequency response function is both obtained. These pave the way for the polynomial kind of nonlinearities identification in the future work. And a series of nonlinearities are given to demonstrate the conclusions and to show how to identify the system nonlinearities.