On the normal forms of certain parametrically excited systems

In this paper, a modified normal form approach for obtaining normal forms of parametrically excited systems is presented. This approach provides a number of significant advantages over the existing normal form approaches, and improves the associated calculations. The approach lends itself more readily to symbolic calculations, like MAPLE, and the calculations of normal forms, together with the associated coefficients, are carried out much more conveniently. Four examples are presented to illustrate the approach. All examples include a comparison of the results obtained by the methods of normal forms and averaging. Example 4 contains a comparison of the results obtained by the normal form approach and Liapunov-Schmidt method as well. (C) 2002 Elsevier Science Ltd. All rights reserved.