A Method On Computing The Transition Boundaries Of Strongly Nonlinear Systems

Here a further modified method of multiple scales is developed. The differenceof the new methods with T.D. Burton's is that it defines a new parameter witch is notto use known results from other methods to guide in the selection of the newexpansion parameter, moreover, the result with this method is in good agreement withT.D.Burton's.Then, this paper uses it with the L—P method for the analysis of thetransition boundaries of a class of strongly nonlinear systems under combinedparametric and forcing excitation; also, the transition boundaries of strongly nonlinearsystems under combined parametric but two forcing excitation are studied. At last, thesteady state of the system is studied more concretely and easylier from the pictures ofthe transition boundaries. The research achievements and main contents are as follows:1.The development of general mechanics and nonlinear systems;2.An introduce of dynamical systems;moreover, let's have an impression on thebifurcation with examples;3.A further modified method of multiple scales is developed. Then, this paper uses itwith the L—P method for the analysis of the transition boundaries of a class ofstrongly nonlinear systems under combined parametric and forcing excitation; also ,the transition boundaries of strongly nonlinear systems under combined parametricbut two forcing excitation are studied.