Based on the non-autonomous two-degree of freedom governing equations of motion for the plate,the dynamical analysis was given by using extended Melnikov method.

Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation.

Melnikov method is an effectively mathematical method which is usually used to prove the existence of chaos in the sense of Smale horseshoes.

Using the Melnikov method, the system s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained.

By using the stochastic nonlinear dynamics theory, based on the stochastic Melnikov method and rate of phase space flux theory, the dynamical stability of ships in random ocean wave and the method on reducing its capsizal are studied.

So higher-order Melnikov method is developed to determine the existence of .

From the averaged equations obtained here, the theory of normal form was used to give the explicit expressions of normal form, based on which, high-dimensional Melnikov method was utilized to analyze the global bifurcations and chaotic motions of composite laminated rectangular thin plates.