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The general nonlinear intrinsic differential equations of a composite beam are solved in order to obtain the elastodynamic response of an accelerating rotating hingeless composite beam. The solution utilizes the results of the linear variational asymptotic method applied to cross-sectional analysis. The integration algorithm implements the finite difference method in order to solve the transient form of the nonlinear intrinsic differential equations. The motion is analyzed since the beam starts rotating from rest, until it reaches the steady state condition. It is shown that the transient solution of the nonlinear dynamic formulation of the accelerating rotating beam converges to the steady state solution obtained by an alternative integration algorithm based on the shooting method. The effects of imposing perturbations on the steady state solution have also been analyzed and the results are shown to be compatible with those of the accelerating beam. Finally, the response of a nonlinear composite beam with embedded anisotropic piezocomposite actuators is illustrated. The effect of activating actuators at various directions on the steady state forces and moments generated in a rotating beam has been analyzed. These results can be used in controlling the nonlinear elastodynamic response of adaptive rotating beams.A list of symbols can be found starting on page 713.

Nonlinear dynamical systems, being more of a realistic representation of nature, could exhibit a somewhat complex behavior. Their analysis requires a thorough investigation into the solution of the governing differential equations. In this paper, a class of third order nonlinear differential equations has been analyzed. An attempt has been made to obtain sufficient conditions in order to guarantee the existence of periodic solutions. The results obtained from this analysis are shown to be beneficial when studying the steady-state response of nonlinear dynamical systems. In order to obtain the periodic solutions for any form of third order differential equations, a computer program has been developed on the basis of the fourth order Runge-Kutta method together with the Newton-Raphson algorithm. Results obtained from the computer simulation model confirmed the validity of the mathematical approach presented for these sufficient conditions,