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.

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Keywords Accelerating beam, Embedded actuators, Intrinsic differential equations of a beam, Rotating beam, Steady state solution, Variational asymptotic method (VAM)
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Journal Journal of Mechanics of Materials and Structures
Ghorashi, M. (Mehrdaad), & Nitzsche, F. (2009). Nonlinear dynamic response of an accelerating composite rotor blade using perturbations. Journal of Mechanics of Materials and Structures, 4(4), 693–718. doi:10.2140/jomms.2009.4.693