Dynamic and Stability Analysis of a Cracked Rotating Flexible إBeam

The free and forced vibration analysis of a rotating large flexible structure with a single crack is investigated using the Homotopy Perturbation Method (HPM). The crack is modeled with a torsional spring element on a structure that follows the Euler-Bernoulli theory. The nonlinear equations of motion of the co-rotational system considering centrifugal forces are derived using the calculus of variation and the Assumed Mode Method (AMM). Applying the Galerkin method, the spatial domain is extracted and the time domain is transformed into a second-order nonlinear differential equation. The results of time response, phase plane, and bifurcation diagrams for different functional parameters variations such as base angular velocity, crack position and stiffness have been analyzed. Moreover, it is shown that as the base angular velocity increases, a tensile force appears along the cracked structure axis, stiff it, and shifts the backbone to the right, this can highly affect the nonlinear features of the system.