Vibration Analysis of Doubly Coupled Cracked Composite Beams: an Exact Dynamic Stiffness Matrix


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Abstract


A Dynamic Stiffness Matrix (DSM) is developed to analyze the free vibration characteristics of doubly coupled, cracked, laminated, unidirectional, unbalanced composite beams. Based on the closed form solution of the governing differential equations, an ‘exact’ DSM formulation for bending-torsion vibration of an intact composite beam is first presented. Both material and geometric/structural couplings are taken into account. Stress intensity factors, corrected for geometry and material anisotropy, are used to develop the local flexibility of a through-thickness cracked uniform beam. The system is modeled using two interconnected  intact beams and the crack is modeled by implementing its local flexibility. The intact elements’ DSMs exhibiting both mass and stiffness properties are then assembled and the boundary conditions are applied to form the nonlinear eigenproblem of the overall system. The natural frequencies and modes are extracted using the well-known Wittrick–William (W-W) root counting algorithm. Numerical tests are conducted for a long, slender, flat, uniform, cantilever, laminated composite beam of solid rectangular cross-section, exhibiting material couplings.  Both intact and damaged scenarios for a ply angle, η=30°, the crack located at 30% of the span, and the crack ratio of α=0.3, are investigated. Numerical results on natural frequencies and modes are in excellent agreement with the literature.
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Keywords


Bending-Torsion Couplings; Cracked Composite Beam; Doubly Coupled Vibrations; Dynamic Stiffness Matrix (DSM); Exact Formulation; Local Flexibility Matrix; Material Coupling

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References


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