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Steel and Composite Structures
  Volume 39, Number 5, June10 2021 , pages 543-564

Investigating the effect of edge crack on the modal properties of composite wing using dynamic stiffness matrix
Ali Reza Torabi, Shahrokh Shams and Mahdi Fatehi-Narab

    In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.
Key Words
    cracked wing; dynamic stiffness matrix; two interconnected Euler–Bernoulli beams
Ali Reza Torabi: Fracture Research Laboratory, Faculty of New Science and Technologies, University of Tehran, Tehran, Iran
Shahrokh Shams and Mahdi Fatehi-Narab: Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran, P.C:1439957131

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