A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings |
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Authors: | JR Banerjee H Su |
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Affiliation: | a School of Engineering and Mathematical Sciences, City University, Northampton Square, London EC1V OHB, United Kingdom b Siemens Industrial Turbomachinery Ltd, Firth Road, Lincoln LN6 7AA, United Kingdom |
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Abstract: | The dynamic stiffness matrix of a composite beam that exhibits both geometric and material coupling between bending and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The formulation is based on Hamilton’s principle leading to the governing differential equations of motion in free vibration, which are solved in closed analytical form for harmonic oscillation. By applying the boundary conditions the frequency dependent dynamic stiffness matrix that relates the amplitudes of loads to those of responses is then derived. Finally the Wittrick-Williams algorithm is applied to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes of an illustrative example. The results are discussed and some conclusions are drawn. The theory can be applied for modal analysis of high aspect ratio composite wings and can be further extended to aeroelastic studies. |
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Keywords: | Dynamic stiffness method Free vibration Composite beams Geometrical and material coupling Wittrick-Williams algorithm |
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