Abstract
The exact dynamic stiffness matrix is derived for a straight and uniform beam element whose elastic and inertial axes are not coincident. Elementary bending-torsion beam theory is used, and bending translation is restricted to one direction. The element matrix can be used in the dynamic stiffness method for calculation of exact natural frequencies, mode shapes, and generalized masses for planar assemblages of connected bending-torsion beams. The dynamic stiffness method is outlined, and details pertinent to the bending-torsion beam element are given. An example of a three-beam assemblage representing an airplane wing is posed, and exact numerical solutions are tabulated for natural frequencies and generalized masses. Solutions calculated by the finite element method are also tabulated for comparison.
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