Coupled bending–torsional dynamic stiffness matrix for axially loaded beam elements

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Abstract
Analytical expressions for the coupled bending–torsional dynamic stiffness matrix elements of an axially loaded uniform beam element are derived in an exact sense by solving the governing differential equations of motion of the beam. The influence of axial force on the coupled bending–torsional frequencies of a cantilever and hinged–hinged beam of thin‐walled section is demonstrated by numerical results. Application of the developed theory includes coupled bending–torsional frequency and mode calculations of helicopter, turbine and propeller blades, plane and space frames, and grillages consisting of axially loaded beam elements with non‐coincident mass centre and shear centre.

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