Vibrations of two beams elastically coupled together at an arbitrary angle

A general analytical method is developed for the vibrations of two beams coupled together at an arbitrary angle. The stiffness of a joint can take any value from zero to infinity to better model many real-world coupling conditions. Both flexural and longitudinal waves are included to account for the cross-coupling effects at the junctions. Each displacement component is here invariantly expressed, regardless of the coupling or boundary conditions, as a Fourier series supplemented by several closed-form functions to ensure the uniform convergence of the series expansions. Examples are presented to compare the current solution with finite element and experimental results.