An Improved Fourier Series Method for the Free Vibration Analysis of the Three-Dimensional Coupled Beams

This paper presents a free vibration analysis of three-dimensional coupled beams with arbitrary coupling angle using an improved Fourier method. The displacement and rotation of the coupled beams are represented by the improved Fourier series which consisted of Fourier cosine series and closed-form auxiliary functions. The coupling and boundary conditions are accomplished by setting coupling and boundary springs and assigning corresponding stiffness values to the springs. Modal parameters are determined through the application of Rayleigh-Ritz procedure to the system energy formulation. The accuracy and convergence of the present method are demonstrated by finite element method (FEM) result. Investigation on vibration of the propulsion shafting structure shows the extensive applicability of present method. The studies on the vibration suppression devices are also reported.