A Fourier series solution for the transverse vibration of rotating beams with elastic boundary supports

Abstract

Rotating beams are usually encountered in various dynamic analyses of rotation machineries, most of the current studies are mainly focused on the classical boundary conditions. From the viewpoint of engineering practice, elastic boundary supports will be of more significance. Motivated by such limitation, a Fourier series solution for vibration analyses of a rotating hub-beam with elastic boundary restraints and centrifugal stiffening is established by solving the governing differential equation and general boundary conditions, simultaneously. For elastic restraints at both ends, two types of boundary springs against translation and rotation are introduced to simulate the general boundary supports. Fourier series supplemented by boundary smoothed terms is constructed for the rotating beam displacement expression. Harmonic balance principle is employed to formulate the system characteristic matrix, from which all the modal information of rotating beam can be derived by solving a standard eigen-value problem. Numerical examples are then presented to verify the correctness and effectiveness of the developed model. The influence of boundary restraining stiffness and rotation speed on modal characteristics of rotating beam are investigated and addressed. The analytical solution established in this work can be used as the benchmark for other solution development, and provide an efficient tool for the parametric studies and/or optimization of dynamic characteristics of rotating beam structure, especially with complicated boundary conditions.