An improved numerical scheme for characterizing dynamic behavior of high-speed rotating elastic beam structures

Abstract

The demand for designing high-speed turbomachinery has led to intensive research in dynamic modeling of rotating elastic mechanisms in recent years. Such a demand in design setting can be addressed more effectively with the development of a more efficient computational scheme. In this paper we present an improved numerical method with three new features. First of all, the time separation concept is introduced to allow time independent terms being computed separately and assembled with time dependent terms in each time marching cycle to form global system equations. Second, the Timoshenko beam with nonlinear geometric stiffness is modeled with exact tangent matrix as opposed to conventional pseudo-tangent matrix approximation. Third, the computational scheme is implemented in homogeneous coordinates that provide a more natural and efficient vector representation. Kane's classic rotating beam problem is used to test for accuracy and computer time. The result matches very well with Kane's solution. However, the computer time needed for the present approach is reduced by more than 70%.