Vibration Analysis of Roll-Tensioned Disks Using Finite Element Method. Efficient Estimation Methods of Initial Stress Stiffness Matrices and Natural Frequencies.

Abstract

This paper proposes an efficient method for estimating natural frequencies of roll-tensioned disks. In addition, initial stress stiffness matrices necessary for calculating natural frequencies are efficiently estimated. The proposed method based on SDM (Structural Dynamics Modification) technique estimates the natural frequencies after roll-tensioning from the natural frequencies and mode shapes before roll-tensioning and initial stress stiffness matrices by roll-tensioning. The examples show that when small rolling load is applied, a one-dimensional eigenvalue problem produces the accurate estimation. When the estimation errors by the one-dimensional eigenvalue problem are large, the coupled eigenvalue problem must be solved. In this case, a small-sized eigenvalue problem is sufficient because the mode shapes after roll-tensioning are expressed by the mode shapes before roll-tensioning with the same number of nodal diameters and the different number of nodal circles.