Dynamic sability of rotating shaft under parametric excitation subjected to specified boundary conditions

Abstract

The dynamic stability behavior of a rotating shaft system under parametric excitation subjected to specified boundary conditions is studied theoretically and theoretical findings with the experimental results. For this theoretical analysis Finite Element Method is applied to derive the governing equation of motion. In this paper, the Ritz finite element procedure and LaGrange’s equation are employed to derive the governing equation of a rotating shaft subjected to axial compressive forces. The effects of gyroscopic moment and the static buckling load parameter on the regions of dynamic instability are studied. Application of Bolotin’s method and under the conditions of constant rotational speed, the boundaries between the regions of stability and instability are constructed. For experimental work the existing experimental setup is redesigned. Suitable End Attachments are designed and fabricated to achieve various conditions of boundary conditions for the rotating shaft.