doi: 10.3850/S2010428611000080

Effects of Boundary Conditions on the Natural Frequencies and Critical Speeds of Rotating Cylindrical Shells

T. Y. Ng^a and R. E. S. Koh School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore. ^amtyng@ntu.edu.sg

ABSTRACT

In this paper, we examine the effects of boundary conditions on the vibration and critical speeds of rotating cylindrical shells. The present work is based on the Love hypothesis for classical thin shells. In addition, the effects due to the shell rotation, namely the centrifugal forces, Coriolis acceleration and initial hoop tension, have been incorporated into the formulation. A Galerkin formulation is presented, with characteristic beam functions being employed to describe the displacement field. Through this numerical procedure, the roots of the determinant of the characteristic matrix of the rotating shell system are calculated, and the natural frequencies and critical speeds can be subsequently obtained. The effects of boundary conditions on the natural frequencies of various modes of vibration of the rotating shells are first examined. Then we investigate the effects of length, axial mode number and boundary conditions, on the critical speeds of the rotating shells.

Keywords: Rotating cylindrical shell, Vibration and critical speed, Boundary conditions, Garlerkin method, Centrifugal forces, Initial hoop tension, Coriolis acceleration.

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