Sophisticated finite strip for vibration analysis of a rotating cylindrical shell

In this article a two-node finite strip with eight degrees of freedom for free vibration analysis of pre-stressed rotating cylindrical shells is formulated. The circumferential mode shape profiles are described exactly using trigonometric functions. The axial mode shape profiles are approximated by bar and beam shape functions for membrane and bending displacements, respectively. In this way a semi-analytical formulation is facilitated so that the discretization is required only in the axial direction. The developed finite strip is validated by comparisons with analytical results. An excellent agreement is observed both for stationary and rotating shells.

Vibration Analysis of Rotating Cylindrical Shells

To simplify the model of rotating cylindrical shell, the static forces are neglected and the vibration equations are established. Transfer matrix method is used to solve the equations and the example shows that the simplified model has little effect on the result. So the simplified model can be used in complex structures such as multilayer and multidiameter shell.

Blocking in the Rotating Axial Flow in a Corotating Flexible Shell

By coupling the Donnell–Mushtari shell equations to an analytical inviscid fluid solution, the linear dynamics of a rotating cylindrical shell with a corotating axial fluid flow is studied. Previously discovered mathematical singularities in the flow solution are explained here by the physical phenomenon of blocking. From a reference frame moving with the traveling waves in the shell wall, the flow is identical to the flow in a rigid varicose tube. When the ratio of rotation rate to flow velocity approaches a critical value, the phenomenon of blocking creates a stagnation region between the humps of the wall. Since the linear model cannot account for this phenomenon, the solution blows up.

VIBRATION ANALYSIS OF A PRESTRESSED ROTATING CYLINDRICAL SHELL UNDER STATIONARY POINT LOAD

The vibration responses of a pre-stressed rotating cylindrical shell under stationary constant point load are analyzed by numerical method. The cylindrical shell is modeled by a nine-node super-parametric finite element which includes the effects of transverse shear deformation, axial deformation and rotary inertia. The geometric nonlinearity due to large deformation is also considered in the model. The numerical integer method is applied to attain the vibration responses. The effects of initial axial stress and rotating speed on the vibration of cylindrical shell are investigated in detail.