Vibration and stability analysis of a rotating multi-layer annular plate with a stationary load system.

Abstract

The purpose of this work is to analyze the nonlinear dynamic behavior of a rotating multi-layer annular plate with a stationary load system such as a suspension arm, a Read/Write head slider and a frictional follower load. Layer-Wise Theory based on the superposition of a global Higher Order Shear Deformation displacement field and a local linear Zig-Zag displacement field (RHOT) is used to derive the governing equations of motion via Hamilton's Principle. This Theory automatically satisfies displacement continuity at the layer interfaces and by further applications of stress continuity at the layer interfaces and traction free boundary conditions, the unknown degrees of freedom are reduced to seven regardless of the number of layers. These are two in-plane displacements, two shear rotations, a transverse displacement and two section rotations. A four-node Sector Finite Element in a Cylindrical coordinate system is developed using RHOT. Two in-plane displacements and two shear rotations which are $C\sp0$ continuous are interpolated using bilinear functions and a transverse displacement and two section rotations which are $C\sp1$ continuous are interpolated using higher order Hermitian functions. Equivalent Single Layer Theories of Kirchoff-Love Plate Theory and Mindlin-Reissner Plate Theory are also used to develop the finite elements. Comparison of numerical results using RHOT is made with Equivalent Single Layer Theories in various analyses. Effect of damping and a frictional follower load on the system stability is derived mathematically and further discussed with numerical results obtained from the finite element program developed in this work. Critical rotational speeds which correspond to the zero backward traveling waves, of a uniform varying thickness disk, a linearly varying thickness disk and a step varying thickness disk are calculated for design consideration using the State-Space method. Free vibration analysis of an Isotropic, Polar-Orthotropic and Rectilinear-Orthotropic multi-layer annular plate is carried out to extract eigenvalues and corresponding eigenmodes with the finite elements developed in this work. Stability of an Isotropic and Polar-Orthotropic laminated rotating disk is investigated by looking at the real and imaginary parts of the backward and forward traveling waves of the system when a frictional follower load is exerted on the surface of the disk. Transient response of the rotating disk, given a rotating speed, is calculated with respect to time to visualize the dynamic behavior.