Analysis of a rotating multi-layer annular plate modeled via layerwise zig-zag theory: Free vibration and transient analysis

Abstract

The purpose of this work is to analyze the free vibration and transient dynamic response of a rotating multi-layer annular plate. Layerwise zig-zag theory (LWZZ) based on the superposition of a global higher-order shear deformation displacement field and a local linear zig-zag displacement field (RHOT) is incorporated in the derivation of the governing equations of motion via Hamilton's principle. LWZZ automatically satisfies displacement continuity at the layer interfaces and by further application 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 0 continuous are interpolated using bilinear functions and a transverse displacement and two section rotations which are C 1 continuous are interpolated using higher-order hermitian functions. Equivalent single layer theories (Kirchhoff-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. Free vibration and transient analysis are carried out to extract eigenvalues and corresponding eigenmodes and investigate the dynamic behavior of a multi-layer annular plate.