Three-dimensional vibration analysis of rotating pre-twisted cylindrical isotropic and functionally graded shell panels

Abstract

A weak-form formulation for three-dimensional vibration analysis of rotating pre-twisted cylindrical isotropic and functionally graded (FG) shell panels is first developed. The present formulation is established with the three-dimensional (3-D) elasticity shell theory and Carrera unified formulation, which enables the expression of the traditional and high-order shell theories into a unified form. The potential energy stored in the boundary is transformed into a quantification form by using the penalty method. The 3-D coupled displacement fields are constructed by a modified version of the Fourier series with several additional boundary smoothed functions to ensure the exact description of displacement and stress fields. The complete second-order nonlinear strain terms in the frame of the curvilinear coordinate system are presented to take into consideration the initial centrifugal stresses that are exactly determined with a separate static deflection analysis. Numerical verifications and comparisons of the vibration results with the 3-D finite element method (FEM) show the capabilities of the developed high-order hierarchical model to accurately predict the frequency results and mode shapes of rotating pre-twisted cylindrical isotropic and FG shell panels. Parametric studies are then carried out to investigate the effect of the rotating speed, presetting angle, pre-twisted angle, subtended angle and power-law exponent on the dynamic characteristics of the pre-twisted cylindrical shell panels. It is expected that the present formulation for the rotating pre-twisted cylindrical shell panels will serve as benchmarks to assess the accuracy of other numerical and analytical models.