Three-Dimensional Vibration Analysis of Rotating Laminated Composite Blades

Abstract

This work offers the first known three-dimensional (3-D) continuum vibration analysis for rotating, laminated composite blades. A cornerstone of this work is that the dynamical energies of the rotating blade are derived from a 3-D elasticity-based, truncated quadrangular pyramid model incorporating laminated orthotropicity, full geometric nonlinearity using an updated Lagrangian formulation and Coriolis acceleration terms. These analysis sophistications are included to accommodate the nonclassical directions of modern blade designs comprising thin, wide chord lifting surfaces of laminated composite construction. The Ritz method is used to minimize the dynamical energies with displacements approximated by mathematically complete polynomials satisfying the vanishing displacement conditions at the blade root section exactly. Several tables and graphs are presented which describe numerical convergence studies showing the validity of the assumed displacement polynomials used herein. Nondimensional frequency data is presented for various rotating, truncated quadrangular pyramids, serving as first approximations of practical blades employed in aircraft engines and fans. A wide scope of results explain the influence of a number of parameters coined to rotating, laminated composite blade dynamics, namely aspect ratio (a/b), chord ratio (c/b), thickness ratio (b/h), variable thickness distribution (hl/ht), blade pretwist angle (ϕo), composite fiber orientation angle (θ), and angular velocity (Ω). Additional examples are given which elucidate the significance of the linear and nonlinear kinematics used in the present 3-D formulation along with the importance of the Coriolis acceleration terms included in the analysis.