A new reduced-order design synthesis technology has been developed for vibration response and flutter control of cold-stream, high-bypass ratio, shroudless, aeroengine fans. To simplify the design synthesis (optimization) of the fan, a significant order reduction of the mechanical response and stiffness-shape design synthesis has been achieved. The assumed cyclic symmetric baseline fan is modeled as a cascade of tuned, shroudless, arbitrarily shaped, wide-chord laminated composite blades, each with a reduced order of degrees of freedom using a three-dimensional (3D) elasticity spectral-based energy model (McGee et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis, ASME J. Turbomach., in press; Fang et al., 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., in press). The uniqueness of the mechanical analysis is that the composite fan was modeled as a “meshless” continuum, consisting of nodal point data to describe the arbitrary volume. A stationary value of energy within the arbitrarily shaped composite fan annulus was achieved using an extended spectral-based Ritz procedure to obtain the dynamical equations of motion for 3D free vibration response of a rotating composite high-bypass fan. No additional kinematical constraints (as in beam, plate, or shell theories) were utilized in the 3D elasticity-based energy formulation. The convergence accuracy of the spectral-based 3D free vibration response predictions was nearly one percent upper-bounds on the exact mechanical response of the baseline composite fan, particularly in the lowest five modes studied closely in this work, as typically seen with spectral-based Ritz procedures employed in the analysis. The spectral-based 3D predictions was validated against those predicted using a general purpose finite element technology widely used by industry. In off-design operation, the frequency margins of the lower flex-torsion modes of a fan may be dangerously close to integral-order resonant and empirical stall flutter boundaries. For a given baseline composite fan, it is proposed that to reduce the likelihood of resonant response and flutter on a Campbell diagram, design analysts can efficiently unite the newly developed reduced-order 3D spectral-based energy reanalysis within a novel reduced-order spectral-based Kuhn–Tucker optimality design synthesis procedure to fairly accurately restructure the Campbell diagram of a composite high-bypass ratio fan using stiffness optimization (by means of proper choices of angle-ply orientations of the blade laminates) and mass-balancing (shape) optimization (by way of blade thickness variation tuning of the lower aerodynamic loading portion of the blades between the dovetail root section and the midradial height section of the composite fan annulus). Fan design optima is summarized that (1) achieves multiple frequency margins and satisfies multiple empirical stall flutter constraints, (2) controls the twist-flex vibratory response in the lowest (fundamental) mode, and (3) ensures the mechanical strength integrity of the optimized angle-ply lay-up under steady centrifugal tension and gas bending stresses. Baseline and optimally restructured Campbell diagrams and design sensitivity calculations are presented, comparing optimum solution accuracy and validity of the proposed reduced-order spectral-based design synthesis technology against optimum solutions generated from open-source nonlinear mathematical programming software (i.e., NASA’s general-purpose sequential unconstrained minimization technique, Newsumt-A) (Miura and Schmit, Jr., 1979, ”NEWSUMT–A, Fortran Program for Inequality Constrained Function Minimization—Users Guide,“ NASA CR-159070). Design histories of fan stiffness and mass balancing (or shape) along with nondimensional constraints (i.e., frequency margins, reduced frequencies, twist-flex vibratory response, first-ply failure principal stress limits, and dovetail-to-midblade height thickness distribution) show that a proper implementation of fan stiffness tailoring (via symmetric angle-ply orientations) and mass-balancing (thickness) optimization of the fan assembly produces a feasible Campbell diagram that satisfies all design goals. An off-design analysis of the optimized fan shows little sensitivity to twist-flex coupling response and flutter with respect to small variability or errors in optimum design construction. Industry manufacturing processes may introduce these small errors known as angle-ply laminate construction misalignments (Graham and Guentert, 1965, “Compressor Stall and Blade Vibration,” Aerodynamic Design of Axial-Flow Compressors, Chap. XI, NASA SP-36; Meher-Hornji, 1995, “Blading Vibration and Failures in Gas Turbines, Part A: Blading Dynamics and the Operating Environment,” ASME Paper 95-GT-418; Petrov et al., 2002, “A New Method for Dynamic Analysis of Mistuned Bladed Disks Based on the Exact Relationship Between Tuned and Mistuned Systems,” ASME J. Eng. Gas Turbines Power, 124(3), pp. 586–597; Wei and Pierre, 1990, “Statistical Analysis of the Forced Response of Mistuned Cyclic Assemblies,” ASME J. Eng. Gas Turbines Power, 28(5), pp. 861–868; Wisler, 1988, “Advanced Compressor and Fan Systems,” GE Aircraft Engines, Cincinnati, Ohio (also 1986 Lecture to ASME Turbomachinery Institute, Ames Iowa)).
Dynamic Response of a Thick Piezoelectric Circular Cylindrical Panel: An Exact Solution