Jonathan E. Cooper

Design of Composite Wings Including Uncertainties: A Probabilistic Approach

A probabilistic method is developed to optimize the design of an idealized composite wing through consideration of the uncertainties in the material properties, fiber-direction angle, and ply thickness. The polynomial chaos expansion method is used to predict the mean, variance, and probability density function of the flutter speed, making use of an efficient Latin hypercube sampling technique. One-dimensional, two-dimensional, and three-dimensional polynomial chaos expansions are introduced into the probabilistic flutter model for different combinations of material, fiber-direction-angle, and ply-thickness uncertainties. The results are compared with Monte Carlo simulation and it is found that the probability density functions obtained using second- and third-order polynomial chaos expansion models compare well but require much less computation. A reliability criterion is defined, indicating the probability of failure due to flutter, and is used to determine successfully the optimal robust design of the composite wing.

Optimization of Aeroelastic Composite Structures using Evolutionary Algorithms

The flutter/divergence speed of a simple rectangular composite wing is maximized through the use of different ply orientations. Four different biologically inspired optimization algorithms (binary genetic algorithm, continuous genetic algorithm, particle swarm optimization, and ant colony optimization) and a simple meta-modeling approach are employed statistically on the same problem set. In terms of the best flutter speed, it was found that similar results were obtained using all of the methods, although the continuous methods gave better answers than the discrete methods. When the results were considered in terms of the statistical variation between different solutions, ant colony optimization gave estimates with much less scatter.

Receptance-Based Active Aeroelastic Control Using Multiple Control Surfaces

Design of next generation aircraft/sensorcraft for improved performance, such as gust load alleviation towards aircraft stability and flutter suppression during its flight operation, may necessitate wing technology that can be controlled and manipulated by active means. Moreover, in recent years the efforts are underway to realize “Fly by Feel” concepts, which are aimed in utilizing on-board sensors (embedded) and actuators (control surfaces) of the aircraft towards the design of active control system for desired performance. This paper presents active control strategies for wings having multiple control surfaces, which are purely based upon in-flight receptance (measured) data. The proposed receptance based control approach has several advantages over the traditional state-space based control because it circumvents approximation errors in reduced order modeling; it captures the true interaction between structure and aerodynamic loads; and it requires modest size of matrices (depending upon the available number of sensors and actuators) for control gain computations. In this study, multi-input state and output feedback control strategies for active aeroelastic control using the method of receptances is developed. The control gains are computed for the extension of flutter boundaries via pole placement. At first, by using numerical receptances obtained from the aeroelastic model of a flexible wing having multiple control surfaces, the proposed methodology is demonstrated. In order to test and demonstrate the receptance method for more complex aircraft geometries, configurations and aerodynamic loading conditions, numerical receptances from Finite Element models of aircraft wings with multiple control surfaces were extracted for the proposed control design. Presented studies and control approach may become the basis for optimal placement and sizing of control surfaces in a given wing section for active aeroelactic control and enhanced flight performance.

Optimization of Tow-Steered Composite Wing Laminates for Aeroelastic Tailoring

Tow-steered composites are optimized for use in tailoring the aeroelastic behavior of a simple two-dimensional composite wing, with particular emphasis on improving both flutter/divergence airspeeds and gust loads. Symmetric layups are considered where the fibers vary in orientation along the wingspan and chord. Tow-steered laminates were found to increase the instability airspeed by up to 7% compared with optimized straight-fiber laminates and by 13% compared with optimized laminates with standard (0/±45/90  deg) plies. Tow-steered laminates were also found to reduce the peak wing root gust loads (up to 52%) and the correlated gust loads (up to 24%). The lowest gust loads were reached with higher order nonlinear fiber angle variations when either all plies were optimized or when two-dimensional fiber angle variations were used. Optimization strategies that allowed the fiber angles to vary freely in each ply generally performed better than optimizations based on the rotation of (0/±45/90  deg)-ply stacks ...

Identification of Multi-Degree of Freedom Systems With Nonproportional Damping Using the Resonant Decay Method

This paper describes an extension of the force appropriation approach which permits the identification of the modal mass, damping and stiffness matrices of nonproportionally damped systems using multiple exciters. Appropriated excitation bursts are applied to the system at each natural frequency, followed by a regression analysis in modal space. The approach is illustrated on a simulated model of a plate with discrete dampers positioned to introduce significant damping nonproportionality. The influence of out-of-band flexible and rigid body modes, imperfect appropriation, measurement noise and impure mode shapes is considered. The method is shown to provide adequate estimates of the modal damping matrix.

Design of a Morphing Wing tip

An initial design of a morphing wingtip for a regional jet aircraft is developed and evaluated. The adaptive wingtip concept is based upon a chiral-type internal structure, enabling controlled cant angle orientation, camber, and twist throughout the flight envelope. A baseline turbofan aircraft configuration model is used as the benchmark to assess the device. Computational fluid dynamics based aerodynamics are used to evaluate the required design configurations for the device at different points across the flight envelope in terms of lift/drag and bending moment distribution along the span, complemented by panel-method-based gust load computations. Detailed studies are performed to show how the chiral structure can facilitate the required shape changes in twist, camber, and cant. Actuator requirements and limitations are assessed, along with an evaluation of the aerodynamic gains from the inclusion of the device versus power and weight penalties. For a typical mission, it was found that savings of around...

Aeroelastic analysis through linear and non-linear methods: a summary of flutter prediction in the PUMA DARP

This paper presents a comparison of linear and non-linear methods for the analysis of aeroelastic behaviour and flutter boundary prediction. The methods in question include NASTRAN and ZAERO, based on linear aerodynamics, and the non-linear coupled CFD-CSD methods RANSMB and PMB, developed at the Universities of Bristol and Glasgow respectively. The test cases used for this comparison are the MDO and AGARD 445.6 weakened wing. In general, it was found that the non-linear methods demonstrate excellent agreement with respect to pressure distributions, deflections, dynamic behaviour, and flutter boundary locations for both cases. This is in contrast to previous studies involving similar methods, where notable differences across the MDO span were found, and is taken to imply good performance of the CFD-CSD interpolation schemes employed here. While the linear methods produce similar flutter boundaries to the coupled codes for the aerodynamically simple AGARD 445.6 wing, results for the transonic ‘rooftop’ MDO wing design did not agree as well.

Aeroelastic Tailoring of a Representative Wing Box Using Tow-Steered Composites

There has been an increasing effort to improve aircraft performance through using composite tailored structures, not only to reduce weight, but to exploit beneficial aeroelastic couplings. Recent work has considered the ability to tow steer the composite plies to achieve better performance. Here, the potential wing weight savings of a full-size aeroelastically tailored wing are assessed by optimizing the properties of a three-dimensional finite element model using straight-fiber and tow-steered composites in the skins. One- and two-dimensional thickness and laminate rotation angle variations are considered as design freedoms. The jig shape is updated to maintain a fixed 1g flight shape, and optimization constraints are implemented on the strains and buckling loads due to maneuver and dynamic gust loads, flutter stability, and control effectiveness for different flight conditions. The optimal main fiber direction is rotated forward of the front spar direction in the outer wing, leading to extension-shear c...

Feedback Linearisation for Nonlinear Vibration Problems

Feedback linearisation is a well-known technique in the controls community but has not been widely taken up in the vibrations community. It has the advantage of linearising nonlinear system models, thereby enabling the avoidance of the complicated mathematics associated with nonlinear problems. A particular and common class of problems is considered, where the nonlinearity is present in a system parameter and a formulation in terms of the usual second-order matrix differential equation is presented. The classical texts all cast the feedback linearisation problem in first-order form, requiring repeated differentiation of the output, usually presented in the Lie algebra notation. This becomes unnecessary when using second-order matrix equations of the problem class considered herein. Analysis is presented for the general multidegree of freedom system for those cases when a full set of sensors and actuators is available at every degree of freedom and when the number of sensors and actuators is fewer than the number of degrees of freedom. Adaptive feedback linearisation is used to address the problem of nonlinearity that is not known precisely. The theory is illustrated by means of a three-degree-of-freedom nonlinear aeroelastic model, with results demonstrating the effectiveness of the method in suppressing flutter.

Experimental Nonlinear Static Deflections of a Subscale Joined Wing

Vanessa L. Bond∗ Air Force Operational Test and Evaluation Center, Edwards Air Force Base, California 93523 Robert A. Canfield Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Jonathan E. Cooper University of Liverpool, Liverpool, England L69 3GH, United Kingdom and Maxwell Blair United States Air Force Research Laboratory, Wright–Patterson Air Force Base, Ohio 45433