Air Vehicles Directorate Research Articles

Enhancement of a Flapping Wing Using Path and Dynamic Topology Optimization

AR = aspect ratio a = dimensionless length from the leading edge to the pivot point b = design variable vector bi = design variable in the ith element b k = design variable vector at the cycle number k b k i = design variable at the cycle number k in the ith element b k = design variable vector at the cycle number k b k i = design variable at the cycle number k in the ith element b 0 = initial design variable vector bmin = lower bound of the design variable C b = viscous damping matrix CD = drag coefficient CD = time-averaged drag coefficient CL = lift coefficient CL = time-averaged lift coefficient CM = pitch moment coefficient CT = thrust coefficient CT = time-averaged thrust coefficient c = chord, m E = Young’s modulus, Gpa Ei = Young’s modulus of the ith element E0 = initial Young’s modulus Fx = x component of the resulting aerodynamics force acting on the airfoil, N Fy = y component of the resulting aerodynamics force acting on the airfoil, N f = frequency, Hz f = static load vector f t = dynamic load vector feq s = equivalent static loads vector f k eq s = equivalent static loads vector at the cycle number k fz = compliance h = reduced plunging amplitude with respect to the chord K b = stiffness matrix k = reduced frequency Ma = Mach number M b = mass matrix Re = Reynolds number S = reference area St = Strouhal number T = period, s u = far-field flow velocity, m=s V = total volume of the structure ve = volume of each element z s = static displacement vector z t = dynamic displacement vector 1 = specified value of density 2 = percent of the total design variable 3 = density value of design update = propulsive efficiency = angle between the chord and the far-field flow speed direction Received 5 August 2010; revision received 22 March 2011; accepted for publication July 2011. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/11 and $10.00 in correspondence with the CCC. ∗Graduate Student, Department of Mechanical Engineering. Postdoctoral Fellow, Department of Mechanical Engineering. Member AIAA. Professor, Department of Mechanical Engineering; gjpark@ hanyang.ac.kr. Senior Member AIAA (Corresponding Author). Professor, Department of Mechanical Engineering. Aerospace Engineer, Air Vehicles Directorate. Member AIAA. AIAA JOURNAL Vol. 49, No. 12, December 2011

Design, Fabrication, and Testing of a Scaled Wind Tunnel Model for the Smart Wing Project

Building on the research performed during the DARPA/AFRL/NASA Smart Wing Phase 1 program (Kudva, J.N. et al. (July 1999). Overview of the DARPA/AFRL/NASA Smart Wing Program, SPIE Symposium on Smart Structures and Materials, Newport Beach, CA, Vol. 3674, pp. 230 6; Martin, C.A. et al. (1999). Smart Materials and Structures Smart Wing Phase 1 Final Report, AFRL-ML-WP-TR-1999-4162, Air Vehicles Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH.) sought to improve vehicle aerodynamic efficiency using control surfaces actuated by smart materials, the goal of the Phase 2 effort was to develop larger scale, smart hingeless control surfaces capable of high-rate actuation and quantify their performance benefits at test conditions representative of operational flight environments. To achieve this goal, a 30-percent geometric scale, full-span wind tunnel model of a proposed Northrop Grumman Corporation (NGC) Uninhabited Combat Air Vehicle (UCAV) was designed and tested. The model incorporated conventional, hinged control surfaces on the left side and smart, hingeless control surfaces on the right to allow incremental aerodynamic performance comparisons; including lift increment due to unit control surface deflection (CL), and roll moment due to unit control surface deflection (Cld). This paper describes the design, fabrication, system integration, and ground test results of the Smart Wing Phase 2 model. Topics that are covered include: (1) wind tunnel model selection; (2) analysis and design procedure; (3) smart control surface integration; (4) model instrumentation; and (5) static load and Ground Vibration Test (GVT) results and correlation.

Multicriteria Optimization for Design of Structures with Active Control

This paper describes a method to design a structure and control system simultaneously using a multiobjective optimization approach based on global criteria. The control system was based on a modified linear quadratic regulator (LQR) with bounds placed on the control forces to simulate limitations of real actuators. In the design of the control system, the state space equations were integrated using a Runge-Kutta method for a specified initial boundary condition. The structural weight, the weight of the actuators, the time required to suppress an initial disturbance, and the performance index were considered as different objective functions to be optimized. The design variables were the bounds on the maximum values of the control force, the cross­ sectional areas of the structural elements, and elements of the weighting matrices in the control design. As an example to illustrate the application of the approach, a box beam idealized by rod elements was used. The actuators and sensors were collocated and assumed to be embedded in structural elements. The results are presented for optimum designs obtained by changing different parameters in the definition of the global criteria. During the past several years, researchers in the field of optimum design have focused on developing algorithms to de­ sign structure in the multidisciplinary domain so as to take advantage of the interaction between different disciplines. The principal goal of this approach was to achieve an optimum design satisfying distinct requirements of various disciplines simultaneously so that the overall system would have peak performance. In this paper, the two disciplines considered are structural design and control design. The traditional approach to the design of a controlled structural system is to design the structure first, by satisfying its requirements, and then to de­ sign the control system. The structure is designed with con­ straints on weight, allowable stresses in the elements, general instability, frequency distribution, etc. When the selection of the geometry, cross-sectional areas of the members, and ma­ terial are completed for a structure, its structural frequencies and vibration modes become input to the control design. Be­ cause the cross-sectional areas of the structural elements influ­ ence the structural frequencies and the distribution of frequen­ cies affects the control design, it is appropriate to integrate these two disciplines in the design algorithm and determine optimum values of the design variables in both systems. In the design of actively controlled structures, most often the objective function is the weight of the structure wherein constraints are imposed on the structural and control response functions, such as structural frequencies, closed-loop damping, control performance defined by the linear quadratic control cost, closed-loop frequency distribution, efficiency require­ ments, and robustness parameters. Hale et aI. (1985) consid­ ered minimizing the sum of the weight of the structure and the quadratic control cost to satisfy specific constraints with structural parameters as the design variables. Haftka et al. (1985) studied the effect of structural changes on the design of the structure and control system. Rew et aI. (1987) used multiple optimization criteria for designing the structural con­ trol system. The problem of integrated design was solved by Khot (1988), using analytical expressions for the sensitivities and imposing constraints on the closed-loop damping and fre- 'Res. Aerosp. Engr., Struct. Div., Air Vehicles Directorate, Air Force Res. Lab., Wright-Patterson AFB, OH 45433-7542.