Incorporating uncertainties in the aeroelastic analysis increases the confidence levels of computational predictions and reduces the need for validation with experimental or flight test data. Helicopter rotor blades, which play a dominant role in the overall vehicle performance, are routinely made of composites. The material properties of composites are uncertain because of the variations in manufacturing process and other effects while in service, maintenance and storage. Though nominal values are listed, they are seldom accurate. In this thesis, the effect of uncertainty in composite material properties on the computational predictions of cross-sectional properties, natural frequencies, blade tip deflections, vibratory loads and aeroelastic stability of a four-bladed composite helicopter rotor is studied. The effect of material uncertainty is studied with the composite rotor blades modeled as components of soft-inplane as well as stiff-inplane hingeless helicopter rotors. Aeroelastic analysis based on finite elements in space and time is used to evaluate the helicopter rotor blade response in hover and forward flight. Uncertainty analysis is performed with direct Monte Carlo simulations based on a sufficient number of random samples of material properties. It is found that the cross-sectional stiffness parameters and natural frequencies of rotor blades show considerable scatter from their baseline predictions. The uncertainty impact on the rotating natural frequencies depends on the level of centrifugal stiffening of each mode. The propagation of material uncertainty into aeroelastic response causes large deviations from the baseline predictions. The magnitudes of 4/rev vibratory loads show deviations of 10 to 600 percent from their baseline predictions. The aeroelastic stability in hover and forward flight conditions also show considerable uncertainty in the predictions. In addition to the effects of material uncertainty, various factors influencing the propagation of material uncertainty are studied with the first-order based reliability methods. The numerical results have shown the need to consider the uncertainties in the helicopter aeroelastic analysis for reliable computational predictions. Uncertainty quantification using direct Monte Carlo simulation is accurate but computationally expensive. The application of response surface methodologies to reduce the computational cost of uncertainty analysis is studied. Response surface approximations of aeroelastic outputs are developed in terms of the composite material properties. Monte Carlo simulations are then performed using these computationally less expensive response surface models. The results of this study show that the metamodeling techniques can effectively reduce the computational cost of uncertainty analysis of composite rotor blades. In the last part of the thesis, an aeroelastic optimization method to minimize the vibration level is developed with due consideration to material uncertainty. Second-order polynomial response surfaces are used to approximate the objective function which smooths out the local minima or numerical noise in the design space. The aeroelastic optimization is carried out with the nominal values of composite material properties and the performance of final design is found to be optimum even for the perturbed values of material properties.

This dissertation presents shape and structural optimization studies on flapping wings for micro air vehicles. The design space of the optimization includes the wing planform and the structural properties that are relevant to the wing model being analyzed. The planform design is parameterized using a novel technique called modified Zimmerman, which extends the concept of Zimmerman planforms to include four ellipses rather than two. Three wing types are considered: rigid, plate-like deformable, and membrane. The rigid wing requires no structural design variables. The structural design variables for the plate-like wing are the thickness distribution polynomial coefficients. The structural variables for the membrane wing control the in-plane distributed forces which modulate the structural deformation of the wing. The rigid wing optimization is performed using the modified Zimmerman method to describe the wing. A quasi-steady aerodynamics model is used to calculate the thrust and input power required during the flapping cycle. An assumed inflow model is derived based on lifting-line theory and is used to better approximate the effects of the induced drag on the wing. A multi-objective optimization approach is used since more than one aspect is considered in flapping wing design. The the epsilon-constraint approach is used to calculate the Pareto optimal solutions that maximize the cycle-average thrust while minimizing the peak input power and the wing mass. An aeroelastic model is derived to calculate the aerodynamic performance and the structural response of the deformable wings. A linearized unsteady vortex lattice method is tightly coupled to a linear finite element model. The model is cost effective and the steady-state solution is solved by inverting a matrix. The aeroelastic model is used to maximize the thrust produced over one flapping cycle while minimizing the input power. / Ph. D.

Helicopter aeroelastic analysis is highly complex and multidisciplinary in nature; the flexibility of main rotor blades is coupled with aerodynamics, dynamics and control systems. A key component of an aeroelastic analysis is the vehicle trim procedure. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which cause the six steady forces and moments about the helicopter center of gravity to be zero. Trim simulates steady level flight of the helicopter. The trim equations are six nonlinear equations which depend on blade response and aerodynamic forcing through finite element analysis. Simulating the behavior of the helicopter in flight requires the solution of this system of nonlinear algebraic equations with unknowns being pilot controls and vehicle attitude angles. The nonlinear solution procedure is prone to slow convergence and occasional divergence causing problems in optimization and stochastic simulation studies. In this thesis, an attempt is made to efficiently solve the nonlinear equations involved in helicopter trim. Typically, nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation. Helicopter aeroelasticity involves the solution of systems of nonlinear equations in a computationally expensive environment. The Newton method is typically used for the solution of these equations. Due to the expensive nature of each aeroelastic analysis iteration, Jacobian calculation at each iteration for the Newton method is not feasible for the trim problems. Thus, the Jacobian is calculated only once about the initial trim estimate and held constant thereafter. However, Jacobian modifications and updates can improve the performance of the Newton method. A comparative study is done in this thesis by incorporating different Jacobian update methods and selecting appropriate damping schemes for solving the nonlinear equations in helicopter trim. A modified Newton method with varying damping factor, Broyden rank-1 update and BFGS rank-2 update are explored using the Jacobian calculated at the initial guess. An efficient and robust approach for solving the strongly coupled nonlinear equations in helicopter trim based on the modified Newton method is developed. An appropriate initial estimate of the trim state is needed for successful helicopter trim. Typically, a guess from a simpler physical model such as a rigid blade analysis is used. However, it is interesting to study the impact of other starting points on the helicopter trim problem. In this work, an attempt is made to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of trim solution in the aeroelastic analysis of helicopter are proposed.

This research investigates on-blade partial span active plain trailing edge flaps (TEFs)with an aim to alleviate the helicopter vibrations. Among all the available smart materials, piezoelectric stack actuator(PEA)has shown its strong candidature for full scale rotor systems. Although, PEAs are quite robust in operation, however, they exhibit rate dependent hysteresis phenomenon and can generate only very small displacements. Dynamic hysteresis is a complex phenomenon which, if not modeled, can lead to drift in the vibration predictions. In this research, a comprehensive experimental analysis is performed on a commercially available piezostack actuator, APA-500L, which is well suited for full scale applications. Rate dependent hysteresis loops are obtained for helicopter operational frequencies. Nonlinear rate-dependent hysteresis loops are modeled using conic section approach and the results are validated with experimental data. Dynamic hysteresis exhibited by the PEA is further cascaded with the helicopter aeroelastic analysis and its effect on helicopter vibration predictions is investigated. PEAs generate high force but are limited by small translational motions. A linear to rotary motion amplification mechanism is required to actuate the TEF for vibration alleviation. A smart flap is designed and developed using computer-aided-design models. A rotor blade test section is fabricated and a lever-fulcrum mechanism (AM-1) is developed for a feasibility study. Smart flap actuation is demonstrated on the rotor blade test section. The conventional motion amplification devices contain several linkages, which are potential sites for structural failure. A novel pinned-pinned post-buckled beam linear-to-rotary motion amplifier (AM-2) is designed and developed to actuate the flaps. A new design of linear-to-linear amplification mechanism (LX-4) is developed and is employed in conjunction with AM-2 to increase the flap angles by an order of magnitude. An analytical model is developed using Mathieu-Hill type differential equations. Static and dynamic tests are conducted on a scaled flap model. Helicopter aeroelastic simulations show substantial reduction in hub loads using AM-2 mechanism. To further enhance the flap angles, an optimization study is performed and optimal beam dimensions are obtained. A new technique is also proposed to actively bias the flaps for both upward and downward motion. Critical flap design parameters, such as flap span, flap chord and flap location influences the flap power requirement and vibration objective function significantly. A comprehensive parametric investigation is performed to obtain the best design of TEFs at various advance ratios. Although, parametric study equips the designer with vital information about various critical system parameters, however, it is a computationally expensive exercise especially when used with large comprehensive helicopter aero elastic codes. A formal optimization procedure is employed to obtain the optimal flap design and location. Surrogate models are developed using design of experiments based on response surface methodology. Two new orthogonal arrays are proposed to construct the second order polynomial response surfaces. Pareto analysis is employed in conjunction with a newly developed computationally efficient evolutionary multi-objective bat algorithm. Optimal flap design and flap locations for dual trailing edge flaps are obtained for mutually conflicting objectives of minimum vibration levels and minimum power requirement to actuate the flaps.