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ItemPERFORMANCE ADVANTAGES AND RESONANCE ANALYSIS OF A VARIABLE SPEED ROTOR USING GEOMETRICALLY EXACT BEAM FORMULATIONS(Georgia Institute of Technology, 2021-12-15) Chandrasekaran, RuthvikThe efficiency and operating envelope of a rotorcraft is constrained by the speed of the rotor. Most of the helicopters operate at a constant rotor speed. Varying the speed of the rotor based on the operating condition could significantly improve the rotor performance. In this study, a hingeless rotor model with elastic blades is built in Dymore to study various aspects of Variable Speed Rotor (VSR) technology. The rotor blades are modeled as one-dimensional beams using state of the art beam theory known as geometrically exact beam theory. An unsteady aerodynamics model with dynamic stall and finite-state dynamic inflow is used to obtain the aerodynamic loads acting on the rotor. A wind tunnel trim procedure is adopted to trim the rotor for a given thrust, roll and pitch moment. An auto-pilot controller is used to trim the rotor during time marching based on the wind tunnel trim values. The rotor model and trim procedure is validated using results from literature. The power savings that can be achieved at various advance ratios by varying the speed of the rotor is evaluated. However, varying the rotor speed leads to vibration issues as the rotor passes through the resonance regions. In this region, the rotor blade's natural frequency coincides with the multiple of rotor's operating frequency. This leads to an increase in vibratory loads. All the resonance points are identified from the fan plot of the rotor blade. It is observed that the lead-lag moment at the blade root increases significantly compared to the nominal value during lag resonance. It is also observed that the flap and torsional moments increase during lag resonance. Transition dynamics of the rotor blade for different operating conditions were analyzed. Load reduction studies during resonance were carried out by changing the transition times and blade properties. The longer the rotor took to traverse a resonance region, greater were the resonance loads. Increasing the structural damping was a very effective way of mitigating resonance loads. An active system called as the Anti-Resonance System (ARS) was conceptualized and modeled in Dymore. The ARS system was able to effectively remove the resonance loads.
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ItemEnhancements in analysis of beam-like structures using asymptotic methods(Georgia Institute of Technology, 2019-04-01) Gupta, MohitAs a complement to conventional FEA, state-of-the-art Variational Asymptotic Method (VAM) and a mixed formulation of Geometrically Exact Beam Theory (GEBT) are employed in this work, which is very fast, provides rigorous physics-based material models for composites while ensuring efficiency and accuracy. In the present work, some major issues with use of VAM-based framework for solving thin-walled structures have been identified and fixed, whose solution involved a theoretical modification in the existing VAM-based framework. Further, the overall framework has been facilitated with analysis of piezoelectric materials, analysis involving structural damping and a method to obtain, store and visualize time-histories of 3D stresses, strains and displacements. Finally, a method to use dimensional reduction techniques for solving beam-like structures, such as aircraft wings, involving complex and intricate 3-D geometries is demonstrated. Thus, the present work enhances the analysis of beams using asymptotic methods, expands the scope of VAM-based beam theory and provides extensive validation for implemented techniques with the commercially available 3-D FEM tools.
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ItemA joined 3D/1D finite element method for aeroservoelastic analysis of damaged HALE aircraft wings(Georgia Institute of Technology, 2018-04-05) Sadat Hoseini Khajuee, Seyed Mohammad HanifNonlinear aeroelastic analysis of damaged High-Altitude-Long-Endurance aircraft wings is considered. The structural model consists of a full three-dimensional finite element continuum model for the damaged area, which is a small localized area of the wing, and a geometrically exact one-dimensional displacement-based finite element model for the undamaged part of the wing. The solid and the beam parts are then rigorously combined using a transformation between the joined nodes of the two models at their intersection. The transformation is derived using the recovery equations of variational asymptotic beam model and employed to eliminate the six degrees of freedom of the single joined node of the beam. The validity and efficiency of the method is demonstrated using test cases involving cracks and delaminations in the solid part. It is shown that although the accuracy remains virtually the same between the full three-dimensional model and the joined one-dimensional/three-dimensional model, the computational cost is considerably lower for the latter. Finite-state induced flow theory of Peters is exploited as the unsteady aerodynamic model to compute aerodynamic forces and moments acting on the wing. Combining the structural and aerodynamic models, a dynamic nonlinear aeroelastic element is developed for the time simulation of the dynamic responses of composite high aspect-ratio wings. The model has been used for analyzing aeroelastic instability boundaries and time simulations, as well as synthesizing an active flutter suppression control system. Numerical results verifying the validity of the method are presented and the results are discussed. The proposed joined model will enables the High-Altitude-Long-Endurance aircraft designers to tackle the problem of aeroelasticity in a computationally efficient manner, without sacrificing accuracy with regard to full three-dimensional models, hence reducing the overall time and cost of the design process.
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ItemParallel computation algorithms for multibody dynamics simulations(Georgia Institute of Technology, 2017-05-18) Heo, Seun DoFlexible multibody dynamics simulations have been performed sequentially on a single processor because the problem sizes for the simulations were not large. How-ever, advanced designs of rotor blades or CSD/CFD (Computational Structural/Fluid Dynamics) coupled problems call for more stringent accuracy requirements and faster computations in multibody dynamics simulations. For parallel computations, a novel non-overlapping domain decomposition method is developed and implemented to perform flexible multibody dynamics simulations in parallel. Non-overlapping domain decomposition methods such as classical substructuring methods and finite element tearing and interconnecting (FETI) methods are also reviewed and compared to see how they have been developed and improved for better domain decomposition. The proposed domain decomposition approach with a localized version of Lagrange multiplier technique and an augmented Lagrangian formulation in conjunction with the Lagrange multipliers, is formulated and discussed in detail. Within the frame-work of direct solvers, the solution procedure with LU factorization and forward and backward substitutions has been designed for parallel computations. The actual implementation of the parallel algorithm with the domain decomposition method on a finite-element-based multibody dynamics simulation program (Dymore), is also described. Finally, the parallel algorithm is tested on parallel hardware with numerical experiments to evaluate the accuracy and scalability of the algorithm for various domain decomposition cases.
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ItemA nonlinear theory of Cosserat elastic plates using the variational-asymptotic method(Georgia Institute of Technology, 2015-08-26) Kovvali, Ravi KumarOne of the most important branches of applied mechanics is the theory of plates - defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions. There is an abundance of plate theories in the literature modeling classical elastic solids that fit this description. Recently, however, there has been a steady growth of interest in modeling materials with microstructures that exhibit length-scale dependent behavior, generally known as Cosserat elastic materials. Concurrently, there has also been an increased interest in the construction of reduced dimensional models of such materials owing to advantages like reduced computational effort and a simpler, yet elegant, resulting mathematical formulation. The objective of this work is the formulation and implementation of a theory of elastic plates with microstructure. The mathematical underpinning of the approach used is the Variational Asymptotic Method (VAM), a powerful tool used to construct asymptotically correct plate models. Unlike existing Cosserat plate models in the literature, the VAM allows for a plate formulation that is free of a priori assumptions regarding the kinematics. The result is a systematic derivation of the two-dimensional constitutive relations and a set of geometrically-exact, fully intrinsic equations gov- erning the motion of a plate. An important consequence is the extraction of the drilling degree of freedom and the associated stiffness. Finally, a Galerkin approach for the solution of the fully-intrinsic formulation will be developed for a Cosserat sur- face analysis which will also be compatible with more traditional plate solvers based on the classical theory of elasticity. Results and validation are presented from linear static and dynamic analyses, along with a discussion on some challenges and solution techniques for nonlinear problems.One of the most important branches of applied mechanics is the theory of plates - defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions. There is an abundance of plate theories in the literature modeling classical elastic solids that fit this description. Recently, however, there has been a steady growth of interest in modeling materials with microstructures that exhibit length-scale dependent behavior, generally known as Cosserat elastic materials. Concurrently, there has also been an increased interest in the construction of reduced dimensional models of such materials owing to advantages like reduced computational effort and a simpler, yet elegant, resulting mathematical formulation. The objective of this work is the formulation and implementation of a theory of elastic plates with microstructure. The mathematical underpinning of the approach used is the Variational Asymptotic Method (VAM), a powerful tool used to construct asymptotically correct plate models. Unlike existing Cosserat plate models in the literature, the VAM allows for a plate formulation that is free of a priori assumptions regarding the kinematics. The result is a systematic derivation of the two-dimensional constitutive relations and a set of geometrically-exact, fully intrinsic equations gov- erning the motion of a plate. An important consequence is the extraction of the drilling degree of freedom and the associated stiffness. Finally, a Galerkin approach for the solution of the fully-intrinsic formulation will be developed for a Cosserat sur- face analysis which will also be compatible with more traditional plate solvers based on the classical theory of elasticity. Results and validation are presented from linear static and dynamic analyses, along with a discussion on some challenges and solution techniques for nonlinear problems.
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ItemDesign strategies for rotorcraft blades and HALE aircraft wings applied to damage tolerant wind turbine blade design(Georgia Institute of Technology, 2014-12-15) Richards, Phillip W.Offshore wind power production is an attractive clean energy option, but the difficulty of access can lead to expensive and rare opportunities for maintenance. Smart loads management (controls) are investigated for their potential to increase the fatigue life of damaged offshore wind turbine rotor blades. This study will consider two commonly encountered damage types for wind turbine blades, the trailing edge disbond (bond line failure) and shear web disbond, and show how 3D finite element modeling can be used to quantify the effect of operations and control strategies designed to extend the fatigue life of damaged blades. Modern wind turbine blades are advanced composite structures, and blade optimization problems can be complex with many structural design variables and a wide variety of aeroelastic design requirements. The multi-level design method is an aeroelastic structural design technique for beam-like structures in which the general design problem is divided into a 1D beam optimization and a 2D section optimization. As a demonstration of aeroelastic design, the multi-level design method is demonstrated for the internal structural design of a modern composite rotor blade. Aeroelastic design involves optimization of system geometry features as well as internal features, and this is demonstrated in the design of a flying wing aircraft. Control methods such as feedback control also have the capability alleviate aeroelastic design requirements and this is also demonstrated in the flying wing aircraft example. In the case of damaged wind turbine blades, load mitigation control strategies have the potential to mitigate the effects of damage, and allow partial operation to avoid shutdown. The load mitigation strategies will be demonstrated for a representative state-of-the-art wind turbine (126m rotor diameter). An economic incentive will be provided for the proposed operations strategies, in terms of weighing the cost and risk of implementation against the benefits of increased revenue due to operation of damaged turbines. The industry trend in wind turbine design is moving towards very large blades, causing the basic design criterion to change as aeroelastic effects become more important. An ongoing 100 m blade (205 m rotor diameter) design effort intends to investigate these design challenges. As a part of that effort, this thesis will investigate damage tolerant design strategies to ensure next-generation blades are more reliable.
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ItemAdvancements in rotor blade cross-sectional analysis using the variational-asymptotic method(Georgia Institute of Technology, 2014-04-07) Rajagopal, AnuragRotor (helicopter/wind turbine) blades are typically slender structures that can be modeled as beams. Beam modeling, however, involves a substantial mathematical formulation that ultimately helps save computational costs. A beam theory for rotor blades must account for (i) initial twist and/or curvature, (ii) inclusion of composite materials, (iii) large displacements and rotations; and be capable of offering significant computational savings compared to a non-linear 3D FEA (Finite Element Analysis). The mathematical foundation of the current effort is the Variational Asymptotic Method (VAM), which is used to rigorously reduce the 3D problem into a 1D or beam problem, i.e., perform a cross-sectional analysis, without any ad hoc assumptions regarding the deformation. Since its inception, the VAM based cross-sectional analysis problem has been in a constant state of flux to expand its horizons and increase its potency; and this is precisely the target at which the objectives of this work are aimed. The problems addressed are the stress-strain-displacement recovery for spanwise non-uniform beams, analytical verification studies for the initial curvature effect, higher fidelity stress-strain-displacement recovery, oblique cross-sectional analysis, modeling of thin-walled beams considering the interaction of small parameters and the analysis of plates of variable thickness. The following are the chief conclusions that can be drawn from this work: 1. In accurately determining the stress, strain and displacement of a spanwise non-uniform beam, an analysis which accounts for the tilting of the normal and the subsequent modification of the stress-traction boundary conditions is required. 2. Asymptotic expansion of the metric tensor of the undeformed state and its powers are needed to capture the stiffnesses of curved beams in tune with elasticity theory. Further improvements in the stiffness matrix can be achieved by a partial transformation to the Generalized Timoshenko theory. 3. For the planar deformation of curved laminated strip-beams, closed-form analytical expressions can be generated for the stiffness matrix and recovery; further certain beam stiffnesses can be extracted not only by a direct 3D to 1D dimensional reduction, but a sequential dimensional reduction, the intermediate being a plate theory. 4. Evaluation of the second-order warping allows for a higher fidelity extraction of stress, strain and displacement with negligible additional computational costs. 5. The definition of a cross section has been expanded to include surfaces which need not be perpendicular to the reference line. 6. Analysis of thin-walled rotor blade segments using asymptotic methods should consider a small parameter associated with the wall thickness; further the analysis procedure can be initiated from a laminated shell theory instead of 3D. 7. Structural analysis of plates of variable thickness involves an 8×8 plate stiffness matrix and 3D recovery which explicitly depend on the parameters describing the thickness, in contrast to the simplistic and erroneous approach of replacing the thickness by its variation.
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ItemEffects of engine placement and morphing on nonlinear aeroelastic behavior of flying wing aircraft(Georgia Institute of Technology, 2013-08-26) Mardanpour, PezhmanEffects of engine placement on flutter characteristics of a very flexible high-aspect-ratio wing are investigated using the code NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft). The analysis was validated against published results for divergence and flutter of swept wings and found to be in excellent agreement with the experimental results of the classical wing of Goland. Moreover, modal frequencies and damping obtained for the Goland wing were found in excellent agreement with published results based on a new continuum-based unsteady aerodynamic formulation. Gravity for this class of wings plays an important role in flutter characteristics. In the absence of aerodynamic and gravitational forces and without an engine, the kinetic energy of the first two modes are calculated. Maximum and minimum flutter speed locations coincide with the area of minimum and maximum kinetic energy of the second bending and torsion modes. Time-dependent dynamic behavior of a turboshaft engine (JetCat SP5) is simulated with a transient engine model and the nonlinear aeroelastic response of the wing to the engine's time-dependent thrust and dynamic excitation is presented. Below the flutter speed, at the wing tip and behind the elastic axis, the impulse engine excitation leads to a stable limit cycle oscillation; and for the ramp kind of excitation, beyond the flutter speed, at 75% span, behind the elastic axis, it produces chaotic oscillation of the wing. Both the excitations above the flutter speed are stabilized, on the inboard portion of the wing. Effects of engine placement and sweep on flutter characteristics of a backswept flying wing resembling the Horten IV are explored using NATASHA. This aircraft exhibits a non-oscillatory yawing instability, expected in aircraft with neither a vertical tail nor yaw control. More important, however, is the presence of a low frequency “body-freedom flutter” mode. The aircraft center of gravity was held fixed during the study, which allowed aircraft controls to trim similarly for each engine location, and minimized flutter speed variations along the inboard span. Maximum flutter speed occurred for engine placement just outboard of 60% span with engine center of gravity forward of the elastic axis. The body-freedom flutter mode was largely unaffected by the engine placement except for cases in which the engine is placed at the wing tip and near the elastic axis. In the absence of engines, aerodynamics, and gravity, a region of minimum kinetic energy density for the first symmetric free-free bending mode is also near the 60% span. A possible relationship between the favorable flutter characteristics obtained by placing the engines at that point and the region of minimum kinetic energy is briefly explored. Effects of multiple engine placement on a similar type of aircraft are studied. The results showed that multiple engine placement increases flutter speed particularly when the engines are placed in the outboard portion of the wing (60% to 70% span), forward of the elastic axis, while the lift to drag ratio is affected negligibly. The behavior of the sub- and supercritical eigenvalues is studied for two cases of engine placement. NATASHA captures a hump body-freedom flutter with low frequency for the clean wing case, which disappears as the engines are placed on the wings. In neither case is there any apparent coalescence between the unstable modes. NATASHA captures other non-oscillatory unstable roots with very small amplitude, apparently originating with flight dynamics. For the clean-wing case, in the absence of aerodynamic and gravitational forces, the regions of minimum kinetic energy density for the first and third bending modes are located around 60% span. For the second mode, this kinetic energy density has local minima around the 20% and 80% span. The regions of minimum kinetic energy of these modes are in agreement with calculations that show a noticeable increase in flutter speed at these regions if engines are placed forward of the elastic axis. High Altitude, Long Endurance (HALE) aircraft can achieve sustained, uninterrupted flight time if they use solar power. Wing morphing of solar powered HALE aircraft can significantly increase solar energy absorbency. An example of the kind of morphing considered in this thesis requires the wings to fold so as to orient a solar panel to be hit more directly by the sun's rays at specific times of the day. In this study solar powered HALE flying wing aircraft are modeled with three beams with lockable hinge connections. Such aircraft are shown to be capable of morphing passively, following the sun by means of aerodynamic forces and engine thrusts. The analysis underlying NATASHA was extended to include the ability to simulate morphing of the aircraft into a “Z” configuration. Because of the “long endurance” feature of HALE aircraft, such morphing needs to be done without relying on actuators and at as near zero energy cost as possible. The emphasis of this study is to substantially demonstrate the processes required to passively morph a flying wing into a Z-shaped configuration and back again.
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ItemDamage modeling and damage detection for structures using a perturbation method(Georgia Institute of Technology, 2012-01-06) Dixit, AkashThis thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sensitivity of structural vibration properties like natural frequencies to the presence of damage. Towards these objectives, a general analytical procedure, which yields nth-order expressions governing mode shapes and natural frequencies and for damaged elastic structures such as rods, beams, plates and shells of any shape is presented. Features of the procedure include the following: 1. Rather than modeling the damage as a fictitious elastic element or localized or global change in constitutive properties, it is modeled in a mathematically rigorous manner as a geometric discontinuity. 2. The inertia effect (kinetic energy), which, unlike the stiffness effect (strain energy), of the damage has been neglected by researchers, is included in it. 3. The framework is generic and is applicable to wide variety of engineering structures of different shapes with arbitrary boundary conditions which constitute self adjoint systems and also to a wide variety of damage profiles and even multiple areas of damage. To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and non-contact Laser-Doppler Vibrometer sensors. Next, the step of damage diagnosis is approached. Damage diagnosis is done using two methodologies. One, the modes and natural frequencies that are determined are used to formulate analytical expressions for a strain energy based damage index. Two, a new damage detection parameter are identified. Assuming the damaged structure to be a linear system, the response is expressed as the summation of the responses of the corresponding undamaged structure and the response (negative response) of the damage alone. If the second part of the response is isolated, it forms what can be regarded as the damage signature. The damage signature gives a clear indication of the damage. In this thesis, the existence of the damage signature is investigated when the damaged structure is excited at one of its natural frequencies and therefore it is called ``partial mode contribution". The second damage detection method is based on this new physical parameter as determined using the partial mode contribution. The physical reasoning is verified analytically, thereupon it is verified using finite element models and experiments. The limits of damage size that can be determined using the method are also investigated. There is no requirement of having a baseline data with this damage detection method. Since the partial mode contribution is a local parameter, it is thus very sensitive to the presence of damage. The parameter is also shown to be not affected by noise in the detection ambience.
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ItemNonlinear static and dynamic analysis of beam structures using fully intrinsic equations(Georgia Institute of Technology, 2011-07-05) Sotoudeh, ZahraBeams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.