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The longitudinal dynamic instability (POGO) of liquid propellant launch vehicle results from the complex interaction between the vehicle structural vibration in the longitudinal direction and liquid propellant feeding system. In the preliminary design phase of a launch vehicle, accurate prediction of the lower-mode longitudinal natural vibration characteristics enables to avoid pogo instability efficiently. In this paper, a complete vehicle including the liquid propellant tanks is analytically modeled for pogo instability analysis, focusing on the longitudinal lower natural frequencies. Moreover, liquid propellant tank modeling methods are established by use of an advanced one-dimensional mass-spring model to refine the complete vehicle model. By using these methods, parametric studies for the hydroelastic effect, evaluations of modal analysis, and pogo estimation were conducted. Consequently, the numerical results obtained by the orthotropic liquid tank modeling method were found to be in good agreement with natural vibration characteristics by the previous analyses and experiments. And, the target vehicle showed the pogo estimated areas at the first structural mode. Thus, the present simplified structural modeling and modal analysis procedure can be used to identify pogo occurrence areas and provide design criteria for pogo instability in the preliminary design phase.

In a flapping wing micro air vehicle (MAV), inspired by an organism of either insects or birds, flexibility of the wing structure induces a crucial effect upon the vehicle performance. Thus, in an analysis upon the flapping wing MAV, coupling between aerodynamics and structural dynamics considering the wing flexibility will be a critical component. This paper presents an accurate computational approach to simulate a flapping wing by coupling between CFD and CSD. Non-linear structural analysis based on the geometrically exact beam formulation was used. Such non-linear beam analysis was coupled with preconditioned Navier-Stokes solutions. For a grid deformation in the aerodynamic analysis, the mesh shearing methodology was used. A coupling between the structural and aerodynamic analyses was conducted by adopting the implicit coupling approach. After that, an aeroelastic analysis was performed and the results are compared with the experimental results. However, the flapping wing configuration is not slender in reality and their vein section geometry is complex generally. Thus, to consider those features, the finite element analysis, beam and shell, based on a co-rotational (CR) theory was developed in parallel. Currently, the CR beam analysis with a warping DOF was developed and validated by comparing it with NASTRAN in static condition.

A bearingless rotor has been used to take advantage of the reduced number of helicopter hub components and maintenance expense. It comprises of three primary components: a main rotor blade, torque tube, and flexbeams. It has another advantage that its structure is simple. But large nonlinear bending-torsion is induced because the flexbeams have low torsional stiffness. Furthemore, since it has multiple load path, its structural modeling and structure-aerodynamics coupled analysis will be complicated. In this paper, a geometrically exact beam formulation was used to describe nonlinear behavior of the rotating beam elements. To conduct the multi-body analysis, multiple beam elements were assembled. The present structural model was coupled with the finite-state dynamic inflow aerodynamics. Finally, trim analysis was carried out, and the blade deformation/internal load was predicted. Its results were compared with those obtained by the rotorcraft comprehensive analysis, CAMRAD II. The blade deformation discrepancies were less than 5% and internal loads average difference was smaller than 10%.

This paper presents a transient time aeroelastic analysis for a supersonic flight vehicle with a ramjet engine. First, computational fluid dynamics (CFD) is conducted to estimate its baseline geometry and the prediction results obtained upon the vehicle surface are transferred to the structural transient time analysis. The structural analysis is then carried out. A brand new finite element domain decomposition structure analysis is developed for the present transient time aeroelastic analysis. To solve a resulting large-scale system equation, FETI method is adopted for the present shell analysis. And comparison results between the present transient time FETI and Dual-primal FETI methods are attempted. During the 500 time steps, both analyses show good agreement with a difference less than 0.01% for the example problem. As a result, a detailed analytical procedure for the transient time aeroelastic analysis is established to predict a possibility of an excessive deformation or buckling induced in the supersonic vehicle during flight.

This paper describes application of an improved computational approach based on domain decomposition technique for a large scale structural analysis. We compared computational algorithms corresponding to the original and an improved FETI approach. In the original FETI approach, Lagrange’s multipliers were introduced to enforce compatibility at the interface DOF’s. Specifically, we adopted local Lagrange’s multipliers with an augmented Lagrangian formulation (ALF) as penalty formulation of the problem to improve computational robustness and efficiency. For validation of the present approach, we compared its results with those obtained by the original FETI. Practical performances of the present approach were demonstrated through several 2-D plane and 3-D shell static analysis results.

An initial version of an advanced rotorcraft preliminary design optimization framework was developed previously. For its further improvement, a new trim and performance subroutines based on the blade element theory is developed and incorporated. Such addition is in order to reflect the effect of the airfoil properties, blade built-in twist, and tip speed, which have a great influence on the required power estimation,. Since the optimization algorithm applied in the present framework is a gradient based method, it is found that the converged value of an objective function is quite sensitive to the initial values of the design variables. Thus application of a genetic algorithm, one of the global optimization schemes, is investigated in this paper. Due to such change, the present design optimization will become more robust. Among the design variables presently considered, influential design variables will be only retained by conducting a sensitivity test. And further improvements upon the engine library and weight trend subroutine are also conducted.

An improved forced response analysis for turbine blades is conducted in both frequency and time domains. For its aerodynamic analysis, a time domain vortex lattice method which can capture a detailed behavior of the vorticities and account for thickness effect of the airfoil is used. To deal with the complex aerodynamic coefficients and express an aeroelastic equation of motion into state-space form, two types of transformation techniques are invoked. First, the z transformation is used to convert the mixed time/frequency domain aerodynamics to frequency domain. The p transform technique is next used to convert the equation of motion back to time domain. The resulting aeroelastic model will be without aerodynamic states or lag equations and can be used to perform various aeroelastic analyses at reduced computational cost. Numerical results from the flutter analysis are presented in both frequency and time domains. For the cascaded blades, the present and the other existing results show a good agreement for aerodynamic analysis and flutter analysis. The forced vibration results are also presented in both domains. For a single airfoil, the transient responses obtained by the present method show a good agreement with those by the full order analysis. The transient response for a cascade shows similar trajectories for the present method and the full order model.

Aeroelastic phenomenon is one of the major factors to limit the flight envelop of an aircraft. A combat aircraft needs high maneuverability during its mission. Thus, it will experience a varying aerodynamic environment. Especially many external stores are installed in a combat aircraft and they are known to influence the flutter stability. In the present paper, a robust flutter analysis is suggested to examine the effect of the store on flutter stability. Structural analysis is performed based on the two models: one-dimensional beam and two-dimensional plate model. The store is assumed as a point mass and a rigid bar model in each model, respectively. Natural frequency results of both clean and tip stored wing are validated with NASTRAN. The natural frequency result for the stored wing is obtained with respect to the store location. To consider compressibility effect, the lift deficiency function is obtained by doublet lattice method in terms of Mach number. It is required to derive a linear time invariant formulation in robust stability analysis, and thus, rational function approximation is applied. Natural frequency validation for a clean wing shows 0.5 ~ 3.9% differences between the present and NASTRAN model, and for the stored wing, it is 0.5 ~ 1.7% and 1.6 ~ 2.2%. Then, the nominal flutter speeds for both a clean and stored wing are predicted. In the non-match point solution, it shows the 1.1~ 6.0% differences between the one-dimensional beam and plate model. Flutter boundaries both including and excluding the store aerodynamics are compared, and those show good agreement. The worst case flutter boundary is obtained by considering the structural variation due to changing natural frequency and aerodynamic variations. The present paper presents the updated store location and flight conditions for the worst case flutter boundary. The robust flutter boundary is more conservative than the nominal flutter boundary is. In the future, improved robust flutter analysis will be conducted considering flexibility of the store mount and more accurate store aerodynamics.

The aeroelastic analysis of the turbine cascade is generally solved in frequency domain because of the computational efficiency. Nevertheless, time domain cascade analysis is also required that the transient response analysis of the cascade is important. Model order reduction in the aeroelastic analysis is one of the techniques to overcome the excessive computational load in time domain cascade analysis. In this paper, both time and frequency domain analysis are conducted since results in both domains are important. For a cascade aerodynamic analysis, a kernel function corresponding to the vortex lattice method is used in discrete time domain. The results in mixed time and frequency domain are transferred to frequency domain by using the z transform. The results obtained by applying the z transform are used to analyze the flutter boundary of the cascade. The p transform is also used to obtain the results in time domain from the results acquired in frequency domain. This transformation can provide advantages in terms of model order reduction without additional aerodynamic states and improvement in computational efficiency. Both frequency and time domain analyses can be conducted at a time by using the present analysis for the turbine cascade.

In this paper , various small -sized modules are combin ed with one an other in order to perform rotorcraft preliminary design and its optimization . At the stage of the preliminary design, analysis fidelity is less important than the rapid assessment of a desig n is . Most of the previous researchers attempt ed to implement sophisticated applications in order to increase the fidelity of analysis, but th e present paper focuse s on a rapid assessment while keeping the similar level of fidelity. Each small -sized module is controlled by an externally -operated global optimization module . Results from each module are automatically handled from one discipline to another which reduc es the amount of computational effort and time greatly when compar ed with manual execution . Au tomatic ally handled process decreases computational cycle and time by factor of approximately two. Previous research ers and the rotorcraft industries developed their own integrated analysis for rotorcraft design task , such as HESCOMP, VASCOMP, and RWS IZE . When a specific mission profile is given to these program s, the program estimat es the aircraft size, performance, rotor performance, component weight , and other aspects . Such results can be come good source s for the supplemental analysis in terms of stabili ty, handling qualities, and cost. If the results do not satisfy the stability criteria or other constraints , additional sizing process es may be used to re -evaluate rotorcraft size based on the result from stability analysis. Trade -off study can be conducte d by connecting disciplines, and it is an important advantage in a preliminary design study.

This paper presents a combination of an analysis between a computational structural dynamics (CSD) and high fidelity unsteady computational fluid dynamics (CFD) analysis. Regarding a helicopter in hover, aerodynamic loads are computed from the threedimensional Navier-Stokes solver in overlapped grids, and blade motions are estimated from the geometrically exact rotor beam analysis. While combining those two analyses, a loosely coupled method is used and the results are validated regarding a civil transport helicopter. The next step is to analyze a periodic steady-state flight condition such as forward flight. In this paper, HART II blade flapping motion in a forward flight acted upon by periodic airloads and collective pitch angle is predicted by using a similar procedure as is used in hover. But the response phase is obtained to be different from that observed in the experiment. Thus, a further consideration upon the periodic excitation forces and the blade response will be required in the foregoing CFD and CSD computation for forward flight.

For the modern aircraft, uncertainty may be an important issue to its aeroelastic stability. Therefore, many researches have been performed regarding this topic. In this paper, we assume that an uncertainty exist in aircraft structural and aerodynamic characteristics. At first, we predict flutter speed and frequencies by using parametric uncertainties. We formulate the generalized mass and stiffness matrices for a three-dimensional wing. We also derive its generalized aerodynamic forces. These matrices are based on the structural mode shapes. We convert them into the modal mass and stiffness matrices and predict an influence by the weight value of uncertainties in the coupled mode. In this paper, we also perform a robust analysis by mu-method which considers aerodynamic uncertainties. We use the doublet lattice method (DLM) to obtain a detailed unsteady aerodynamic force. We verify aerodynamic uncertainty magnitude by DLM in accordance with Mach number. Then, we obtain a state-space form of the aerodynamic force by rational function approximation to find the variation range of the poles and zeros. Finally, we analyze the worst case by the mumethod which considers an aerodynamic uncertainty.

This paper presents the initial development of an optimization framework for designing active twist helicopter rotor blade cross sections with embedded anisotropic piezocomposite actuators. Optimum design of active twist blades is a complex task, since it involves a rich design space with tightly coupled design variables, e.g., the simple orientation of the actuators aects the blade natural frequencies. Therefore, it becomes advantageous to apply the principle of mathematical optimization to the design task. In the proposed framework, the blade cross-sectional internal layout is designed to maximize the static twist actuation while satisfying a series of blade requirements. These requirements are associated with locations of the center of gravity and elastic axis, blade mass per unit span, fundamental rotating blade frequencies, and the blade strength based on local threedimensional stress and strain fields under worst loading conditions. An active composite cross-sectional analysis and a geometrically exact one-dimensional beam analysis, along with other related analysis routines, are combined with a gradient-based optimizer within MATLAB. The developed optimization framework is exemplified by using the NASA/Army/MIT Active Twist Rotor blade and its baseline design.

This paper investigates potential improvements that can be accomplished by integral twist-actuated rotor blades regarding helicopter performance and its vibration. The twist deformation is obtained using anisotropic piezocomposite actuators embedded in the composite blade construction. A four-bladed fullyarticulated Active Twist Rotor (ATR) system was built and tested at Langley Transonic Dynamics Tunnel. From these tests, the integral twist control authority exerted upon the fixed system was determined. Significant control authority in hub vertical shear load component is observed from dierent blade actuation modes. Similar control authority is found in the other components of the fixed-system loads. Exploiting those authorities, vehicle performance enhancement can be achieved using low-frequency actuation, for example, 0P, 1P and 2P. Payload increase in hover can be obtained with a steady collective actuation of blade twist. Power consumption can be reduced by employing a certain mode of blade actuation at 2P in forward flight. Vehicle pitch and roll moments are generated by longitudinal and lateral blade actuation mode at 1P frequency. On the other hand, actuation at higher frequencies can be used to reduce hub vibratory loads. The closed-loop control algorithm used for this reduction is an improved version of the traditional Higher Harmonic Control. Multiharmonic and multi-mode controller is designed and tested as part of the present study.

Dynamic characteristics of active twist rotor (ATR) blades during forward flight is investigated analytically in this paper. An aeroelastic model for an active rotor system is developed to identify dynamic characteristics of ATR blades with integral strain actuators embedded in their composite construction. More specifically, a time domain integration scheme for the geometrically exact formulation of passive beams is extended with the active materials constitutive relations for the forward flight analysis of the ATR system. In parallel, forward flight wind-tunnel tests are conducted at NASA Langley to collect control sensitivity functions experimentally using dynamically-scaled four-active-bladed rotor system. Preliminary results from the present analytical model are presented and compare well with experimental observations. The theoretical model will be used as a design and evaluation tool for closed-loop controller for twist actuation of the ATR system.

Dynamic characteristics of active twist rotor (ATR) blades are investigated analytically and experimentally in this paper. The ATR system is intended for vibration and potentially for noise reductions in helicopters through individual blade control. An aeroelastic model is developed to identify frequency response characteristics of the ATR blade with integral, generally anisotropic, strain actuators embedded in its composite construction. An ATR prototype blade was designed and manufactured to experimentally study the vibration reduction capabilities of such systems. Several bench and hover tests were conducted and those results are presented and discussed here. Selected results on sensitivity of the ATR system to collective setting (i.e. blade loading), blade rpm (i.e. centrifugal force and blade station velocity), and media density (i.e. altitude) are presented. They indicated that the twist actuation authority of the ATR blade is independent of the collective setting up to approximately 10P, and dependent on rotational speed and altitude near the torsional resonance frequency due to its dependency on the aerodynamic damping. The proposed model captures very well the physics and sensitivities to selected test parameters of the ATR system. The numerical result of the blade torsional loads show an average error of 20% in magnitude and virtually no difference in phase for the blade frequency response. Overall, the active blade model is in very good agreement with the experiments and can be used to analyze and design future active helicopter blade systems.