Modified Strip Theory Research Articles

A modified unsteady-nonlinear aeroelastic model for flapping wings

A novel integrated aeroelastic model of flapping wings (FWs) undergoing a prescribed rigid body motion is presented. In this respect, the FW nonlinear structural dynamics is enhanced via a newly proposed modification of implicit condensation and expansion (MICE) method that better considers the structural nonlinear effects. In addition, the unsteady aerodynamic model is also an extension of the widely utilized modified strip theory (MST) in which the flexibility effects are accounted for (MST-Flex). The integrated utility of the proposed generalized MICE and MST-Flex is demonstrated to be more realistic for elastic FW flight simulation applications. The prescribed rigid body motion is produced via a servo motor whose dynamics is also considered for the analysis. A special case study is also performed whose combined aeroelastic solution is determined and validated under a sinusoidal flapping motion. To this end, an experimental setup is designed and tested in order to validate the proposed integrated approach for aeroelastic modeling of FWs. There is very good agreement between the numerical and experimental results for elastic FW aerodynamics. It should be noted that the proposed integrated aeroelastic approach is readily adaptable to all kinds of elastic wings with arbitrary geometry and various combination of structural elements.

Verification of a low fidelity fast simulation framework through RANS simulations

Verification and validation of simulation models are critical steps in engineering. This paper aims at verifying the suitability of reduced order aerodynamic models used in an aeroservoelastic framework designed to analyze the flight dynamics of flexible aircraft, known as the Cranfield Accelerated Aircraft Loads Model. This framework is designed for rapid assessment of aircraft configurations at the conceptual design stage. Therefore, it utilizes or relies on methods that are of relatively low fidelity for high computational speeds, such as modified strip theory coupled with Leishmann–Beddoes unsteady aerodynamic model. Hence, verification against higher order methods is required. Although low fidelity models are widely used for conceptual design and loads assessments, the open literature still lacks a comparison against higher fidelity models. This work focuses on steady-trimmed flight conditions and investigates the effect of aerodynamic wing deformation under such loads on aerodynamic performance. Key limitations of the reduced order models used, namely fuselage and interference effects, are discussed. The reasons for the overall agreement between the two approaches are also outlined.

A Hybrid Reduced-Order Model for the Aeroelastic Analysis of Flexible Subsonic Wings—A Parametric Assessment

A hybrid reduced-order model for the aeroelastic analysis of flexible subsonic wings with arbitrary planform is presented within a generalised quasi-analytical formulation, where a slender beam is considered as the linear structural dynamics model. A modified strip theory is proposed for modelling the unsteady aerodynamics of the wing in incompressible flow, where thin aerofoil theory is corrected by a higher-fidelity model in order to account for three-dimensional effects on both distribution and deficiency of the sectional air load. Given a unit angle of attack, approximate expressions for the lift decay and build-up are then adopted within a linear framework, where the two effects are separately calculated and later combined. Finally, a modal approach is employed to write the generalised equations of motion in state-space form. Numerical results were obtained and critically discussed for the aeroelastic stability analysis of a uniform rectangular wing, with respect to the relevant aerodynamic and structural parameters. The proposed hybrid model provides sound theoretical insights and is well suited as an efficient parametric reduced-order aeroelastic tool for the preliminary multidisciplinary design and optimisation of flexible wings in the subsonic regime.

Wing shape and dynamic twist design of bio-inspired nano air vehicles for forward flight purposes

The wing shape and kinematics of flapping wing nano air vehicles play a crucial role in the effectiveness of the system. Optimizing these design parameters allows for greater endurance during flight due to a reduction in the needed aerodynamic power. In this study, seven insects' wings are considered in order to investigate which wing shape requires less amount of aerodynamic power for forward flight missions. A strip theory model is employed and verified for two types of birds, namely, Jack Daw, and Mew Gull. Then, this aerodynamic theory is utilized to model and optimize the kinematics of the seven wings with a particular investigation on the impacts of the dynamic twist on the performance of bio-inspired nano air vehicles. Each wing is divided into strips that are individually analyzed and integrated over the full wingspan to determine the needed aerodynamic power and propulsive efficiency. The use of this modified strip theory is beneficial because it includes the unsteady aerodynamic effects and the possible change in the wings' dimensions. A parametric study is then carried out to determine the optimum wing shape and associated dynamic twist of the flapping wing nano air vehicle when considering two scenarios. In the first scenario, the wingspan for all considered seven wing shapes is considered the same. As for the second scenario, the seven wing shapes are considered with same wing surface. The results show that for same wingspan and wing surface, the bio-inspired honeybee and bumblebee wing shapes have the optimum performances, respectively. The performed analysis gives guidelines on the optimum design of flapping wing nano air vehicles for forward flight applications.

Improving Prediction of Flapping-Wing Motion By Incorporating Actuator Constraints With Models of Aerodynamic Loads Using In-Flight Data

Flapping-wing flight is a challenging system integration problem for designers due to tight coupling between propulsion and flexible wing subsystems with variable kinematics. High fidelity models that capture all the subsystem interactions are computationally expensive and too complex for design space exploration and optimization studies. A combination of simplified modeling and validation with experimental data offers a more tractable approach to system design and integration, which maintains acceptable accuracy. However, experimental data on flapping-wing aerial vehicles which are collected in a static laboratory test or a wind tunnel test are limited because of the rigid mounting of the vehicle, which alters the natural body response to flapping forces generated. In this study, a flapping-wing aerial vehicle is instrumented to provide in-flight data collection that is unhindered by rigid mounting strategies. The sensor suite includes measurements of attitude, heading, altitude, airspeed, position, wing angle, and voltage and current supplied to the drive motors. This in-flight data are used to setup a modified strip theory aerodynamic model with physically realistic flight conditions. A coupled model that predicts wing motions is then constructed by combining the aerodynamic model with a model of flexible wing twist dynamics and enforcing motor torque and speed bandwidth constraints. Finally, the results of experimental testing are compared to the coupled modeling framework to establish the effectiveness of the proposed approach for improving predictive accuracy by reducing errors in wing motion specification.

모션캡쳐 실험을 통한 조류모방 날갯짓 비행체 구동 특성 분석

본 논문에서는 모션캡쳐 카메라를 사용한 실험을 통해 날갯짓 비행체의 주 날개, 꼬리날개 구동기 특성 분석에 대하여 기술하였다. 실험은 빛이 차단된 실내에서 진행되었고 지그에 기체를 고정하여 날갯짓으로 인한 영향을 줄였다. 주 날개와 꼬리날개 끝단에 마커를 부착하였고 모션캡쳐 카메라는 입력 신호에 대한 각각의 반응을 측정한다. 실험 결과 주 날개는 날갯짓의 주파수에 따라 진폭이 변하는 경향을 보였고, Modified Strip Theory에 실험 결과와 비행체 제원을 적용하여 양력 및 추력 발생 시뮬레이션을 구현 하였다. 꼬리날개는 종 횡축별로 스텝 신호를 인가하여 이에 따른 결과를 2차 전달함수 형태로 정의하였고, 각 축별로 구동기의 구조 차이로 인하여 최종 응답시간, 오버슈트, 최대값 등에서 차이를 나타내는 것을 확인하였다. This paper analyzes actuator characteristics for main wing and tail surfaces of an ornithopter by using a motion capture test. Experiments with the ornithopter are conducted indoor, and its fuselage is held on a jig to reduce interaction with vibration generated by flapping motion. The motion capture system detects the movement of markers attached on the main wing and tail wing tip. Experimental results show that the main wings tend to change its amplitude according to the flapping frequency, and the lift and thrust generation simulation is implemented by applying the experimental results and the ornithopter specification to Modified Strip Theory. Step input excitation is applied for experimental analysis of the tail wing in horizontal and vertical directions. As a result, horizontal and vertical tail wings have different characteristics in terms of overshoot, final value, damping ratio and natural frequency because they have different wing structures and linkages.

MODELLING FRAMEWORK FOR FLIGHT DYNAMICS OF FLEXIBLE AIRCRAFT

The flight dynamics and handling qualities of any flexible aircraft can be analysed within the Cranfield Aircraft Accelerated Loads Model (CA2LM) framework. The modelling techniques and methods used to develop the framework are presented. The aerodynamic surfaces were modelled using the Modified Strip Theory (MST) and a state-space representation to model unsteady aerodynamics. With a modal approach, the structural flexibility and each mode’s influence on the structure deflections are analysed. To supplement the general overview of the framework equations of motion, models of atmosphere, gravity, fuselage and engines are introduced. The AX-1 general transport aircraft model is analysed as an example of the CA2LM framework capabilities. The results showed that, according to the Gibson Dropback criterion, the aircraft with no control system lacks the stability and its longitudinal handling qualities are unsatisfactory. Finally, the steps for future developments of the CA2LM framework are listed within conclusions.

Seakeeping Analysis of a Wave-Piercing Catamaran Using URANS-Based Method

Wave-piercing catamarans (WPCs) consist of two demihulls with wave-piercing bows that may immerse into or emerge out of the free surface when advancing in waves. Therefore, it is questionable whether linear theories like modified strip theory (STF) can precisely predict the seakeeping performance of WPCs in general cases. In this paper, the unsteady Reynolds-averaged Navier–Stokes equations (URANS) method is used to predict the pitch and heave motions of WPCs under various speeds and wave frequencies in head seas, while the STF method is employed for comparison. Furthermore, some parametric studies, such as modifying the shape of wave-piercing bows, disregarding the interaction between demihulls, neglecting the viscosity of water, and altering wave steepness, are also carried out using the URANS-based method. Comparison of numerical and experimental results shows that, under the Froude numbers of interest 4003 ≤ Fn ≤ 0065, acceptable agreement is achieved by using the URANS-based method, while only a similar trend is obtained by using the STF method at the small Froude number Fn = 003. Based on the numerical results of parametric studies, it is shown that the effects of wave steepness and forward speed on the free surface are significant, while the viscous effect is unimportant to the heave and pitch motions.

Semi-analytical static aeroelastic analysis and response of flexible subsonic wings

A semi-analytical model for the combined static aeroelastic analysis and response of flexible subsonic wings is presented. Based on a general variational formulation, the proposed aeroelastic models allow any arbitrary distribution of the flexible wing’s physical properties and provide with a continuous solution of the wing’s displacement along the span, as suitable for parametric optimisation studies within preliminary wing design. Numerical results which provide sound insights on the behaviour of a flexible wing in subsonic flow are obtained and critically discussed for all aeroelastic models, with respect to the most relevant aerodynamic and structural parameters as well as the computational efficiency. Different degrees of fidelity are considered for the aerodynamic modelling and the formulated modified strip theory is shown to be an excellent compromise between the lower complexity of standard strip theory and the higher accuracy of lifting line theory. The modified strip theory is hence suggested as a general and effective steady aerodynamic tool for the multidisciplinary design and optimisation of flexible wings in the subsonic regime.

Uncertainty quantification of aeroelastic stability of composite plate wings using lamination parameters

An approach is presented for modelling the aeroelastic stability of composite laminate wings with ply orientations subject to uncertainty. An aeroelastic model is constructed using the Rayleigh–Ritz technique coupled with modified strip theory aerodynamics. Lamination parameters are used as inputs to a Polynomial Chaos Expansion (PCE), enabling efficient propagation of the uncertainty through the aeroelastic model for a composite laminate with any number of plies. The Rosenblatt transformation is used to adapt the lamination parameter distributions for use with the PCE. A modified approach for modelling the uncertain aeroelastic response near the boundaries of different regimes of behaviour is also presented. Two case studies demonstrate application of the techniques; the first applies a simple PCE to a number of example balanced and symmetric laminates, the second applies the modified approach in a parametric investigation of the effects of bend–twist coupling on response mechanism. The proposed techniques offer at least an order of magnitude reduction in computation time compared to baseline Monte Carlo Simulation for all of the cases investigated.

Improved aeroelastic tailoring using tow-steered composites

The use of tow-steered composites to tailor the aeroelastic behaviour of composite wings is investigated. A Rayleigh–Ritz type approach is used to model the aeroelastic behaviour of a simple rectangular unswept composite wing combined with modified strip theory aerodynamics. Symmetric lay-ups have been considered where the outer fibres are allowed to vary in orientation along the wing span, and the effects on free vibration, flexural axis, flutter and divergence speeds, and gust loads are examined. It was found that it is possible to influence the aeroelastic behaviour in both a beneficial and detrimental manner using tow steering. By increasing the design space, tow-steered laminates allow improved designs compared to traditional unidirectional composite laminates.

Aeroelastic analysis of wind turbine blades based on modified strip theory

This study investigates the performance and aeroelastic characteristics of wind turbine blades based on flexible multibody dynamics, a new aerodynamic model, and the fluid–structure interaction approach. A new aerodynamic model is proposed based on modified strip theory (MST). MST was established for flapping wing aerodynamic models and considers a high relative angle of attack and dynamic stall effects. A simulated wind turbine blade was modeled using multibody dynamics software (MSC.ADAMS), where the flexible parts can be included by importing a finite element model built in finite element analysis software (ANSYS). The aeroelastic responses of the blade were obtained by coupling these aerodynamic and structural models. The proposed aeroelastic analysis method was validated using the predicted performance of the NREL 5MW model reported in the literature.

A dragonfly inspired flapping wing actuated by electro active polymers

An energy-based variational approach is used for structural dynamic modeling of the IPMC (Ionic Polymer Metal Composites) flapping wing. Dynamic characteristics of the wing are analyzed using numerical simulations. Starting with the initial design, critical parameters which have influence on the performance of the wing are identified through parametric studies. An optimization study is performed to obtain improved flapping actuation of the IPMC wing. It is shown that the optimization algorithm leads to a flapping wing with dimensions similar to the dragonfly Aeshna Multicolor wing. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the IPMC wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

Non-linear Dynamic Analysis of a Piezoelectrically Actuated Flapping Wing

An energy method is used in order to derive the non-linear equations of motion of a smart flapping wing. Flapping wing is actuated from the root by a PZT unimorph in the piezofan configuration. Dynamic characteristics of the wing, having the same size as dragonfly Aeshna Multicolor, are analyzed using numerical simulations. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the smart wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

Ornithopter Flight Simulation Based on Flexible Multi-Body Dynamics

This paper introduces a flight simulation of an ornithopter (flapping-wing air vehicle) based on the flexible multi-body dynamics, a refined flapping-wing aerodynamic model and the fluid-structure interaction approach. A simulated ornithopter was modeled using the multi-body dynamics software, MSC.ADAMS, where the flexible parts can be included by importing a finite element model built in the finite element analysis software, ANSYS. To model the complex aerodynamics of flapping-wing, an improved version of modified strip theory was chosen. The proposed integrative simulation framework of ornithopter was validated by the wind tunnel test data reported in the literature. A magpie-sized model ornithopter was numerically designed and simulated to have the longitudinal trim flight condition. We observed a limit-cycle-oscillation of flight state variables, such as pitch attitude, altitude, flight speed, during the trimmed flight of the model ornithopter. Under the trimmed condition of free flight of the model ornithopter, we fixed all the degrees of freedom at the center of gravity to measure the constraint forces and moment. The concept of the “zero moment point” is introduced to explain the physics of ornithopter trimmed longitudinal flight.

Aeroelastic Tailoring of Composite Wings Exhibiting Nonclassical Effects and Carrying External Stores

Structural and aeroelastic tailoring applied to advanced straight and swept aircraft wings carrying external stores is addressed. The wing structure is modeled as a laminated composite plate exhibiting flexibility in transverse shear and warping restraint effects. The equations of motion and boundary conditions are obtained via Hamilton's variational principle and application of generalized function theory. For a comprehensive representation of the stores, their static weights and inertia terms are considered. Three-dimensional modified strip theory aerodynamics is employed, and the obtained eigenvalue/boundary value problems are solved using the extended Galerkin method. The model is used to investigate the implications of external stores and ply angle orientation on divergence, free vibration, and flutter. Within the context of aeroelastic tailoring, the influence of external stores attached to the wing structure has to be considered during the preliminary aircraft design phases.

An aerodynamic model for flapping-wing flight

AbstractA design-oriented model for the unsteady aerodynamics of a flapping wing has been developed using a modified strip theory approach. Within this constraint, vortex-wake effects are accounted for as well as partial leading edge suction and post stall behaviour. Also, the contributions of sectional mean angle of attack, camber, and friction drag are added, which allows this model to be used for the calculation of the average lift, as well as the thrust, power required, and propulsive efficiency of a flapping wing in equilibrium flight. An example of such calculations is presented in the performance prediction of a mechanical flying pterosaur replica.

Nonlinear transonic flutter analysis

A numerical procedure is presented for predicting the static and dynamic aeroelastic characteristics of thin, clean swept wings in flow. The method is based upon the simultaneous time integration of the equations governing the coupled nonlinear fluid dynamic and structural aeroelastic system. Governing equations for the system are developed and the numerical algorithm, including the coupling procedure for their solution, is discussed. As a computational example, the flutter of a simple rectangular wing is considered. Solutions are presented for a range of Mach numbers and dynamic pressures and compared to other existing flutter analysis methods including doublet lattice, modified strip theory, and time linearization. Unlike other procedures, the method presented here is capable of predicting the nonlinear interaction between unsteady shock wave motions and the dynamic response of an elastic wing. Computed results indicate the existence of the transonic bucket.

Comment on "Effect of Stabilizer Dihedral and Static Lift on T-Tail Flutter"

I is reassuring in an engineering sense to see in Ref. 1 that the archaic methods of strip theory and lifting-line theory can still be made to arrive at reasonable solutions to modern problems. However, the strip theory employed in Ref. 1 lacks many of the refinements of the modified strip theory of Yates and, more significantly, it does not possess the growth potential to treat the general problem of the T-tail with partial span elevators and rudders. Hence, the experimental correlation achieved (a posteriori?) in Ref. 1 is a necessary but insufficient condition for validation of the authors' method. It would have been more informative if the authors had utilized their experimental data to evaluate modern methods for calculating the aerodynamic interference loads on the T-tail. However, before surveying these modern methods we might add four historical references on early Ttail investigations to the authors' list. The earliest applications of lifting-surface theory to the Ttail configuration were made by Stark and Davies. General discussions of interference problems have been given by Ferrari, Ashley and Landahl, Landahl and Stark, Laschka, and Ashley and Rodden. A symposium on Unsteady Aerodynamics for Aeroelastic Analyses of Interfering Surfaces was sponsored by AGARD in 1970 and eight of the fifteen papers contained in the conference proceedings were related to the T-tail problem. A comparison of results computed by different methods for wingtail-fin combinations, taken two a time, is the subject of a recent AGARD report by this commentator. Interfering lifting-surface methods contain none of the limitations on aspect ratio, taper ratio, sweep, and compressibility effects that are implicit in strip theory and lifting-line theory.! The importance of static deformation of the stabilizer should not have come as such a surprise to the authors since the change in dihedral of a wing under load factor has been recognized for many years (although not in the stability and control textbooks) as an important aspect of lateraldirectional motion at limit load factor. This was first considered by Lovell in 1948, and an analysis of the problem by lifting-surface methods was outlined by this commentator in 1965; Ref. 20 also contains some experimental correlation but only with an earlier simplified method and not with a lifting-surface method. The fact that the dihedral effect of a flexible wing typically doubles at limit load factor suggests that the stabilizer trim load is an essential parameter in T-tail flutter analysis, as the authors of Ref. 1 eventually observed. A final criticism of Ref. 1 is the authors' inconsistency in treating the rotary effects of the stabilizer. The rolling moment due to yawing was included, but the yawing moment

Estimating the Design Values of Horizontal Wave Shearing Force Induced on the Ship Hull in Waves

The authors present the results of statistical predictions on the horizontal wave shearing force for a gigantic oil tanker of 310 meters length and similar ships of different lengths.In the first place, the response functions of horizontal wave shearing force are calculated by the aid of the modified strip theory. Then, the standard deviations of horizontal wave shearing force are evaluated based upon the linear superposition theory, by using the caluculated response functions and the formulated wave spectra for given sea conditions. Finally, the longterm predictions of horizontal wave shearing force are determined by the obtained standard deviations and the wave statistics of the North Atlantic Ocean.According to the systematic prediction analysis, the longitudinal distributions of horizontal wave shearing force, which are predicted with the exceeding probability of 10-6, are investigated in relation to the ship speed, heading angle and ship length.