2023 | Book

# Introduction to Aeroelasticity

## With Case-Studies

Author: Harijono Djojodihardjo

Publisher: Springer Nature Singapore

2023 | Book

Author: Harijono Djojodihardjo

Publisher: Springer Nature Singapore

This textbook is intended as a core text for courses on aeroelasticity or aero-elasto-mechanics for senior undergraduate/graduate programs in aerospace and mechanical engineering. The book focuses on the basic understanding of the concepts required in learning about aeroelasticity, from observation, reasoning, and understanding fundamental physical principles. Fundamental and simple mathematics will be introduced to describe the features of aeroelastic problems, and to devise simple concurrent physical and mathematical modeling. It will be accompanied by the introduction and understandings of the mechanisms that create the interactions that generate the aeroelastic phenomena considered. The students will also be led to the relation between observed phenomena, assumptions that may have to be adopted to arrive at physical and mathematical modelling, interpreting and verifying the results, and the accompanied limitations, uncertainties and inaccuracies. The students will also be introduced to combine engineering problem solving attitude and determination with simple mechanics problem-solving skills that coexist harmoniously with a useful mechanical intuition.

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Abstract

As an introductory chapter, it delves into the realm of aeroelasticity, which is also known as aeroelastomechanics; it will lead the reader from original query to observing the environment and identify of those phenomena that can be classified as aeroelastic phenomena, or something similar in day-to-day life. Any answer to this original question can lead one to explore one’s imagination and satisfy one’s understanding. Eventually, one could position oneself to get the best benefit and gain comprehensive understanding and significance of the subject. Historical background of aeroelasticity provides further perspectives, in particular to address aeroelastic phenomenon and eventually take necessary steps if necessary in responding to the demands of engineering solutions. Historical perspective is the study of a subject in light of its earliest phases and subsequent evolution. Such perspective may assist in obtaining an introductory or intermediate account that is needed to facilitate students and practitioners to understand and grasp the basic principles which can be used as mandatory tools for understanding and mapping solution approach to the problem at hand, as well as to obtain some fundamental principles that can be applied to the problem. Examples of aeroelastic problems and their system (block diagram) representation are introduced for illustration of the scope of aeroelasticity, such as some illustrative examples on the influence of aeroelastic phenomena on aircraft design for creative and proactive class discussions (Most Figures that appear in this chapter originated from NASA (or NACA)-based publication, including Garrick IE and Reed III WH in J Aircraft, 1981 [1], Garrick, I. E. and W. H. Reed, III. 2013. Document ID 19810045015, Conference Proceedings, NASA Langley Research Center Hampton, VA, United States, August 11, 2013 [2], and Dick SJ (ed) NASA'S First 50 Years Historical Perspectives, NASA SP-2010-4704:2010 [3]).

Abstract

The present chapter provides a review and fundamentals of elasticity as one of the building blocks in aeroelasticity as well as aircraft structures, which may have overlapping significance in aerospace engineering. The presentation is intended to give the students, engineers and readers a comprehensive account on the principles and fundamentals of elasticity that contribute to the physical properties of engineering structures, their strength and integrity. In revealing the fundamentals of elasticity, mathematical representation is utilized, which requires some basic understanding of applied mathematics. The presentation starts with the mathematical foundation of aeroelasticity based on the equilibrium and compatibility equations for structures that can deform elastically. To obtain information on the elastic response which is an internal characteristic of the system, stress and strain relationships in the system are required and elaborated. The formulation of equation of motion for deformable bodies and the relationship between stress and deformation is elaborated in detail as required. The use of energy methods of analysis in deflection calculations and some structural problems for which energy methods are employed are elaborated. The deformation of aircraft structures under distributed forces and the influence functions approach is addressed and exemplified. Applications to aircraft structures such as for wings and bodies are elaborated comprehensively for fundamental understanding.

Abstract

The present chapter elaborates physical principles that govern theoretical, analytical and experimental fluid mechanics and aerodynamics, based on principles of mechanics, including those incorporated in thermodynamics that dictates conservation principles. Four generalh assumptions regarding the properties of the liquids and gases that form the subject of this book are made and retained throughout except cases where there are needs to consider more accurate considerations of more advanced and modern physics. These are assumptions that the fluid is a continuum, inviscid and adiabatic and either a perfect gas or a constant-density fluid (unless viscous fluids are considered). If there are discontinuities, such as shocks, compression and expansion wave or vortex sheets that are present, more physical aspects have to be incorporated in the considerations. For this purpose, these discontinuities will normally be treated as separate and serve as boundaries for continuous portions of the flow field. The laws of motion of the fluid are fundamental and can be found in any fundamental text on hydrodynamics or gas dynamics. The differential equations which apply the basic laws of physics to this situation are then elaborated. The concept of lifting flow over a cylinder will be utilized in the development of the theory of the lift generated by airfoils. Much of the materials here have been taken from the author’s book “Mekanika Fluida” in Indonesian [1].

Abstract

Typical section has been widely employed to analyze the aeroelasticity of the wing and the aircraft. Typical section typically represents the aeroelastic properties at about 70–75% of the half-wingspan (or the tail surface). Concept of typical section to represent the wing of aircraft has been introduced for multiple purposes, such as to give a fundamental and very instructive treatment of the problem of aeroelasticity, and accompanied by simple computation to provide quick estimate and general understanding of the problem of aircraft aeroelasticity, and can be employed in the early development of aeroelastic engineering approach. One advantage of the concept of typical section is that it can be applied for wings or aerodynamic surfaces of large aspect ratio. Relevant parameters of the wing, however, should be appropriately considered, such as the geometrical and stiffness parameters, the aerodynamic parameters and the kinematic and dynamic parameters commensurate with the aircraft flight. The aeroelastic differential equations of motion are then generated based on Newton’s second Law of Motion, with progressive treatment of the wing configuration as on the essential element of the aircraft aeroelasticity [1, 2].

Abstract

Further discussions in the utilization of typical section to analyze aircraft wing aeroelasticity in this chapter cover selected basic topics in static aeroelasticity. Torsional divergence, aileron reversal, control surface effectiveness will first be discussed (The present chapter has been written as an update of the author’s lecture notes on Aeroelasticity at Institut Teknologi Bandung (1982–2005) [1] and Universiti Sains MalaysIa (2004–2008) [2]. The theoretical development then proceeds with one-dimensional wing model. In formulating the governing equations for static aeroelasticity, divergence is viewed as an eigenvalue problem. In the analysis of the equilibrium equation for a wing with variable properties, Galerkin method is introduced and elaborated. A physically and mathematically more complex analysis of static aeroelasticity is introduced in analyzing the rolling of a straight wing. Here the problem is formulated in terms of an integral equation as compared to differential equation formulation approach, as well as the utilization of aerodynamic induction as compared to strip theory and Lumped element method as compared to modal approach or eigenfunction approach in previous problems. Then control surface reversal and rolling effectiveness, as well as two-dimensional aeroelastic models of lifting surface, are analyzed to give a comprehensive account of static aeroelasticity of aircraft wings and aerodynamic beam-like surfaces.

Abstract

One of the aircraft mandatory requirements demands that aircraft flight is flutter-free. Flutter is a dynamic aeroelastic instability due to the interaction of inertial, elastic and aerodynamic forces. It is an undesirable phenomenon for safety requirements in aircraft since it causes divergent oscillations that may lead to structural damage or failure, performance and ride comfort degradation, or loss of control, in addition to comfort. Costly redesign is required if flutter is discovered at the aircraft certification stage. Emergence of flutter compromises not only the long-term durability of the wing structure but also the operational safety, flight performance and energy efficiency of the aircraft. Effectual means of flutter prevention are, therefore, mandatory in the certification of new flight vehicles. In the present chapter, flutter problems and solution in predicting their occurrence are discussed in a fundamental and elementary manner, to reveal the physical principles and their essential characteristics. The treatment is manifested by the use of simplified aerodynamic models and examples. However, this should not distract our attention to the relevant phenomenon to be revealed, which will be more complex with the presence of other physical elements that are here neglected and simplified mathematical approach adopted.

Abstract

Fundamental fluid dynamics, which is founded on conservation principles related to mass, momentum and energy (first law of thermodynamics), as well as equation of state (which in most cases degenerates into the equation of ideal gas) is also one of the founding pillars of aeroelasticity, more so in the discipline of unsteady aerodynamics. Therefore this chapter elaborates the mandatory principles in great detail, including their mathematical formulation. The unsteady (or non-stationary) aerodynamics is an essential part of aeroelasticity and is usually the most difficult for the student and practitioner alike. Pioneering approach has been initiated by Wagner [1], Küssner [2] and Theodorsen [3] among others. Their work can be followed in their original work as well as classical books on aeroelasticity. The discussion presented here is developed from the fundamental theory of Fluid Mechanics Conservation Principles and Potential Flow Aerodynamics as elaborated in Chap. 3. Further discussions are elaborated in Chaps. 8 and 11 which incorporate some case studies. The present chapter is also introductory and focused on two-dimensional inviscid flow, where linearized principle can be applied. More advanced topics are elaborated in other chapters.

Abstract

Unsteady aerodynamic theory and computational procedure are essential for calculating the aerodynamic forces in any aeroelastic problem. To gain a fundamental and comprehensive, and yet simple understanding, a two-dimensional physical model is elaborated. The model will be limited to an unsteady two-dimensional linearized model in an irrotational flow environment. Lifting and non-lifting configurations are illustrated. Illustrative examples and a case study are elaborated to obtain a good impression of problems and analytical approaches.

Abstract

Proceeding with the elaboration of the foundation of dynamic aeroelasticity established in the earlier chapter, the present chapter then focuses on establishing the flutter calculation method, starting from basic illustrative cases to more complex problems. The chapter first elaborates a review of theoretical foundation for flutter stability for binary-bending-torsion flutter of typical section. Several methods of solving the aeroelastic stability of binary system will be introduced and discussed. Several case studies are elaborated for illustrative and instructional purposes.

Abstract

The study for the dynamics of aeroelastic system can be best illustrated by analyzing a generic aeroelastic system: the typical section. Such approach will be instructive as a device for exploring the mathematical tools and the physical content associated with the system. The present chapter elaborates dynamic aeroelasticity and flutter of typical section. Basic approach for the treatment of the dynamic aeroelasticity of a typical section will be discussed. Then a review will be made on the theoretical foundation of flutter stability for binary-bending-torsion flutter of typical section. The final section provides an example of the basic approach by elaboration to some detail of a case study on a parametric study on aeroelastic stability and flutter characteristics of aircraft wings as a case study. For the elaboration of dynamic aeroelasticity and flutter and review of the theoretical foundation for flutter stability for binary-bending-torsion flutter of typical section, the review presented here follows closely the elaboration in Zwaan (Zwaan [1]) and Mark R. Pletzer (Ed) (Max R Platzer, Ed., AGARD MANUAL on Aeroelasncity in Axial-Flow Turbomachines Volume 2, Structural Dynamics and Aeroelasticity, AGARD-AG-298-Vol-2.) for instructiveness. As instructive illustration, the case study is drawn from the author’s work (Djojodihardjo, H and Yee, H H, Parametric Study of The Flutter Characteristics of Transport Aircraft Wings, Proceedings of AEROTECH-II 2007 Conference on Aerospace Technology of XXI Century, 20–21 June 2007, Kuala Lumpur; Djojodihardjo, H and Yee, H H, Parametric Study of The Flutter Characteristics of Transport Aircraft Wings, Proceedings of AEROTECH-II 2007 Conference on Aerospace Technology of XXI Century, 20–21 June 2007, Kuala Lumpur). For conceptual study purposes, it would be of advantage to look into a simple method that may give instructive results. In this connection, various modern transport aircrafts are classified and investigated in view of their structural dynamic and aeroelastic characteristics of their wing structure. The basic philosophy and formulation of flutter phenomena as reflected in the generic binary flutter problem is revisited and reflected to real aircraft for general understanding and conceptual design purposes.

Abstract

Three-dimensional unsteady aerodynamics and computational approaches for continuation of Chap. 8 in unsteady Aerodynamics are elaborated in the present chapter (Reproduced from and based on several papers: [1‐4]). Further it illustrates some of the contributions in lifting surfaces based on potential aerodynamic approaches and serves to provide and elaborate a good spectrum of problems and analytical approaches focusing on case studies in three-dimensional unsteady aerodynamic theory and computational methods. The first case study illustrates one of the first attempts in unsteady lifting potential flow solution method using geometric discretization and singularity distributions on the aerodynamic surface, which contributes to the present Boundary Element Method. The second case study addresses a more complex situation, that is the unsteady subsonic three-dimensional flow with separation bubble, and utilizes the singularity method. The third case study reflects the application of these previous techniques in addressing aircraft buffeting phenomena, a practical aeroelastic problem, using dynamic response approach The last case study elaborates the application of the three-dimensional unsteady aerodynamics lifting surface method to address combined aeroelasticity and acoustic excitation in a unified boundary element approach. These case studies are presented to provide an illustration of the application of lifting surface or boundary element method to solve unsteady aerodynamic problems.

Abstract

Aeroservoelasticity (ASE) extends the concept of aeroelasticity to address the aeroelastic interactions between aerodynamic forces and a flexible structure, which may include a control system. Then the classic Collar aeroelastic triangle can be extended to form the aeroservoelastic pyramid, where there are now forces resulting from the control system as well as the aerodynamic, elastic and inertial forces. Considerations of the aeroservoelastic interactions increase the importance of engineering efforts to incorporate lightweight and flexible structures, as well as high-gain digital flight control systems. Such considerations are important to account for aeroservoelastic instability. The dynamics of the guidance and control system may significantly affect aeroelastic problems, or vice versa, hence the term aeroservoelasticity. The FEM-based structural analysis is also essential for static aeroelastic studies in the nascent field of compliant blade performance modification. By way of introduction, mathematical modeling of a simple aeroelastic system with a control surface is elaborated. As a basic aeroservoelastic System that can shed some light on its state of affairs, the binary aeroelastic model will be helpful in analyzing flutter behavior as a baseline. Consideration is given to the effect of gusts. A particular case study on Aeroelastic Analysis of an Aircraft with Stand-By Actuator Using State-Space Approach is also presented for detailed treatment of the problem. Other examples discussed are the Design and Optimization of an Aeroservoelastic Wind Tunnel Model and Aeroservoelastic Modelling and Analysis of a Highly Flexible Flutter Demonstrator.

Abstract

The basic understanding of the significance of aircraft loads and their relationship to aeroelasticity will be elaborated comprehensively. The estimation of loads acting on an aircraft structure is an indispensable task ranging from conceptual, preliminary and detailed design to loads flight testing and the manufacturing and operation of aircrafts, when an aircraft is already in service, there are a large range of topics that need to be elaborated and proven, analytically as well as by experiments. Much of these problems can be understood and mastered, by looking into selected topic which can be classified into those related to (a) stability (e.g. flutter), (b) static deformation (e.g. static aeroelastic effects, steady flight maneuvers) and (c) dynamic response (e.g. maneuvers, gusts, turbulence). Once the response deformations and accelerations are obtained, the loads and stresses generated in the aircraft must also be determined so that the strength and fatigue/damage tolerance behavior may be assessed. Structural loads are the major reason for degradation of structures. Loads is a general term that incorporates both forces and moments. Various basic concepts relevant to loads in general will be introduced, including Newton’s laws of motion for a particle and their generalization to a body, as well as D’Alembert’s principle as sources of externally applied/reactive loads, which will further generate internal load within a structure. Basic analysis using the principles of mechanics, strength of materials, aerodynamics and flight mechanics will be elaborated. The determination of loads together with the qualification for static strength and fatigue by calculation and test for all important structural components is a main prerequisite for successful design and safe operation of any aircraft.

Abstract

Aircraft operations demand that every aircraft should be safe to fly, and to that end it is mandatory that the conception, design, manufacturing and operations for every aircraft follow the fail-safe paradigm. Therefore, in addition that the design of aircraft could guarantee such mandatory requirements, physical experiments along the design, manufacturing and operation of aircraft need to be proved and validated by physical experiments, which is indeed highly challenging. Important aspects of carrying out experiments have many useful purposes, such as to assess the accuracy and validity of theoretical models, to study phenomena beyond the current reach of theory, and in the field of aeroelasticity, to verify the safety and integrity of aeroelastic systems through various test, from ground vibration tests to wind tunnel tests and to flight tests. In the present chapter, some of the prevailing fundamental aspects of experimental aeroelasticity are discussed. To provide hands-on impression, a case study on flight flutter test will be elaborated.

Abstract

Piezoaeroelastic energy harvesters convert airflow-induced vibrations into electrical energy, while the availability and affordability of piezoelectric transducers offer a class of flapping foil energy harvesters mostly in micro- to milliwatts scale which need to be tuned to match the characteristic frequencies. The present work presents a brief review of aeroelastic instability of a generic typical wing section due to the free-stream flow field which is utilized as an oscillating foil energy converter. For propaedeutic analysis a generic piezoaeroelastic cantilevered beam is defined and treated as a typical section. The basic governing equation of this generic structure is treated as a three degree-of-freedom electrodynamic system, with the first two degree of freedom comprising the standard binary aeroelastic system with additional relevant terms to represent the influence of a piezoelectric embedded element on the cantilevered wing. Following the philosophical approach of binary aeroelastic system, the problem is mathematically formulated and solved for the range of solutions that can be obtained depending on the prevailing physical properties of the system, focusing on the stability characteristics of the generic system. The characteristics of the unsteady aerodynamics of the oscillating system associated with favorable energy harvesting capabilities are assessed.

Abstract

As a generic definition, hydroelasticity can further be defined as a branch of science concerned with the motion and distortion of deformable bodies responding to environmental excitations in the sea, as it evolves and is modified from the original Collar triangle. The discipline is concerned with phenomena involving interaction between inertial, hydrodynamic, i.e. the fluid pressure acting on the structure, and elastic forces on the structure which modifies its dynamic state and, in return, the motion and distortion of the structure. Considerations on hydroelasticity relevant to offshore oil production platforms, low-speed conventional ships and high-speed monohull or multihull vessels, which are affected by several types of dynamic loads including environmental actions, such as wind and waves, will be discussed to provide comprehensive understanding of the state of affairs. Then engineering analyses for the prediction of induced dynamic responses of such engineering systems will be elaborated in terms of a formulation of fluid–structure interaction via integration of hydrodynamics, structural mechanics and use of novel modeling techniques. Specific example in this subject is the author and colleague work on numerical boundary element computation of submerged body-surface wave interaction, which will be elaborated in detail. To provide some introductory examples in hydroelasticity, attention is given to the state of affairs and equation of motion of hydrofoils moving in incompressible and inviscid or viscous flow, and discussions on methods of solutions for stability and dynamic response. Inviscid fluid–structure coupling modeling and solution scheme will also be discussed, employing finite element method and representing the hydrofoil by a typical section. Many figures utilized in this chapter have been adopted or adapted from recent publications, for which the author would like to thank the corresponding authors whole-heartedly.

Abstract

The application of BE-FE acoustic-structure interaction on a structure subject to acoustic load is elaborated using the boundary element–finite element acoustic-structural coupling and the utilization of the computational scheme developed earlier. The plausibility of the numerical treatment is investigated and validated through application to generic cases. The analysis carried out in the work is intended to serve as a baseline in the analysis of acoustic-structure interaction for lightweight structures. Results obtained thus far exhibit the robustness of the method developed.

Abstract

Design of structures, including buildings and bridges, is dictated by safety and economy, which, due to progress in technology, materials and computational methods, has led to the utilization of light structures with optimum strength. In this regard, aeroelastic phenomenon that has been observed with great interest and concern by aerodynamicists, aeroelasticians and engineers is observed in civil structures, most spectacular of which are the aeroelastic flutter phenomena on a relatively slender bridge structure, due to vortex shedding. Tall buildings, now approaching the frontier of 1000 m height, have enormously spread worldwide in recent years and led to new challenging problems facing the international engineering community. Wind-induced vibration results in one issue that may be of concern for the serviceability design of tall buildings and which produces discomfort. The wind action on slender structures with low natural frequencies can introduce uncomfortable vibrations which could affect general well-being and interfere with the daily activities of the occupants. Consequently, the risk of exceeding acceptable vibration limits and of causing discomfort should be estimated and eliminated. These topics are here illustrated and discussed, accompanied by selected examples that should provide a comprehensive understanding. Analytical and experimental means of incorporating wind-induced vibration in bridges and structures will be discussed to gain a comprehensive, although introductory understanding. Method used for the study of flutter stability analysis of the structure during motion will be exemplified. Some illustrations are presented without elaborate discussions, since pictures implicitly contain a large body of information that may need lengthy elaboration, but most importantly, pictures will incite creativity and curiosity for further active learning efforts by the readers.

Abstract

A methodology for including maximum flutter speed requirement in the preliminary structural wing design is developed. The problem of minimizing structural weight while satisfying static strength, dynamic characteristics and aeroelastic behavioral constraints is stated in a nonlinear mathematical form, with beam width and thickness taken as design variables, and solved using gradient-based optimization technique. Dynamic characteristics of the structure are calculated using finite element model. Laplace form of the unsteady aerodynamics forces is obtained from Fourier transform of unit pulse aerodynamics response. The frequency-domain p-k method is applied for the calculation of aeroelastic stability boundaries. Based on constraint values and the required gradients, a first-order Taylor series approximation is used to develop an approximation linear programming for weight minimization. A modified feasible direction method is, then applied iteratively to solve the optimization problem. Validation of the method is carried out in the design of cantilever straight wing structure with 6% hyperbolic airfoil. It will be shown that the optimized wing design can significantly differ from those obtained without optimization process.

Abstract

Acoustics is the science concerning the study of sound. The effects of sound on structures attract overwhelming interests and numerous studies were carried out in this particular area. Many of the preliminary investigations show that acoustic pressure produces significant influences on structures such as thin plate, membrane and also high impedance medium like water (and other similar fluids). Thus, it is useful to investigate structural response to acoustics on aircraft, especially on aircraft wings, tails and control surfaces which are vulnerable to flutter phenomena. The present paper describes the modeling of structure-acoustic interaction to simulate the external acoustic effect on binary flutter model. Here, the model is illustrated as a rectangular wing where the aerodynamic wing model is constructed using strip theory with simplified unsteady aerodynamics involving the terms for flap and pitch degree of freedom. The external acoustic excitation, on the other hand, is modeled using a four-node quadrilateral isoparametric element via finite element approach. Both equations are then carefully coupled and solved using eigenvalue solution. Next the mentioned approach is implemented in MATLAB, and the outcome of the simulated results is later described, analyzed and illustrated.

Abstract

The commercial feasibility of active noise control (ANC) is very promising due to its capability beyond passive noise control (PNC). To some extent ANC becomes a complement of PNC. The active noise reduction is also capable and beneficial in reducing noise selectively. However, the active noise reduction using a conventional secondary source can become very complicated if a significant noise level reduction is required, since a large number of secondary sources will be needed. The active noise reduction is also less effective for reducing high-frequency noise. With such perspectives, a novel approach has been developed using a multipole secondary source to address the problems mentioned. In addition, the multipole secondary source will be used for numerical simulation of noise reduction in of propeller noise source in a free field.

Abstract

The potential of Flapping-Wing Micro-Air Vehicles (MAVs) for sensing and information gathering relevant for environmental and disaster monitoring and security surveillance leads to the identification and modeling the salient features and functional significance of the various components in the flying reasonably sized biosystems. The dynamics, kinematics and aerodynamics of their wing systems and the production of mechanical power output for lift and thrust will be synthesized following a simplified and generic, but meticulous, model for a flapping-wing ornithopter. Basic unsteady aerodynamic approach incorporating viscous effect and leading-edge suction is utilized. The first part of the study is focused on a bi-wing ornithopter. Later, parametric study is carried out to obtain the lift and thrust physical characteristics in a complete cycle for evaluating the plausibility of the aerodynamic model and for the synthesis of an ornithopter model with simplified mechanism. Further analysis is carried out by differentiating the pitching and flapping motion phase lag and studying its respective contribution to the flight forces. A similar procedure is then applied to flapping quad-wing ornithopter model. Results are discussed in comparison with various selected simple models in the literature, with a view to develop a practical ornithopter model.

Abstract

The present work addresses the aerodynamics, aeroelasticity and flight dynamics of birdlike bio-inspired bi-wing flapping-wing ornithopter in forward flight. The main interest is to compare the dynamics of rigid and flexible flapping wing in forward flight. First, a generic approach is followed to model the geometry, kinematics and aerodynamics of flapping-wing ornithopter by considering a three-dimensional rigid and thin wing in flapping and pitching motion with and without phase lag. The unsteady aerodynamic approach incorporates viscous effects and leading-edge suction. Next a fundamental representation of unsteady air loads and structural flexibility interaction is developed for the analysis and numerical simulation based on a generic linear aeroelastic analysis using forward speed and oscillatory flapping motion as disturbances, to find out the influence of wing flexibility on its aeroelastic stability and aerodynamic performance. Further, a simplified and generic model flight dynamic model is presented based on using the same aerodynamic approach, by only considering the equation of motion in the plane of symmetry to gain insight for further development of refined model. Parametric studies are carried out both for the aeroelastic and flight dynamic problems to assess the plausibility of the present approach. The elaboration in this chapter follows Djojodihardjo in (Analysis and computational study of the aerodynamics, aeroelasticity and flight dynamics of flapping wing ornithopter using linear approximation, 2016, [6]).

Abstract

A series of work has been carried out to develop the foundation for the computational scheme for the calculation of the influence of the acoustic disturbance to the aeroelastic stability of the structure. The generic approach consists of three parts. The first is the formulation of the acoustic wave propagation governed by the Helmholtz equation by using boundary element approach, which then allows the calculation of the acoustic pressure on the acoustic-structure boundaries. The structural dynamic problem is formulated using finite element approach. The third part involves the calculation of the unsteady aerodynamics loading on the structure using generic unsteady aerodynamics computational method. Analogous to the treatment of dynamic aeroelastic stability problem of structure, the effect of acoustic pressure disturbance to the aeroelastic structure is considered to consist of structural motion-independent incident acoustic pressure and structural motion-dependent acoustic pressure, referred to as the acoustic-aerodynamic analogy. Results are presented and compared to those obtained in earlier work.

Abstract

An efficient analytical method for vibration analysis of a Euler–Bernoulli beam with spring loading at the tip has been developed as a baseline for treating flexible beam attached to central-body space structure, followed by the development of MATLAB^{©} finite element method computational routine. Extension of this work is carried out for the generic problem of active vibration suppression of a cantilevered Euler–Bernoulli beam with piezoelectric sensor and actuator attached as appropriate along the beam. Such generic example can be further extended for tackling lightweight structures in space applications, such as antennas, robot’s arms and solar panels. For comparative study, three generic configurations of the combined beam and piezoelectric elements are solved. The equation of motion of the beam is expressed using Hamilton’s principle, and the baseline problem is solved using Galerkin-based finite element method. The robustness of the approach is assessed.

Abstract

For drag minimization of slender body of revolution in transonic flow purposes, computational schemes are developed. Selected methods are reviewed and adapted to obtain relatively simple and fast procedures to facilitate parametric studies for drag optimization. The slender body integral approach was first resorted to for its elegance and its simplicity to facilitate parametric studies for fast, analytical and structured search procedure in the optimization scheme, such as that provided by MATLAB code. The scheme was incorporated in the preliminary step of an optimization cycle that will have refined search using more accurate codes at later stages. The finite difference transonic small disturbance schemes will then be used to assess the aerodynamic characteristics of the candidate geometries in better detail. Two different finite difference computational schemes have been pursued. The finite difference schemes follow the well-known transonic small disturbance computational techniques. Resort is also made to commercially available Navier–Stokes flow solvers, to validate computational schemes developed as well as an instrument for numerical experimental studies.

Abstract

A computational modeling and simulation study is carried out to gain insight and formulate strategy for the design and tailoring of panel-like space structure that can withstand space debris impact without penetration. To represent a generic engineering structure, the impacted panel structure is modeled as a set of bonded Mindlin plates. The analysis is based on fundamental principles which are elaborated and numerically simulated. The objective is to identify optimum configuration in terms of loading, structural dimensions, material properties and composite layup. The analyses are based on dynamic response with emphasis on the elastic region. The direct numerical simulation is carried out in parallel for the analysis, synthesis, parametric study and optimization. Simulation results of impact loading by a spherical rigid body at certain velocity perpendicular to the panel show how fiber-metal laminates can be structurally tailored to achieve a non-penetrating impact.