Laith K. Abbas

Non-linear aeroelastic investigations of store(s)-induced limit cycle oscillations:

In the current work, the study of the aeroelastic behaviour of a wing with external store(s), such as a missile or drop fuel tank, is presented. The aeroelastic governing equations derived for a cantilever wing with coupled bending and torsion modes account for structural and aerodynamic non-linearities. Coupling terms retained in the aeroelastic governing equations are due to: (a) the non-linear beam theory, (b) the aerodynamic non-linearities of a quasi-steady model with stall, and (c) the non-linear kinematics terms of the store(s). As presented in the paper, this aircraft configuration can induce pathologies, such as store(s)-induced limit cycle oscillations (or si-LCOs), very different from the one of a clean wing configuration, and from the one obtained from the linearized form of the aeroelastic governing equations. Time domain simulation, phase portrait, and bifurcation analyses are performed for various velocities, initial conditions, and store(s)-sensitive parameters — such as store mass, number, location along the wing — to examine the dynamic aeroelastic instabilities of the system (e.g. the onset of flutter and LCO). Numerical studies indicate the presence of regions of subcritical Hopf-bifurcation, corresponding to an unstable LCO, for velocities below the linear flutter velocity.

Active Aerothermoelastic Control of Hypersonic Double-wedge Lifting Surface

Designing re-entry space vehicles and high-speed aircraft requires special attention to the nonlinear thermoelastic and aerodynamic instability of their structural components. The thermal effects are important since temperature environment brings dramatic influences on the static and dynamic behaviors of flight structures in supersonic/hypersonic regimes and is likely to cause instability, catastrophic failure and oscillations resulting in structural failure due to fatigue. In order to understand the dynamic behaviors of these “hot” structures, a double-wedge lifting surface with combining freeplay and cubic structural nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes has been analyzed. A third order piston theory aerodynamic is used to estimate the applied nonlinear unsteady aerodynamic loads. Also considered is the loss of torsional stiffness that may be incurred by lifting surfaces subject to axial stresses induced by aerodynamic heating. The aerodynamic heating effects are estimated based on the adiabatic wall temperature due to high speed airstreams. As a recently emerging technology, the active aerothermoelastic control is aimed at providing solutions to a large number of problems involving the aeronautical/aerospace flight vehicle structures. To prevent such damaging phenomena from occurring, an application of linear and nonlinear active control methods on both flutter boundary and post-flutter behavior has been fulfilled. In this paper, modeling issues as well as numerical simulation have been presented and pertinent conclusions outlined. It is evidenced that a serious loss of torsional stiffness may induce the dynamic instability; however active control can be used to expand the flutter boundary and convert unstable limit cycle oscillations (LCO) into the stable LCO and/or to shift the transition between these two states toward higher flight Mach numbers.

Transfer Matrix Method for the Determination of the Natural Vibration Characteristics of Realistic Thrusting Launch Vehicle—Part I

The feasibility of using the transfer matrix method (TMM) to compute the natural vibration characteristics of a flexible rocket/satellite launch vehicle is explored theoretically. In the approach to the problem, a nonuniform free-free Timoshenko and Euler-Bernoulli beamlike structure is modeled. A provision is made to take into consideration the effects of shear deformation and rotary inertia. Large thrust-to-weight ratio leads to large axial accelerations that result in an axial inertia load distribution from nose to tail which causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. Once the transfer matrix of a single component has been obtained, the product of all component matrices composes the matrix of the entire structure. The frequency equation and mode shape are formulated in terms of the elements of the structural matrices. Flight test and analytical results validate the present TMM formulas.

Static/Dynamic Edge Movability Effect on Non-Linear Aerothermoelastic Behavior of Geometrically Imperfect Curved Skin Panel: Flutter and Post-Flutter Analysis

This paper addresses the problem of the aerothermoelastic modeling behavior and analyses of skin curved panels with static and dynamic edge movability effect in high supersonic flow. Flutter and post-flutter behavior will be analyzed toward determining under which conditions such panels will exhibit a benign instability, that is a stable limit cycle oscillation, or a catastrophic instability, that is an unstable LCO. The aerothermoelastic governing equations are developed from the geometrically non-linear theory of infinitely long two dimensional curved panels. Von Karman non-linear strain-displacement relation in conjunction with the Kirchhoff plate-hypothesis is adopted. A geometrically imperfect curved panel forced by a supersonic/hypersonic unsteady flow is numerically investigated using Galerkin approach. These equations are based on the third-order piston theory aerodynamic for modeling the flow-induced forces. Furthermore, the effects of thermal degradation and Kelvins model of structural damping independent of time and temperature are also considered in this model. Computational analysis and discussion of the finding along with pertinent conclusions are presented.

Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

In this paper, an approach based on transfer matrix method of linear multibody systems (MS-TMM) is developed to analyze the free vibration of a multilevel beam, coupled by spring/dashpot systems attached to them in-span. The Euler-Bernoulli model is used for the transverse vibration of the beams, and the spring/dashpot system represents a simplified model of a viscoelastic material. MS-TMM reduces the dynamic problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundaries are composed of displacements, rotation angles, bending moments, and shear forces, which are partly known and partly unknown, and end up with reduced overall transfer matrix. Nontrivial solution requires the coefficient matrix to be singular to yield the required natural frequencies. This paper implements two novel algorithms based on the methodology by reducing the zero search of the reduced overall transfer matrixs determinate to a minimization problem and demonstrates a simple and robust algorithm being much more efficient than direct enumeration. The proposal method is easy to formulate, systematic to apply, and simple to code and can be extended to complex structures with any boundary conditions. Numerical results are presented to show the validity of the proposal method against the published literature.

Numerical Calculation of Effect of Elastic Deformation on Aerodynamic Characteristics of a Rocket

The application and workflow of Computational Fluid Dynamics (CFD)/Computational Structure Dynamics (CSD) on solving the static aeroelastic problem of a slender rocket are introduced. To predict static aeroelastic behavior accurately, two-way coupling and inertia relief methods are used to calculate the static deformations and aerodynamic characteristics of the deformed rocket. The aerodynamic coefficients of rigid rocket are computed firstly and compared with the experimental data, which verified the accuracy of CFD output. The results of the analysis for elastic rocket in the nonspinning and spinning states are compared with the rigid ones. The results highlight that the rocket deformation aspects are decided by the normal force distribution along the rocket length. Rocket deformation becomes larger with increasing the flight angle of attack. Drag and lift force coefficients decrease and pitching moment coefficients increase due to rocket deformations, center of pressure location forwards, and stability of the rockets decreases. Accordingly, the flight trajectory may be affected by the change of these aerodynamic coefficients and stability.

About the Aerothermoelastic Stability of Panels in Supersonic Flows

This article provides new insights into the aerothermoelastic stability of thin plates. Particularly, the issue of loss of stability of an isotropic plate-strip of constant thickness immersed in a supersonic flow field and subjected to a variable temperature field through the thickness is examined. Using the basic principles of the theory of aerothermoelasticity of isotropic bodies, the theories of flexible panels, and the linear law of temperature field through the thickness of the panel, the stability equations and associated boundary conditions are obtained. As expected, the coefficients of the aerothermoelastic governing equations depend on the thermal load, and consequently the panel-flutter critical speed depends on temperature. The model takes into account quadratic and cubic aerodynamic non-linearities as well as cubic geometric non-linearities. Due to the inhomogeneity of the temperature field distribution across the thickness plate buckling instability occurs. This instability accounts for the deformed shape of the plate and the stability boundary depends on the variables characterizing the flow speed, the temperature of the middle plane and the temperature gradient in the direction normal to the plane. It is shown that the combined effect of the temperature field and free-stream regulates the process of stability and the temperature field can significantly change the flutter critical speed and flutter behavior. The problem of stability is also considered in the non-linear framework. The existence and behavior of flutter-type vibrations is investigated at pre- and post-critical speeds. The influence of the temperature field on the dependency of the limit cycle amplitude as a function of speed is studied. Results and discussions are presented along with pertinent concluding remarks.

AEROELASTIC BEHAVIOR OF LIFTING SURFACES WITH FREE-PLAY, AND AERODYNAMIC STIFFNESS AND DAMPING NONLINEARITIES

Aeroelastic instabilities are dangerous phenomena, where aerodynamic load interacting with the inertia and elastic structural loads can induce catastrophic failures. In this paper the effects of aerodynamic nonlinearities as well as coupled plunging/pitching structural concentrated cubic type and freeplay nonlinearities in the dynamic of a two-dimensional double-wedge airfoil immersed in supersonic/hypersonic flow has been examined. The unsteady nonlinear aerodynamic force and moment on the airfoil are evaluated using the Piston Theory Aerodynamics modified to take into account the effect of the airfoil thickness. The resulting aeroelastic equations are numerically integrated to obtain time responses and to investigate the dynamic instability of the lifting surface under various initial displacement conditions. Results of the complex nonlinear aeroelastic system are presented in the form of bifurcation diagrams constructed from the response amplitude for various types of the system nonlinearity. It is shown that there exist regions, in which the system exhibit Limit Cycle Oscillations (LCOs), strongly dependent on the initial conditions of the aeroelastic system. Concentrated structural nonlinearities, that are freeplays and cubic type nonlinearities, can have significant effects on the flutter behavior and can cause large amplitude oscillations at lower airspeeds than for a linear system. It is also shown that larger amplitude LCOs occur when a pitching freeplay is considered, as compared with the case when a plunging freeplay is taken into account.

Transfer Matrix Method for the Determination of the Free Vibration of Two Elastically Coupled Beams

The feasibility of using the transfer matrix method (TMM) to compute the free vibration characteristics of a system composed of continues and discrete elements vibrating in a plane is explored theoretically. In the approach to the problem, a general analytical method based on TMM is developed for the vibrations of two uniform Euler-Bernoulli beams coupled by a spring. The components of the transfer matrix are all functions of the systems natural frequency. The overall transfer equation only involves boundary state vectors, whereas the state vectors at all other connection points do not appear. The state vectors at the boundary are composed of displacements, rotation angles, bending moments and shear forces, which are partly known and partly unknown. Moreover, the overall transfer matrix is independent of the degrees of the freedom. A non-trivial solution of the final overall transfer equation requires the coefficient matrix to be singular. This paper reduces the zero search of its determinate to a minimization problem and demonstrates a simple, robust algorithm being much more efficient than direct enumeration. A numerical result is presented to demonstrate the proposal method.

Nonlinear Aero-Thermo-Visco-Elastic Behavior of Geometrically Imperfect Curved Skin Panel

This paper deals with the aero-thermo-visco-elastic modeling and analyses of curved panels. Flutter and post-flutter behavior will be analyzed toward determining under which conditions such panels will exhibit a benign instability, that is a stable limit cycle oscillation, or a catastrophic instability, that is an unstable LCO. The aero-thermo-visco-elastic governing equations are developed from the geometrically non-linear theory of infinitely long two dimensional curved panels. Von Karman non-linear strain-displacement relation in conjunction with the Kirchhoff plate-hypothesis is adopted. A geometrically imperfect curved panel forced by a supersonic/hypersonic unsteady flow is numerically investigated using Galerkin approach. These equations are based on the third-order piston theory aerodynamic for modeling the flow-induced forces. Furthermore, the effects of thermal degradation and Kelvin’s model of structural damping are also considered in this model. Computational analysis and discussion of the finding along with pertinent conclusions are presented. Nomenclature a Panel length, m b Panel width, m c Speed of sound of undisturbed flow, m/s D Flexural panel stiffness ] ) 1 ( 12 [ 2 3 Eh , Nm 1 0 , , E E E , T e Elastic moduli, N/m ; rate of change in elastic moduli/rate of change in temperature, 1/C sb sm s g g g , , Viscoelastic structural damping, membrane and bending coefficients, respectively H camber of the curved panel, m h h, Panel thickness, m; its dimensionless counterpart ) / ( a h , respectively x N M , Bending moment resultant, N.m; and axial stress force resultant measured per unit length, N/m F F V M , Mach number at flutter and flutter speed, respectively, m/s q M , Undisturbed flight Mach number and dynamic pressure ) 2 / ( 2 U , N/m n Number of modes, , 2 , 1 n p Free stream pressure of the undisturbed flow, N/m 2 1 Post Doctoral Research Fellow, School of Power Engineering, AIAA member; laithabbass@yahoo.com 2 Professor of Mechanical Engineering, School of Power Engineering; rui@163.com 3 Associate Professor, Mechanical and Aeronautical Engineering Department, AIAA member; pmarzocc@clarkson.edu 4 Assistant Professor, Department of Aerospace Structures, AIAA member; M.M.Abdalla@tudelft.nl 5 Research Associate, Department of Aerospace Structures, AIAA member; R.deBreuker@tudelft.nl 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 17th 4 7 May 2009, Palm Springs, California AIAA 2009-2596 Copyright