Franco Mastroddi

Matrix fraction approach for finite-state aerodynamic modeling

A least-square procedure for the finite-state approximation of the aerodynamic matrix is introduced, which is more efficient and/or simpler to use than those currently available. This is accomplished by starting from the approximation of the aerodynamic matrix as ND -1 or D -1 N, where N and D are matrices with polynomial dependence on complex reduced frequency p. Three different finite-state realizations based on the same matrix polynomial approximation are presented. The advantages of the approach and problems encountered in using the method are discussed. Numerical results are included

Shunted piezoelectric patches in elastic and aeroelastic vibrations

Abstract A procedure for a modal-based modeling and analysis of the effectiveness of shunted piezoelectric devices in increasing passive damping of elastic and aeroelastic systems is presented. Dynamical models with different levels of complexity, including both elastic and aeroelastic systems, have been considered in order to show the capability of the proposed approach. The numerical tests presented concern the description of several systems of aeronautical interest with piezoelectric devices to achieve a selective control of different modes. The linear aeroelastic modeling has been reduced to a rational polynomial transfer function, i.e., it has been represented in a linear state–space form which has allowed to extend the proposed piezo modeling to a general linear aeroelastic system. In particular, the aeroelastic application showed a weak capability of improving the stability margin, but a significant performance in the reduction of the gust response level in proximity of the critical condition of the system (e.g., when the flight speed is close to the flutter speed). Thus, a suitable performance of the piezo damper should be designed for any flight speed, altitude and Mach number. An optimal strategy to evaluate the electrical load for the tuning of piezo devices, as function of the flight speed (semi-active control), has been also proposed.

Study of Reduced-Order Models for Gust-Respnse Analysis of Flexible Fixed Wings

Three types of aeroelastic reduced-order models (ROMs) for flutter and gust-response analyses are examined, one of which is introduced here. One is based on the finite-state description of unsteady aerodynamics obtained through a rational-matrix approximation of the frequency-domain transcendental aerodynamic operator. Coupling this with the equations of the structural dynamics yields the aeroelastic ROM. The drawback of this approach is that some aerodynamic states have to be added to the structural states in the state-space format description of the aeroelastic system. The second model that is discussed yields directly the finite-state description of the aeroelastic operator without altering the dimensions of the state space. This model is iterative in nature, in that it requires an estimate of aeroelastic eigenvalues and eigenvectors from the original eigenproblem. Finally, an alternate ROM formulation for the gust-response problem is proposed. It combines good level of accuracy with reduction of additional aerodynamic states and thus can be conveniently used in preliminary design process and control-law synthesis

Nonlinear Dynamics of a Beam on Elastic Foundation

The nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing the oscillations of flexural structures vibrating on nonlinear supports and then it can be considered as a simple investigation for the analysis of more complex systems of the same type. Indeed, the possibility of the model to exhibit actually interesting nonlinear phenomena (primary, superharmonic, subharmonic and internal resonances) has been shown in a range of feasibility of the physical parameters. The singular perturbation approach is used to study both the free and the forced oscillations; specifically two parameter families of stationary solutions are obtained for the forced oscillations.

Linearized Aeroelastic Analysis for a Launch Vehicle in Transonic Flight Conditions

The purpose of the present work is the development of a linearized aeroelastic modeling and analysis for a launch vehicle in the neighborhood of a transonic flight condition. A two-dimensional airfoil transonic case selected from the technical literature (specifically, a MBB-A3 supercritical airfoil in unsteady transonic regime) has been studied to validate the procedure for identifying the linearized unsteady aerodynamics. The present methodology has been successively performed for the system identification of the linearized aerodynamics of the VEGA European small launch vehicle in a transonic flow phase and in presence of an angle of attack. This has been achieved by performing several prescribed modal-transient boundary conditions on a Euler-based computational-fluid-dynamics code and postprocessing the input/output data in the frequency domain. Finally, both a standard eigenanalysis and an iterative eigenanalysis have been performed to study the aeroelastic stability on the linearized model of the launch vehicle in transonic flow. The nature of the methodology is quite general and can be applied in the neighborhood of any arbitrary parametric flight condition of a launch vehicle.

Aeroelastic Sensitivity Analyses for Flutter Speed and Gust Response

Two methods for the aeroelastic eigensensitivity analysis and the sensitivity analysis of an aeroelastic discrete-gust response have been developed. Finite state modeling of the unsteady aerodynamics allows one to determine explicitly the aeroelastic sensitivity with respect to a structural design variable and the aeroelastic behavior with respect to other design variables such as fuel weight, wing stiffness, and engine location. An analytical method based on the matched filter theory has been developed that allows one to estimate the sensitivity, with respect to the same design variable, of the maximum peak reached by the gust response due to a discrete gust. This approach allows one to evaluate the maximum value of the response corresponding to a discrete-gust input once the energy level of the input has been established. The sensitivity of this maximum value with respect to an aeroelastic-design variable can be evaluated too. The structural and aerodynamic contributions to the sensitivity have been separately identified following several levels of approximation. Numerical results, in the case of an ultrahigh capacity aircraft wing, are presented. Because of the large flexibility of the wing, the aeroelastic behavior has been included in the stability margin estimate and in the gust response. The application limits of the sensitivity approximations are discussed. The proposed approach, which uses structural and aerodynamic data by standard codes, could be useful in the preliminary design to evaluate and preestimate the aeroelastic performances.

Multidisciplinary Design and Optimization for Fluid-Structure Interactions

The paper presents an introductory overview of modeling techniques used by the authors for MDO–PD (MultiDisciplinary Optimization – Preliminary Design). The algorithms used by the authors in their MDO–PD code for modeling aerodynamics and aeroelasticity are reviewed. For the aerodynamic analysis, a boundary–element potential–flow method is used (for simplicity, only the incompressible–flow formulation is presented). The methodology is geared specifically towards MDO–PD for civilian aircraft. The numerical formulation is applied to a specific, highly–innovative aircraft configuration proposed by Frediani, which has, as a distinguishing feature, a low induced drag. A comparison with an MDO-PD of a standard wing configuration has been included.Copyright

Linearized Aeroelastic Gust Response Analysis of a Launch Vehicle

Amethodology for aeroelastic gust response of launch vehicles inflight is developedbyusing apreviously validated aeroelastic stability analysis. The effects on the aeroelastic vibrations of a launch vehicle encountering a wind gust while operating at a particular supersonic flight condition are determined. A linearized dynamic aeroelastic analysis of the launch vehicles is performed using the previously developed procedure, but this time in supersonic flow. Then, the pressure on the moving launcher surface resulting from the combined motion induced by each elastic mode is obtained from the solution of the Euler equation. These effects are superimposed to determine the combined aerodynamic effects of all themodes. Thus, a generalized aerodynamic forcematrix of the aerodynamic loads caused by themotion of the launch vehicles (rigid body, aswell as elastic deformations) and the effect of a gust encountered in the flight is constructed. Finally, a generalized (iterative) eigenvalue analysis is performed to evaluate the aeroelastic stability of the linearizedmodel of the launch vehicles, operating at the prescribedflowconditions,when it encounters a gust. This approach, along with the use the matched-filter theory on the resulting frequency response function, allows one to evaluate the effects of the worst-case excitation on the launch vehicle’s aeroelastic response. The methodology has been applied to predict successfully the aeroelastic stability of LYRA launch vehicles when it flies through transverse gusts.

Sensitivity Analysis for the Dynamic Aeroelasticity of a Launch Vehicle

launcherintermsofthe firstnonzeronaturalfrequenciesandmodesofvibrationiscarriedout.Moreover,areducedorder model for the unsteady transonic aerodynamics is obtained, performing several prescribed modal transient boundary conditions by laminar-based computational fluid dynamics. Thus, a modal input/output system identification for the aerodynamics, performed in the frequency domain, allows one to identify the linearized unsteady aerodynamic operator in the neighborhood of the specific transonic flight condition. Both the structural andaerodynamic modelsare finally employedin the aeroelastic coupledmodel given bythe generalized Lagrangian equations of motion. An eigenanalysis, in terms of aeroelastic-system poles and complex eigenvectors on the linearized model, is performed to check the local dynamic stability of the launch vehicle. Finally, the proposed approach also allows one to give an evaluation of the uncertainty in the obtained stability scenario in terms of perturbing flight parameters like angle of attack, Mach number, flight speed, and air density.

Aeroelastic Response of Composite Aircraft Swept Wings Impacted by a Laser Beam

A closed-form solution for the thermoaeroelastic response of an aircraft swept wing made of advanced composite materials and exposed to a thermal impact generated by a laser beam is presented. For the aircraft wing, an advanced one-dimensional structural model that includes a number of nonclassical effects, such as transverse shear, warping inhibition, and thermoelastic anisotropy of constituent materials, is developed. It is supposed that the wing is immersed in an incompressible flowfield whose speed is below the flutter critical speed of the system. The solution of the problem has been obtained analytically in the space-time Laplace transform domain. Within this approach, the problem is reduced to the solution of an algebraic equation system in the transformed kinematical unknowns that is afterward inverted in the physical space. Although confined to the dynamic aeroelastic response, the approach of the dynamic response can provide important information on the conditions yielding the occurrence of the flutter instability.