Luigi Morino

Perturbation and harmonic balance methods for nonlinear panel flutter.

A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clampe d plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.

Helmholtz decomposition revisited: Vorticity generation and trailing edge condition

The use of the Helmholtz decomposition for exterior incompressible viscous flows is examined, with special emphasis on the issue of the boundary conditions for the vorticity. The problem is addressed by using the decomposition for the infinite space; that is, by using a representation for the velocity that is valid for both the fluid region and the region inside the boundary surface. The motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. It is shown that at each instant of velocity discontinuity, vorticity is generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is then diffused into the surroundings: this yields that the no-slip conditions are thus automatically satisfied (since the presence of a vortex layer on the surface is required to obtain a velocity slip at the boundary). This result is then used to show that in order for the solution to the Euler equations to be the limit of the solution to the Navier-Stokes equations, a trailing-edge condition (that the vortices be shed as soon as they are formed) must be satisfied. The use of the results for a computational scheme is also discussed. Finally, Lighthills transpiration velocity is interpreted in terms of Helmholtz decomposition, and extended to unsteady compressible flows.

Stability Analysis of Nonlinear Differential Autonomous Systems with Applications to Flutter

This paper deals with the general theory of stability analysis of nonlinear differential autonomous systems of the type x=A(\)x+f(x, X), with the linear system stable (unstable) for \ *0>- T116 analysis is performed by a singular perturbation method, the multiple time scaling. The solution is obtained in the form of an asymptotic expansion in the neighborhood of the stability boundary, X= \0 . It is shown that there always exists a limit cycle, either for X \0 (stable limit cycle). The analytical expression for the limit cycle amplitude also is given. Applications to nonlinear flutter of panels and wings are included. Numerical results are in excellent agreement with existing ones.

Optimal Predictor-Corrector Method for Systems of Second-Order Differential Equations

A very general class of predictor-corrector schemes for numerically integrating a system of equations of the type x + f(x, t) = 0 is examined. This class includes the schemes obtained by combining one explicit predictor with p implicit correctors (allowing the use of a different corrector for each evaluation). Both the predictor and the correctors are assumed to be two- or three-step operators. It is shown that all of the schemes within this class are conditionally stable, that is, are stable only if the time increment A/ does not exceed a critical value. Furthermore, it is shown that the central difference scheme is the optimal one in the sense that for all the schemes within the above class, the value of Ar divided by the number of evaluations of f(x, t) is never greater than for the central difference one. The same conclusions are valid for any scheme with a characteristic equation of the type p3+ d^p2 + d 2p + d3 = 0, where dk are polynomials in (coAr)2, where co is the largest natural frequency of the system.

Dynamic behavior of fluttering two-dimensional panels on an airplanein pull-up maneuver

The governing equations, derived using Lagrangian mechanics, include geometric nonlinearities associated with the occurrence of tensile stresses, as well as coupling between the angular velocity of the maneuver and the elastic degrees of freedom. Longtime histories, phase plane plots, and power spectra of the response are the dynamics tools used in studying the system considered here. The effect of the maneuver on the flutter speed and on the amplitude of the limit cycle are presented for different load conditions. A new type of limit cycle has been observed for the nonmaneuvering case. It is also shown that the presence of a maneuver can transform the panel response from a fixed point into a simple periodic or even chaotic state. It can also suppress the periodic character of the motion, transforming the response into a fixed point. For a prescribed time-dependent maneuver, a remarkable response transition between the different types of limit cycles is presented.

Vector green's function method for unsteady Navier-Stokes equations

SommarioSi riformula in termini generali il metodo della funzione di Green per estenderlo al caso di equazioni vettoriali e non lineari. In particolare si ricavano le espressioni della formula di Green e della rappresentazione integrale della soluzione per le equazioni di Navier Stokes non stazionarie. Si ottengono le soluzioni fondamentali in forma chiusa sia per il caso di fluidi comprimibili che incomprimibili. Si discutono infine brevemente i lati positivi ed i possibili limiti della metodologia illustrata.SummaryThe Greens function method is reformulated in general terms to treat vector unsteady and nonlinear equations. The particular expressions of the adjoint linear operator, the Greens formula and the integral representation of the solution are derived for unsteady Navier Stokes equations. The appropriate fundamental solutions for incompressible and for certain compressible flows have been obtained in closed form. Both the positive features and the possible limits of the method are briefly outlined.

Community Noise Impact on the Conceptual Design of Innovative Aircraft Configurations

The paper presents recent work to include community noise considerations based on costs in an existing framework for MDO-CD (Multi-Disciplinary Optimization for Conceptual Design) of highly innovative configurations for civil aviation. The paper presents an extension of the formulation used in the code MAGIC (Multidisciplinary Analysis and desiGn of Innovative Configurations), developed by the authors and their collaborators, which comprises models for structures, aerodynamics, aeroelasticity, flight mechanics, and propulsion, along with the recent addition of aeroacoustics and life-cycle costs models. The community noise is treated here as a cost and included in the objective. It should be noted that the cost of noise depends a lot upon government regulation and community perception, and hence is not known during the conceptual design phase. Thus, the paper presents a parametric study of conceptual design based on life-cycle costs, with the cost of noise used as a varying parameter. The paper includes applications to the optimization of innovative configurations, such as the box-wing configuration (Prantl-Plane) proposed by Frediani. The box-wing configuration is particularly interesting because of the greatly reduced induced drag. This implies a reduction of the power required, and hence a reduction of community noise.

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

Community Noise Considerations in Multidisciplinary Optimization for Preliminary Design of Innovative Configurations

The paper proposes an approach for MDO/PD (Multi‐Disciplinary Optimization for Preliminary Design) of innovative aircraft configurations in the presence of aeroacoustics considerations. The specific innovative configuration of interest here is a box‐wing aircraft denoted as the Prandtl-Plane, which has, as a distinguishing feature, a low induced drag. Thus, one of the advantages is less noise at take-o. Hence here, as a very first step towards our long range goal, we apply the algorithm to the optimization of the Prandtl-Plane with the objective function modified by adding an empirical term representative of the take-o noise. The fact that the configurations are innovative requires that the formulation be first‐principle based, since in this case the designer cannot rely upon past experience. The mathematical model used is reviewed. The formulation is based upon an integrated modeling of structures, aerodynamics, aeroelasticity and flight mechanics developed primarily by the authors. The methodology is geared specifically towards MDO/PD for civil aviation. The emphasis here is on wing design ‐ the fuselage is assumed as given. The stress analysis is based on finite elements for beams, whereas the structural dynamics is based upon natural modes, which are evaluated by the same finite‐ element algorithm. For the aerodynamic analysis, a boundary‐element quasi‐potential‐flow method is used for both steady and unsteady aerodynamics. An elementary boundary layer model is used to include the steady viscous eects and estimate the drag. A reduced order model (ROM) for the unsteady‐aerodynamics forces is used in dynamic aeroelasticity. Numerical results on the optimized Prandtl-Plane configuration are included. It is shown how the addition of the community-noise term in the objective function aects the configuration and produces noise reduction.

A New Potential—Vorticity Decomposition for the Boundary—Element Analysis of Viscous Flows

This paper deals with a computational formulation for the analysis of viscous flows about arbitrary bodies. A new decomposition for unsteady compressible viscous flows is presented in Morino5, where the theoretical issues, such as vorticity generation and the relationship betweeen viscous and inviscid flows, are emphasised. Here, we focus on the issues arising in the use of the decomposition as a computational technique.