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Part II of the two‐part paper describes an aeroelastic analysis program and its application for stability computations of turbomachinery blade rows. Unsteady Euler or Navier‐Stokes equations are solved on dynamically deforming, body fitted, and grid to obtain the aeroelastic characteristics. Blade structural response is modeled using a modal representation of the blade and the work‐per‐cycle method is used to evaluate the stability characteristics. Non‐zero inter‐blade phase angle is modeled using phase‐lagged boundary conditions. Results are presented for a flat plate helical fan, a turbine cascade and a high‐speed fan, to highlight the aeroelastic analysis method, and its capability and accuracy. Obtained results showed good correlation with existing experimental, analytical and numerical results. Numerical analysis also showed that given the computational resources available currently, engineering solutions with good accuracy are possible using higher fidelity analyses.

Transonic flutter and active flap control, in two dimensions, are simulated by coupling independent structural dynamic and inviscid aerodynamic models, in the time domain. A flight control system, to actively control the trailing edge flap motion, has also been incorporated and, since this requires perfect synchronisation of fluid, structure and control signal, the “strong” coupling approach is adopted. The computational method developed is used to perform transonic aeroelastic and aeroservoelastic calculations in the time domain, and used to compute stability (flutter) boundaries of 2D wing sections. Open and closed loop simulations show that active control can successfully suppress flutter and results in a significant increase in the allowable speed index in the transonic regime. It is also shown that active control is still effective when there is free‐play in the control surface hinge. Flowfield analysis is used to investigate the nature of flutter and active control, and the fundamental importance of shock wave motion in the vicinity of the flap is demonstrated.

The purpose of this paper is to present the development and application of a numerical formulation for the structural dynamics and aeroelastic analysis of new generation helicopter and tiltrotor rotor blades. These are characterized by a curvilinear elastic axis, typically with the presence of tip sweep and anhedral angles.

The structural dynamics model implemented is based on nonlinear, flap‐lag‐torsion, rotating beam equations that are valid for slender, homogeneous, isotropic, non‐uniform, twisted blades undergoing moderate displacements. A second‐order approximation scheme for strain‐displacement is adopted. Aerodynamic contributions for aeroelastic applications are derived from sectional theories, with inclusion of wake inflow models to take into account three‐dimensional effects. The numerical integration is obtained through implementation within the COMSOL Multiphysics Finite‐Element‐Method (FEM) software code, considering the elastic axis of arbitrary curvilinear shape.

The computational tool developed is validated by comparisons with results available in the literature. These demonstrate the capability of the tool to accurately predict structural dynamics and aeroelastic behavior of curved‐axis rotor blades. In particular, the influence of sweep and anhedral angles at the blade tip is successfully captured.

The numerical tool developed is limited to the analysis of isotropic blades, with a simple sectional aerodynamic modeling for aeroelastic applications. However, the flexibility of the process through which the proposed tool has been developed is such that a moderate effort is required for its extension to composite blades and more accurate aerodynamic loads predictions.

The proposed computational solver is a reliable tool for preliminary design and optimal design processes of helicopter and tiltrotor rotor blades.

Computational tools for rotors with advanced‐geometry blades are not commonly available. Therefore, the presentation of a successful way to implement structural dynamics/aeroelastic mathematical formulations for rotor blades with curvilinear elastic axis in highly flexible, multiphysics, FEM‐based, commercial software may be of interest for designers and researchers.

To propose an integrated algorithm for aerodynamic shape optimization of aircraft wings under the effect of aeroelastic deformations at supersonic regime.

A methodology is proposed in which a high‐fidelity aeroelastic analyser and an aerodynamic optimizer are loosely coupled. The shape optimizer is based on a “CAD‐free” approach and an exact gradient method with a single adjoint state. The global iterative process yields optimal shapes in the at‐rest condition (i.e. with the aeroelastic deformations substracted).

The methodology was tested under different conditions, taking into account a combined optimization goal: to reduce the sonic boom production, while preserving the aerodynamic performances of flexible wings. The objective function model contains both aerodynamic parameters and an acoustic term based on the sonic boom downwards emission.

This paper proposes a shape optimization methodology developed by researchers but aiming at the final strategic goal of creating tools that can be really integrated in design processes.

The paper presents an original loosely coupled method for the shape optimization of flexible wings in which recent and modern techniques are used at different levels of the global algorithm: the aerodynamic optimizer, the aeroelastic analyser, the shape parametrization and the objective function model.

The purpose of this paper is to analyze the stability of aeroelastic systems using a novel reduced order aeroelastic model.

The proposed aeroelastic model is a reduced-order model constructed based on the aerodynamic model identification using the generalized aerodynamic force response and the unsteady boundary element method in various excitation frequency values. Due to the low computational cost and acceptable accuracy of the boundary element method, this method is selected to determine the unsteady time response of the aerodynamic model. Regarding the structural model, the elastic mode shapes of the shell are used.

Three case studies are investigated by the proposed model. In the first place, a typical two-dimensional section is introduced as a means of verification by approximating the Theodorsen function. As the second test case, the flutter speed of Advisory Group for Aerospace Research and Development 445.6 wing with 45° sweep angle is determined and compared with the experimental test results in the literature. Finally, a complete aircraft is considered to demonstrate the capability of the proposed model in handling complex configurations.

The paper introduces an algorithm to construct an aeroelastic model applicable to any unsteady aerodynamic model including experimental models and modal structural models in the implicit and reduced order form. In other words, the main advantage of the proposed method, further to its simplicity and low computational effort, which can be used as a means of real-time aeroelastic simulation, is its ability to provide aerodynamic and structural models in implicit and reduced order forms.

Ground vibration testing (GVT) results can be used as system parameters for predicting flutter, which is essential for aeroelastic clearance. This paper aims to compute GVT-based flutter in time domain, using unsteady air loads by matrix polynomial approximations.

The experimental parameters, namely, frequencies and mode shapes are interpolated to build an equivalent finite element model. The unsteady aerodynamic forces extracted from MSC NASTRAN are approximated using matrix polynomial approximations. The system matrices are condensed to the required shaker location points to build an aeroelastic reduced order state space model in SIMULINK.

The computed aerodynamic forces are successfully reduced to few input locations (optimal) for flutter simulation on unknown structural system (where stiffness and mass are not known) through a case study. It is demonstrated that GVT data and the computed unsteady aerodynamic forces of a system are adequate to represent its aeroelastic behaviour.

Airforce of every nation continuously upgrades its fleet with advanced weapon systems (stores), which demands aeroelastic flutter clearance. As the original equipment manufacturers does not provide the design data (stiffness and mass) to its customers, a new methodology to build an aeroelastic system of unknown aircraft is devised.

A hybrid approach is proposed, involving GVT data to build an aeroelastic state space system, using rationally approximated air loads (matrix polynomial approximations) computed on a virtual FE model for ground flutter simulation.

The purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.

First of all a 1D model problem is selected, for which both the fluid and structural behavior are represented through a minimum number of parameters. Different coupling algorithm and time integration schemes are then applied to the simplified model problem and their properties are discussed depending on the values assumed by the parameters. Both exact and approximate time integration schemes are considered in the same framework so to allow an assessment of the different sources of error.

The properties of staggered coupling schemes are confirmed. An insight on the convergence behavior of iterative coupling schemes is provided. A technique to improve such convergence is then discussed.

All the results are proved for a given family of time integration schemes. The technique proposed can be applied to other families of time integration techniques, but some of the analytical results need to be reworked under this assumption.

The problems that are commonly encountered in FSI can be justified by simple arguments. It can also be shown that the limit at which trivial iterative schemes experience convergence difficulties is very close to that at which staggered schemes become unstable.

All the results shown are based on simple mathematics. The problems are presented so to be independent of the particular choice for the solution of the fluid flow.

The purpose of this paper is to present a formulation that couples equivalent plate and beam models for aircraft structures analysis, suitable in conceptual design in which fast model generation and efficient analysis capability are required.

Assembling the complete model with common techniques such as Lagrange multipliers or penalty function method would require a solver capable of handling the combined set of linear equation. The alternative approach proposed here is based on a static reduction of the beam model at specified connection points and the subsequent “embedding” into the equivalent plate model using a coordinate transformation, translating physical dfs in Ritz coordinates, i.e. polynomial coefficients. Displacements and forces on beam elements are recovered with the inverse transformation once the solution is computed.

An aeroelastic trim analysis on a Transonic CRuiser (TCR) civil aircraft conceptual model validates the hybrid model: as the TCR features a slender flexible fuselage and a wide root chord wing, the capability to reduce the beam model for the fuselage at more than one connection point improved aeroelastic corrections to steady longitudinal aerodynamic derivatives.

Although the equivalent model proposed is simpler than others found in literature, it offers automatic mesh generation capabilities, and it is fully integrated into an aeroelastic framework. The hybrid model represents an enhancement allowing both dynamical and static analyses.

To provide a general review of the flight flutter test techniques utilized in aeroelastic stability flight testing of aircraft, and to highlight the key items involved in flight flutter testing of aircraft, by emphasizing all the main information processed during the flutter stability verification based on flight test data.

Flight flutter test requirements are first reviewed by referencing the relevant civil and military specifications. Excitation systems utilized in flight flutter testing are overviewed by stating the relative advantages and disadvantages of each technique. Flight test procedures followed in a typical flutter flight testing is described for different air speed regimes. Modal estimation methods, both in frequency and time domain, used in flutter prediction are surveyed. Most common flight flutter prediction methods are reviewed. Finally, key considerations for successful flight flutter testing are noted by referencing the related literature.

Online, real time monitoring of flutter stability during flight testing is very crucial, if the flutter character is not known a priori. Techniques such as modal filtering can be used to uncouple response measurements to produce simplified single degree of freedom responses, which could then be analyzed with less sophisticated algorithms that are more able to run in real time. Frequency domain subspace identification methods combined with time‐frequency multiscale wavelet techniques are considered as the most promising modal estimation algorithms to be used in flight flutter testing.

This study gives concise but relevant information on the flight flutter stability verification of aircraft to the practicing engineer. The three important steps used in flight flutter testing; structural excitation, structural response measurement and stability prediction are introduced by presenting different techniques for each of the three important steps. Emphasis has been given to the practical advantages and disadvantages of each technique.

This paper offers a brief practical guide to all key items involved in flight flutter stability verification of aircraft.

This study aims to analyse slender thin-walled anisotropic box-beams. Fiber-reinforced laminated composites could play an important role in the design of current and future generations of innovative civil aircrafts and unconventional unmanned configurations. The tailoring characteristics of these composites not only improve the structural performance, and thus reduce the structural weight, but also allow possible material couplings to be made. Static and dynamic aeroelastic stability can be altered by these couplings. It is, therefore, necessary to use an accurate and computationally efficient beam model during the preliminary design phase.

A proper structural beam scheme, which is a modification of a previous first-level approximation scheme, has been adopted. The effect of local laminate stiffness has been investigated to check the possibility of extending the analytical approximation to different structural configurations. The equivalent stiffness has been evaluated for both the case of an isotropic configuration and for simple thin-walled laminated or stiffened sections by introducing classical thin-walled assumptions and the classical beam theory for an equivalent system. Coupling effects have also been included. The equivalent analytical and finite element beam behaviour has been determined and compared to validate the considered analytical stiffness relations that are useful in the preliminary design phase.

The work has analyzed different configurations and highlighted the effect of flexural/torsion couplings and a local stiffness effect on the global behaviour of the structure. Three types of configurations have been considered, namely, a composite wing box configuration, with and without coupling effects; a wing box configuration with sandwich and cellular constructions; and a wing box with stiffened panels in a coupled or an uncoupled configuration. An advanced aluminium experimental test sample has also been described in detail. Good agreement has been found between the theoretical and numerical analyses and the experimental tests, thus confirming the validity of the analytical relations.

The equivalent beam behaviour that has been determined and the stiffness calculation procedure that has been derived could be useful for future dynamic and aeroelastic analyses.

The article presents an original derivation of the sectional characteristics of a thin-walled composite beam and a numerical/experimental validation.