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Volume 1, Number 3, July 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin\'s polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli\'s and Timoshenko\'s can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.

Key Words
beam structure; hierarchical modelling; closed form solution; buckling load

(1) Gaetano Giunta, Salim Belouettar, Fabio Biscani:
Centre de Recherche Public Henri Tudor, 29, av. John F. Kennedy, L-1855, Luxembourg-Kirchberg, Luxembourg;
(2) Erasmo Carrera:
Politecnico di Torino, 24, Duca degli Abruzzi, 10129, Turin, Italy.

Accuracy of a reconstruction technique assuming a constant characteristic exhaust velocity (c*) efficiency for reducing hybrid rocket firing test data was examined experimentally. To avoid the difficulty arising from a number of complex chemical equilibrium calculations, a simple approximate expression of theoretical c* as a function of the oxidizer to fuel ratio (ξ) and the chamber pressure was developed. A series of static firing tests with the same test conditions except burning duration revealed that the error in the calculated fuel consumption decreases with increasing firing duration, showing that the error mainly comes from the ignition and shutdown transients. The present reconstruction technique obtains ξ by solving an equation between theoretical and experimental c* values. A difficulty arises when multiple solutions of ξ exists. In the PMMA-LOX combination, a ξ range of 0.6 to 1.0 corresponds to this case. The definition of c* efficiency necessary to be used in this reconstruction technique is different from a c* efficiency obtained by a general method. Because the c* efficiency obtained by average chamber pressure and ξ includes the c* loss due to the ξ shift, it can be below unity even when the combustion gas keeps complete mixing and chemical equilibrium during the entire period of a firing. Therefore, the c* efficiency obtained in the present reconstruction technique is superior to the c* efficiency obtained by the general method to evaluate the degree of completion of the mixing and chemical reaction in the combustion chamber.

Key Words
hybrid rocket; static firing test; data reduction

(1) Harunori Nagata, Masashi Wakita, Tsuyoshi Totani:
Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan;
(2) Hisahiro Nakayama, Mikio Watanabe:
Graduate School of Engineering, Hokkaido University, Kita 13 Noshi 8, Sapporo 060-8628, Japan.

An advanced model for the linear flutter analysis is introduced in this paper. Higher-order beam structural models are developed by using the Carrera Unified Formulation, which allows for the straightforward implementation of arbitrarily rich displacement fields without the need of a-priori kinematic assumptions. The strong form of the principle of virtual displacements is used to obtain the equations of motion and the natural boundary conditions for beams in free vibration. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick-Williams algorithm to carry out free vibration analyses. According to the doublet lattice method, the natural mode shapes are subsequently used as generalized motions for the generation of the unsteady aerodynamic generalized forces. Finally, the g-method is used to conduct flutter analyses of both isotropic and laminated composite lifting surfaces. The obtained results perfectly match those from 1D and 2D finite elements and those from experimental analyses. It can be stated that refined beam models are compulsory to deal with the flutter analysis of wing models whereas classical and lower-order models (up to the second-order) are not able to detect those flutter conditions that are characterized by bending-torsion couplings.

Key Words
flutter; higher-order models; unified formulation; beams; doublet lattice method; dynamic stiffness method

(1) Alfonso Pagani:
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy;
(2) Marco Petrolo:
School of Aerospace, Mechanical and Manufacturing Engineering RMIT University, Bundoora VIC 3083, Australia;
(3) Erasmo Carrera:
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (Currently at SAMME, RMIT University, Melbourne, Australia).

Environmental impact of aircraft emissions can be addressed in two ways. Air quality impact occurs during landings and takeoffs while in-flight impact during climbs and cruises influences climate change, ozone and UV-radiation. The aim of this paper is to investigate airports related local emissions and fuel consumption (FC). It gives flight path optimization model linked to a dispersion model as well as numerical methods. Operational factors are considered and the cost function integrates objectives taking into account FC and induced pollutant concentrations. We have compared pollutants emitted and their reduction during LTO cycles, optimized flight path and with analysis by Döpelheuer. Pollutants appearing from incomplete and complete combustion processes have been discussed. Because of calculation difficulties, no assessment has been made for the soot, H2O and PM2.5. In addition, because of the low reliability of models quantifying pollutant emissions of the APU, an empirical evaluation has been done. This is based on Benson\'s fuel flow method. A new model, giving FC and predicting the in-flight emissions, has been developed. It fits with the Boeing FC model. We confirm that FC can be reduced by 3% for takeoffs and 27% for landings. This contributes to analyze the intelligent fuel gauge computing the in-flight fuel flow. Further research is needed to define the role of NOx which is emitted during the combustion process derived from the ambient air, not the fuel. Models are needed for analyzing the effects of fleet composition and engine combinations on emission factors and fuel flow assessment.

Key Words
environmental impact; airports; aircraft; fuel consumption; pollutant emissions

French Institute of Science and Technology for Transport, Development and Networks, AME Department, Transport and Environment Laboratory, 25, avenue Francois Mitterrand 69500 Bron, France.

The paper presents the development of numerical models referred to a morphing actuated aileron. The structural solution adopted consists of an internal part made of a composite chiral honeycomb that bears a flexible skin with an adequate combination of flexural stiffness and in-plane compliance. The identification of such structural frame makes possible an investigation of different actuation concepts based on diffused and discrete actuators installed in the skin or in the skin-core connection. An efficient approach is presented for the development of aeroelastic condensed models of the aileron, which are used in sensitivity studies and optimization processes. The aerodynamic performances and the energy required to actuate the morphing surface are evaluated and the definition of a general energetic performance index makes also possible a comparison with a rigid aileron. The results show that the morphing system can exploit the fluid-structure interaction in order to reduce the actuation energy and to attain considerable variations in the lift coefficient of the airfoil.

Key Words
smart structures; chiral topologies; morphing structures; aeroelastic design

Alessandro Airoldi, Giuseppe Quaranta, Alvise Beltramin and Giuseppe Sala:
Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156, MILANO, ITALY.

This paper deals with the early development of the Anuloid, an innovative disk-shaped VTOL aircraft. The Anuloid concept is based on the following three main features: the use of a ducted fan powered by a turboshaft for the lift production to take-off and fly; the Coanda effect that is developed through the circular internal duct and the bottom portion of the aircraft to provide further lift and control capabilities; the adoption of a system of ducted fixed and swiveling radial and circumferential vanes for the anti-torque mechanism and the flight control. The early studies have been focused on the CFD analysis of the Coanda effect and of the control vanes; the flyability analysis of the aircraft in terms of static performances and static and dynamic stability; the preliminary structural design of the aircraft. The results show that the Coanda effect is stable in most of the flight phases, vertical flight has satisfactory flyability qualities, whereas horizontal flight shows dynamic instability, requiring the development of an automatic control system.

Key Words
VTOL; Coanda effect; aircraft design; flyability analysis; CFD

(1) Marco Petrolo, Erasmo Carrera:
School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora VIC 3083, Australia;
(2) Erasmo Carrera:
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy;
(3) Michele D\'Ottavio:
Laboratoire Energétique, Mecanique et Electromagnétisme (LEME), Université Paris Ouest, 50 rue de Sèvres, 92410 Ville d\'Avray, France;
(4) Coen de Visser:
Control and Simulation Division, Faculty of Aerospace Engineering, Delft University of Technology, Delft 2600GB,The Netherlands;
(5) Zdenĕk Pátek:
VZLÚ Aerospace Research and Test Establishment, Prague, Czech Republic;
(6) Zdenek Janda:
6FESA s.r.o., Prague, Czech Republic.

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