A Model for Polar Shells with Thickness Extension for Aeroacoustic Applications

The paper presents a novel exact formulation for the equilibrium equations of a shell-like body, whose material fibers, or directors, are free to distend and rotate. In this formulation the use of material coordinates, proper internal constraints added ad hoc, and the virtual-work approach, allows one to reformulate the Reissner-Mindlin model as a novel one that consists of the Kirchhoff-Love model plus an additional vector equation describing the difference between the two models. The ultimate aim of this approach is directed towards the actuation ofthe thickness distension feature of a piezoelectric shell for the control of the sound radiated from the shell surface itself. In the numerical application, in order to simplify the mathematical treatment of the problem, the case of a shell infinitely long in one direction experiencing only small deformations is considered.The numerical results and the equilibrium equations are limited to statics; furthermore, the shell is assumed to be loaded by means of an external electric field imposed across the boundaries, with the electric field constant across the thickness (ie a linear electric potential). As a consequence of this hypothesis, the first Maxwell's equation that governs the electrical unknowns of the problem, is considered to be independent of (but influencing) the displacement field. This is true as well for the constitutive equations that relate the electrical displacement field with the deformations and the electric potential. Consequently, one obtains an equivalent beam model capable of describing shear effects and thickness change. Finally, it should be noted that the results areintended to demonstrate the potentiality of the model foraero-acoustic control and so a special fiber distribution is assumed throughout the main surface

Aeroelastic response of composite aircraft swept wings impacted by a laser beam

A closed form solution for the aeroelastic response of an aircraft swept wing made of advanced composite materials and exposed to a time-dependent thermal field is presented. The thermal field is supposed to be generated by a laser beam impacting the upper surface of the wing, and, within this context, an uncoupled thermo-elastic model is adopted. The wing structure is modeled as a plate-like body with appropriate internal constraints (in the sense that no thickness extension is permitted into the model) and including warping effects. Although considered in a linearized context, the structural model of the wing incorporates the transverse shear effects, the anisotropy of the constituent materials, as well as the sweep angle. It is supposed that the wing is immersed in a subsonic incompressible flow whose speed is below the flutter critical speed of the system. The solution of the problem has been obtained analytically in a double Laplace transform domain, where both the space and time co-ordinates are converted to their Laplace variable space counterparts. Within this approach, the problem is reduced to the solution of an algebraic problem in the transformed kinematical unknowns. Although this paper is confined to the study of the dynamic aeroelastic response in the subcritical flight speed regime, the approach of the dynamic response in the time domain provides important information on the occurrence of the flutter instability when the wing is exposed to a time-varying thermal field. Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved

Dynamics of Microstructured Shells with Thickness Extension

The analysis of the natural frequencies of a plate model is carried out in this paper starting from a model of shells which incorporates the effect of thickness extension and that is derived from the Virtual Work Theorem using material coordinates in the deformed configuration. Moreover, the shell is regarded as a micro-structured body whose fibers are free to rotate and distend. Finally, introducing proper internal constraints, and suitable stress resultant definitions, the equilibrium equations are reduced, in the framework of properly modified Reissner-Mindlin kinematical assumptions, to ones formally equivalent to that that can be obtained in the framework of properly modified Kirchhoff-Love hypotheses, but with additional equations describing the equilibrium in the fiber direction. Using a numerical approach based on a finite difference scheme, it is shown how the naturalfrequencies of the Reissner-Mindlin model reduce when the Kirchhoff-Love constraints are retained. In particular, results indicate that, in the limit in which the Kirchhoff-Love hypotheses tend to become valid, the numerical frequencies of the pure Reissner-Mindlin model are affected by some round-off error, whereas in the case corresponding to the formulation adopted, where the solution is sought in terms of transversal displacementand dierence between the RM and the KL rotation of the fiber, the numerical solution reproduces exactly the analytical solution, and, notably, this behavior is emphasized at the highest frequencies. Therefore, in the case in which the transverse shear is treated independently one obtains good results, whereas, in the case in which the transverse shear has to be obtained as the difference of the derivative of the transverse displacement and of the fiber rotation, the numerical solution introduces numerical errors due to the closenessof the present model to the KL kinematical hypotheses

A model for polar shells with thickness extension for aeroacoustic applications

The paper presents a novel exact formulation for the equilibrium equations of a shell-like body, whose material fibers, or directors, are free to distend and rotate, In this formulation the use of material coordinates, proper internal constraints added ad hoc, and the virtual-work approach, allows one to reformulate the Reissner-Mindlin model as a novel one that consists of the Kirchhoff-Love model plus an additional vector equation describing the difference between the two models. The ultimate aim of this approach is directed towards the actuation of the thickness distension feature of a piezoelectric shell for the control of the sound radiated from the shell surface itself. In the numerical application, in order to simplify the mathematical treatment of the problem, the case of a shell infinitely long in one direction experiencing only small deformations is considered. The numerical results and the equilibrium equations are limited to statics; furthermore, the shell is assumed to be loaded by means of an external electric field imposed across the boundaries, with the electric field constant across the thickness (ie a linear electric potential). As a consequence of this hypothesis, the first Maxwell's equation that governs the electrical unknowns of the problem, is considered to be independent of (but influencing) the displacement field. This is true as well for the constitutive equations that relate the electrical displacement field with the deformations and the electric potential. Consequently, one obtains an equivalent beam model capable of describing shear effects and thickness change. Finally, it should be noted that the results are intended to demonstrate the potentiality of the model for aero-acoustic control and so a special fiber distribution is assumed throughout the main surface. Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved

A Model for Polar Shells with Thickness Extension

AIAA 2004-197

Aerothermoelastic Response of a Functionally-Graded Aircraft Wing to Heat oads

In this paper, a coupled aerothermoelastic dynamic stability analysis of a functionally-graded composite wing featuring non-classical effects, and immersed in an incompressible gas flow is developed. Specifically, the study concerns the aerothermoelastic stability of aircraft swept wing made of advanced functionally-graded composite materials and exposed to a heat flow generated by a laser beam impacting its deformed surface. The structural model is specialized in the computations to the case of a rectangular, single-layered, swept wing made of functionally graded material (FGM) with a ceramic-metallic-ceramic phase gradient. In particular, aluminun and alumina have been chosen as metallic and ceramic phases respectively. The evaluation of the temperature field on the deformed (actual) configuration of the wing permits to address the problems of the aerothermoelastic response and stability in a coupled framework. As a result, the exact analytical expression of the aerothermoelastic response of the heated wing is obtained in the Laplace space domain and, following this, the static and dynamic aeroelastic instabilities of the wing model are determined. The obtained results indicate that the aeroelastic stability is substantially affected by the thermo-elastic coupling and that the presence of FGM can also significantly influence the aerothermoelastic behavior. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved