Comput Mech (2008) 41:325–334 DOI 10.1007/s00466-007-0188-4 ORIGINAL PAPER Non-linear panel flutter for temperature-dependent functionally graded material panels Hesham Hamed Ibrahim · Mohammad Tawfik · Mohammed Al-Ajmi Received: 29 September 2006 / Accepted: 23 April 2007 / Published online: 13 July 2007 © Springer-Verlag 2007 Abstract The non-linear flutter and thermal buckling of an FGM panel under the combined effect of elevated tem- perature conditions and aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The aerodynamic pressure is modeled using the quasi-steady first order piston theory. The governing non-linear equations are obtained using the prin- cipal of virtual work adopting an approach based on the ther- mal strain being a cumulative physical quantity to account for temperature dependent material properties. This system of non-linear equations is solved by Newton–Raphson nume- rical technique. It is found that the temperature increase has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decrea- sing the volume fraction enhances flutter characteristics but this is limited by structural integrity aspect. The presence of aerodynamic flow results in postponing the buckling tempe- rature and in suppressing the post buckling deflection while the temperature increase gives way for higher limit cycle amplitude. H. H. Ibrahim Vibration and Acoustics Control Center, Noon for Research and Development, noonrd.org, Cairo, Egypt e-mail: Hesham.ibrahim@noonrd.org M. Tawfik (B ) Modeling and Simulation in Mechanics Department, German University in Cairo, Cairo, Egypt e-mail: Mohammad.Tawfik@guc.edu.eg M. Al-Ajmi Mechanical Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait e-mail: malajmi@kuc01.kuniv.edu.kw Keywords Functionally graded materials · Panel flutter · Thermal buckling 1 Introduction Panel flutter is a self-excited oscillation of a plate or a shell in supersonic flow. Because of aerodynamic loading on the panel, two eigen modes of the structure merge and lead to this dynamic instability. Panel flutter differs from wing flut- ter only in that the aerodynamic force resulting from the air flow acts only on one side of the panel [1]. Supersonic flutter of plates and shells was recognized to be an important aspect of the design of high speed vehicles when Jordan [2] obser- ved that a number of the early V-2 rocket failures were due to panel flutter. Since then, extensive analytical and experimen- tal research on that subject has been performed. A common remedy to the flutter problem is to stiffen those panels in danger of flutter, a method that usually introduces additional weight to the design. Thin plates are a commonly used form of structural com- ponents especially in aerospace vehicles, such as high-speed aircraft, rockets, and spacecrafts, which are subjected to ther- mal loads due to aerodynamic and/or solar radiation heating. This results in a temperature distribution over the surface and thermal gradient through the thickness of the plate. The presence of these thermal fields results in a flutter motion at lower dynamic pressure or a larger limit-cycle amplitude at the same dynamic pressure. In addition, a high temperature rise may cause large thermal deflections (thermal buckling) of the skin panels, which could affect flutter response [3]. Accordingly, it is important to consider the interactive effect of both aforementioned failure characteristics (flutter and buckling). However, it appears that in most past studies, the 123