Prediction of statistical dynamics of thermally buckled composite panels

Abstract

In hypersonic flights, a thermal loading reaching up to 2000° F and acoustic loads in the anticipated range of 135-175dB are considered for the thermal-acoustic structural fatigue. In this paper, we report the numerical simulation of composite buckled panels heated up to 2000 °F over the sound pressure range of 120-150dB. What is new is imposing a large temperature differential across the panel thickness, which is usually found in thermal protection skin panels. We have found that not only the rms displacement and stress/strain are independent of the sound pressure at high temperatures, but they obey simple temperature relations as the plate temperature rises. This is due to that statistical panel dynamics are governed by the static snap-through displacement at high temperatures. INTRODUCTION For high performance military aircraft and future high-speed civil transports, certain structural skin components are subjected to very large acoustic loads in an elevated thermal environment [1]. This is because high-speed flights call for very powerful propulsions and thereby engendering acoustic loads in the anticipated range of 135-175dB. More importantly, because of the aerodynamic heating in hypersonic flights and the modern design trend in integrating propulsion sub-systems into the overall vehicular configuration, some structural components must operate at a high temperature above 2000°F. Hence, the dual effect of thermal and acoustic loading has given rise to the so-called thermal-acoustic structural fatigue [2,3]. Generally, raising the panel temperature uniformly but with an immovable edge boundary constraint would *Supported by AFOSR New World Vista and the laboratory Extreme Environments core technology. This paper is declared a work of US Government and is not subject to copyright protection in the United States. result in thermal buckling, just as one observes flexural buckling as the inplane stress along plate edges is increased beyond a certain critical value. This equivalence has been recognized [4,5] and exploited in analytical and experimental investigations of the thermal-acoustic structural fatigue [6,7]. Under the acoustic loading of 140-160dB in the NASA's Thermal Acoustic Fatigue Apparatus, Ng and Clevenson [8] have measured strain root-mean-square (rms) values and power spectral densities on an aluminum plate heated up to 250°F. More recently, Istenes et al. [9] reported strain measurements on a graphite 8-ply composite plate excited by a shaker. Clearly, Ng and his colleagues [7,8,10] were the first to achieve sufficient plate heating to observe the erratic snap-through under random excitations. Further, they pointed out that certain of the plate experiment may be understood by a single-mode model of plate equations. We therefore initiated a study of the single-mode equation for a thermally buckled isotropic plate, in which are clearly identified three thermal terms [11]. Namely, the uniform plate temperature rise above room temperature, temperature variation over the midplane of plate, and temperature gradient across the plate thickness. The first two contribute to thermal expansion and hence thermal buckling, whereas the third thermal term introduces an additional forcing. In the nonlinear dynamics vernacular, the single well potential energy of prebuckled plate splits into a double well after buckling, yet symmetry still holds. The role played by a temperature gradient across the plate thickness is to skew the symmetric potential energy, just as does the presence of structural imperfection [12]. Then, in terms of distributions, the displacement distribution of a prebuckled plate has a single peak, but it is bimodal after the plate buckles. Nevertheless, the displacement distributions, unior bi-modal, are symmetric when no temperature gradient exists across the plate thickness [13]. In contrast, because of the