Thin-Walled Beams Made of Functionally Graded Materials and Operating in a High Temperature Environment: Vibration and Stability

ABSTRACT In this study, problems related to the thermoelastic modeling and behavior of thin-walled beams made of functionally graded materials (FGMs) are addressed. In this context, two structural systems are considered: (i) rotating turbomachinery blades, and (ii) thin-walled beam structures spinning about their longitudinal axis. In all these cases, the structures operate in a high temperature environment. Under the spinning speed, gyroscopic forces are generated. Although conservative in nature, under their influence, as in nonconservative systems, instabilities by flutter and divergence can occur. In this context, the implications on their vibration and instability of conservative and gyroscopic forces considered in conjunction with a temperature field that yields the degradation of elastic properties are investigated. A continuously graded variation in composition of the ceramic and metal phases across the beam wall thickness in terms of a simple power law distribution is implemented. Results highlighting the effects of the volume fraction, temperature gradient, considered in conjunction with the temperature degradation of materials properties, compressive axial load and rotational/spinning speed on vibration, and instability are presented and pertinent conclusions are drawn. The thin-walled structural beam model considered in this study is an advanced one. In this sense, in addition to the transverse shear and the secondary warping, the effect of the pretwist and nonuniformity of the beam cross-section along its span are considered. Both box-beams and circular cross-section spinning beams are considered in the analysis. Validation of the obtained results against those obtained via the Mori–Tanaka scheme is carried out, and excellent agreements are reported. In addition, issues related to the foundation and behavior of geometrically nonlinear rotating/spinning thin-walled beams build-up of FGMs and operating in a temperature field are addressed. It should be stressed that the supplied results are based entirely on the research by these authors, and that there are no parallel works in the specialized literature on rotating/spinning systems made of functionally graded materials.

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