Parametric Stability Analysis of a Parabolic-Tapered Rotating Beam Under Variable Temperature Grade

Abstract

The static and dynamic stability of a parabolic-tapered beam of circular cross-section subjected to an axial alive load and rotating in the X-Y plane about the Z-axis is analyzed cosidering a variable temperature grade along the centroidal axis of the beam as the beam is in steady state condition. The stability is analyzed for clamped-clamped and pinned-clamped boundary conditions. The parametric instability regions are acquired by means of Saito-Otomi conditions. The consequences of variation parameter, revolution speed, temperature grade and boundary conditions on the instability regions are examined for dynamic load and static buckling loads for 1st, 2nd and 3rd modes and are represented by a number of graphs. The results divulge that the stability is increased by increasing revolution speed; however, increase in thermal grade and the variation parameter leads to destabilize the converging system for all boundary conditions. This research can be useful for vibration isolation of rotating non-uniform beams with high surrounding temperature and moderate rotational speeds and the design of rotor blades with high strength to weight ratio by choosing the suitable parameters obtained from this computational analysis.