Study of Static and Dynamic Stability of an Exponentially Tapered Circular Revolving Beam Exposed to a Variable Temperature Grade under Several Boundary Arrangements

Abstract

This research work is concerned with the static and dynamic stability study of an exponentially tapered revolving beam having a circular cross-section exposed to an axial live excitation and a variable temperature grade. The stability is analysed for clamped-clamped, clamped-pinned, and pinned-pinned end arrangements. Hamilton’s principle is used to develop the equation of motion and accompanying end conditions. Then, the non-dimensional form of the equation of motion and the end conditions are found. Galerkin’s process is used to find a number of Hill’s equations from the non-dimensional equations. The parametric instability regions are acquired by means of the Saito-Otomi conditions. The consequences of the variation parameter, revolution speed, temperature grade, and hub radius on the instability regions are examined for both static and dynamic load case and represented by a number of plots. The legitimacy of the results is tested by plotting different graphs between displacement and time using the Runge-Kutta fourth-order method. The results divulge that the stability is increased by increasing the revolution speed; however, an increase in the variation parameter leads to destabilization in the system and for same parameters, the stability is less in the case of a variable temperature grade than that of a constant temperature grade condition.