Parametric Investigation of a Rotational Parabolic-Tapered Cantilever with Elliptical Sectional Area Exposed to Variable Thermal Gradient and Axial Dynamic Load

Designing the blades for steam turbine and gas turbine, rotor blades, robotic manipulators, horn antenna, etc., needs practical study of the stability of the rotating beams. Investigation of the transient stability of a parabolic-tapered rotating beam with an elliptical area of cross section having different taper parameters for the major axis and minor axis with an inconsistent temperature gradient along the centroid axis subjected to a pulsating axial excitation at the centroid of the far end is done. Hamilton’s norm has been utilized for obtaining the non-dimensional system equation of motion and related boundary conditions. Galerkin’s technique is applied to the non-dimensional equation of motion to obtain a set of Hill’s equations. Then, the influence of various non-dimensional parameters like taper parameter, rotational speed, constant and variable thermal gradient on the stability of the system is studied. The results obtained using the proposed model are attested by using the fourth-order Runge–Kutta method. The numerical results reveal that improved stability is achieved by increasing the revolving speed; conversely, arise in temperature gradient and the taper parameter destabilized the proposed system.