Comments on “Parametric instability of a cantilever beam with magnetic field and periodic axial load”

In a recent study, Pratiher and Dwivedy [1] investigated the parametric instability regions of a cantilever beam with tip mass that was subjected to a periodic axial load and a magnetic field. Such investigations are still at an early stage, with very few published studies. To derive the discretized nonlinear equation of motion, Pratiher and Dwivedy excluded two linear terms from the eigen-state of the beam, one from the differential equation and the other from the boundary conditions. They also overlooked the important requirement that basis functions used for modal decoupling must be mutually orthogonal for single-mode approximation. As shown in the present study, the approach used in Ref. [1] may yield significantly flawed solutions for the parametric instability problem.