Dynamic stability of linear parametrically excited twisted Timoshenko beams under periodic axial loads

In this paper, the parametric instability of twisted Timoshenko beams with various end conditions and under an axial pulsating force is studied. The equations of motion in the twisted frame are derived using a finite element method. Based on Bolotin’s method, a set of second-order ordinary differential equations with periodic coefficients of Mathieu–Hill type is formed to determine the instability regions for twisted Timoshenko beams. A dynamic instability index is defined and used as an instability measure to study the influence of various parameters. The effects of beam length, inertia ratio, pre-twist angle, dynamic component of axial force and restraint condition on the instability regions and dynamic instability index of the twisted beam are investigated and discussed.