Stability of a Tapered, Pretwisted, and Rotating Sandwich Beam under Temperature Gradient

In this work the parametric instability regions of an exponentially tapered, pretwisted, and rotating symmetric sandwich beam under a temperature gradient, subjected to a periodic axial load has been studied for clamped-free boundary condition. Pretwist angle has been assumed to vary linearly along the length. The equations of motion along with the boundary conditions have been derived using Hamilton's principle for coupled bending-bending vibration of the beam and the instability regions for principal resonance and combination resonance have been obtained by using the conditions derived by Saito and Otomi. The static buckling loads have been also obtained. Finally, the effect of pretwist angle, taper parameter, temperature gradient, angular velocity of rotation, and properties of the viscoelastic core on beam dynamic and static stability have been represented graphically. It was observed that beam stability improves with angular velocity of rotation and the pretwist angle seemed to have a very complex relationship with dynamic stability of the beam.