Stability analysis of an exponentially tapered, pre-twisted asymmetric sandwich beam on a variable Pasternak foundation with viscoelastic supports under temperature gradient

Abstract

The purpose of this work is to study the stability of an exponentially tapered, pre-twisted and asymmetric sandwich beam on a variable Pasternak foundation, propped at ends. Viscoelastic translational and rotational springs have been employed to include the resistance offered by pinned–pinned end supports. The system is subjected to pulsating axial loads, and the elastic layers are subjected to a temperature gradient due to steady heat flow. A set of equations of motion was obtained by using Hamilton’s principle, and instability regions were plotted using formulae developed by Saito and Otomi. The effects of pre-twist angle, temperature gradient, taper parameter, shear modulus of the core, core loss factor, stiffness of the Pasternak foundation and rotational spring stiffness on static stability and regions of parametric instability were studied. Increase in the value of pre-twist angle was observed to be detrimental to both dynamic and static stability of the system. It was found that the dynamic stability of the system also degraded with an increase in the taper parameter.