Buckling, Vibration and Dynamic Stability of Sandwich Beams with Functionally Graded Material Constraining Layer

Abstract

The present investigation is an attempt to contribute towards the improved understanding of the buckling, vibration and dynamic stability of sandwich beams with viscoelastic core and functionally graded material (FGM) constraining layer under parametric excitation. The equations of motion have been derived using finite element method in conjunction with Hamilton's principle. The governing equations are a set of linear system of Mathieu-Hill type equations from which the boundaries of stable and unstable regions are determined by using Hsu's criteria in the parameter space. FGMs are microscopically inhomogeneous spatial combination of constituents, usually made up of ceramic-metal constituents. The properties of the functionally graded material constraining layer are assumed to vary along the thickness direction according to a power law distribution in terms of the volume fractions of the constituents.
The effect of power law index on the critical buckling loads, natural frequencies and dynamic stability of the sandwich beam is investigated. An increase of power law index value decreases the natural frequencies. It is also observed that increase of power law index value decreases critical buckling load. With the increase of the power index there is deterioration effect on the dynamic stability. Increase in core thickness, increases both the resonant frequencies and buckling loads and also improves the stability of the beam.
The influence of temperature rise on the buckling loads, frequencies and dynamic instability regions of the beam in high thermal environment is investigated. The resonant frequencies, buckling loads and dynamic stability behavior are found to be highly sensitive to the temperature change between the bottom and top surfaces of the constraining layer. The presence of a temperature rise degrades the structural stiffness, and hence lowers the vibration frequencies and buckling loads. Also the dynamic stability of the beam deteriorates.
Parametric investigation is carried out thoroughly to study the effect of the hub radius ratio and rotational speed on buckling, vibration and the dynamic stability of rotating sandwich beam. Increase in the rotational speed and hub radius results in the increase of natural frequencies and buckling loads. Increase in the rotational speed and hub radius enhances the dynamic stability of the beam.
The effects of foundation stiffness coefficients on the dynamic stability of sandwich beam are examined in detail through parametric studies. The frequencies of the beam resting on Pasternak foundation increase with the increase of Winkler foundation constant and shear layer constant. The Winkler and shear foundation constants have a noticeable effect on the critical buckling load of the beam resting on Pasternak foundation and under axial loading. An increase in each of these constants increases the critical buckling load of the beam. With an increase of Winker foundation constant and shear layer constant improves the dynamic stability of the beam. Shear layer constant has got more dominating effect compared with the Winkler foundation constant on the dynamic stability of the sandwich beam resting on Pasternak foundation.