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

Abstract

The present investigation is carried out to study the buckling, vibration and dynamic instability behavior of sandwich plates with viscoelastic core and func­tionally graded material (FGM) constraining layer using finite element method. The finite element model of the problem is developed based on the first order shear deformation theory, to incorporate the effect of shear deformation of the face sheets. The shear, transverse and longitudinal deformations of the viscoelas­tic layer also taken into account and the model's suitability to be applicable to thin and thick cores. An eight node rectangular finite sandwich plate element with ten degrees of freedom per node is considered for the finite element dis­cretization of the sandwich plate. The governing equations of motion are derived using Hamilton's principle. The dynamic stability of the system is attributed with stable and unstable regions, which are separated by stability boundary and these boundaries have been established using Hsu's criteria. FGMs are special class of advanced materials usually made of ceramic-metal constituents, engi­neered to vary its material and mechanical properties along its geometrical di­mensions such as thickness, length or breadth. A simple power law distribution in terms of the volume fraction of the different constituents of the FG M is as­sumed for the mathematical modelling of the property variation. The buckling, free vibration and dynamic stability studies of the sandwich plate are conducted for various operating conditions.
The natural frequencies, buckling loads are calculated and the regions of in­stabilities under external parametric excitation are established for various aspect ratios and core thickness ratios with different boundary conditions. Both uni­axial and bi-axial loadings are considered in the buckling analysis. Both the natural frequencies and buckling loads decrease with the increasing aspect ratio.
The natural frequencies decrease with increase in the core thickness ratio, but the buckling loads show a decreasing nature for certain limit and then has an increasing nature if the core thickness ratio increases further.
The variation of the critical buckling loads, natural frequencies and the re­gions of instabilities of the sandwich plate with power law index is examined. The critical buckling loads and the natural frequencies get reduced with increas­ing power law index and an increase in the power law index has a destabilizing effect on the sandwich plate.
The temperature rise on the top surface of the FGM constraining layer has significant effect on static and dynamic behaviour of the sandwich plate. Both the buckling loads and natural frequencies decrease with increasing external tem­perature. The temperature rise also has a destabilizing effect on the dynamic stability of the sandwich plate.
The critical buckling loads and natural frequencies of a rotating sandwich plate increase with increase in rotational speed and dynamic stability of the plate also enhances. The buckling loads and natural frequencies decrease with increase in the setting angle but the increase in the setting angle has negligible effect on the stability of the sandwich plate. The increase in hub radius increases the natural frequencies, buckling loads and enhances the dynamic stability of the sandwich plate.
The effect of skewness on the static and dynamic characteristics of a skew sandwich plate is analysed. Both the critical buckling load and natural frequency increase and the dynamic stability of the system improves with increasing skew angle. The increase in power law index, aspect ratio and core thickness of the skew sandwich plate decreases the natural frequency and buckling load and also the dynamic stability deteriorates.
The sandwich plate resting on two-parameter elastic foundation is considered for the static and dynamic analyses. The critical buckling loads, natural frequency and critical buckling load of the sandwich plate increase with increase in both Winkler's and shear layer parameters. Increase in foundation parameters enhances stability of the plate. Pasternak's elastic foundation model is found to have more stabilising effect than Winkler's. The increase in power law index and the core thickness ratio decreases the natural frequency and buckling load, the dynamic instability of the plate also enhance.