On the Dynamic Stability of Functionally Graded Material Plates Under Parametric Excitation

Abstract

The objective of this thesis is to study the dynamic stability of functionally graded material (FGM) plates under parametric excitation. Third order shear deformation theory is used for the analysis of the plates. The equations of motion have been derived using finite element method in conjunction with Hamilton’s principle. The boundaries of stable and unstable regions in the parameter space are determined by using Floquet’s theory. FGMs are microscopically inhomogeneous spatial combination of materials, usually made up of ceramic and metal constituents. A steel-alumina FGM plate with steel-rich bottom and alumina reach top is considered for the analysis. The properties of the functionally graded material plates 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 load, natural frequencies and dynamic stability of plates is determined. In case of FGM plate, an increase of power law index value decreases the natural frequencies. If aspect ratio is increased, the critical buckling load decreases for both uniaxial and biaxial loading cases and it is also observed that increase of power law index value decreases critical buckling load. With increase of the power index there is deteriorating effect on the dynamic stability of the FGM plate.
The influence of temperature rise on the dynamic stability of the FGM plate in thermal environment is investigated. The natural frequencies and dynamic stability behaviour are found to be highly sensitive to the temperature change between the bottom and top surfaces. In high temperature environment the dynamic stability of the plate deteriorates. The effect of foundation stiffness coefficients on the dynamic stability of FGM plates are examined in detail through parametric studies. The frequencies of FGM plate resting on Pasternak foundation increase with the increase of Winkler foundation constant and shear layer constant. The Winkler and shear foundation constants have significant effect on the critical buckling load of FGM plates resting on Pasternak foundation. An increase of these constants increases the critical buckling load of the plate. Increase of Winker foundation constant and shear layer constant improves the dynamic stability of FGM plate. Shear layer constant has got more prominent effect compared to the Winkler foundation constant, on the dynamic stability of FGM plate resting on Pasternak foundation. Parametric investigation is carried out to study thoroughly the effect of the temperature rise, hub radius and rotational speed on the vibration and dynamic stability of rotating plate in
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thermal environment. It is observed that the natural frequencies reduce with an increase in temperature rise. The increase in rotational speed and hub radius results in increase of natural frequencies. The increase in temperature leads to reduction in the dynamic stability of plate. Increase in hub radius and rotational speed improves the stability of the rotating plate.
The effects of moisture concentration, temperature rise and power law index on the dynamic stability of FGM plates in hygrothermal environment are investigated. The observations made from the dynamic stability diagrams are: with increase in moisture concentration and temperature the instability of the plate is more probable, the combined effect of moisture and temperature on the dynamic instability of FGM plates is more severe than the effect of individual parameter.
The effect of skew angle on dynamic stability of FGM plate in thermal environment is discussed. The natural frequencies increase with an increase of skew angle. Increase in aspect ratio of FGM skew plate increases its instability. The increase in the value of power law index is found to have enhancing effect on the parametric instability of the skew FGM plate. The increase in skew angle of the plate reduces the chance of dynamic instability of the plate.