Static, free vibration and dynamic stabilty analysis of sandwich beam with functionally graded material constraining layer in high temperature environment

Abstract

The main objective of present work is to study the static, free vibration and dynamic stability of a sandwich beam with functionally graded material as constraining layer in high thermal environment. The top layer is the FGM layer with ceramic on its top face and stainless steel on its bottom. The sandwich beam is subjected to axial dynamic loading. The top face of the FGM layer is subjected to high temperature. All the rest of the layers are at room temperature. Two cases of temperature variation along the thickness are considered i.e. linear and non-linear. The material properties of FGM depend on the volume fraction distribution of constituent materials and on the subjected temperature. The material properties are assumed to follow the power law distribution along the thickness direction. The sandwich beam is modeled using finite element method. The beam element has four degrees of freedom for each node. The degrees of freedom per node are two longitudinal displacement for the two outer layers, lateral displacement and rotation. Free vibration, static and dynamic load analyses are done by varying different system parameters such as core thickness parameter, power law index and temperature of top face of FGM layer. Boundaries for stable and unstable regions are found out using Saito and Otomi conditions. It is found that the buckling load of the beam decreases with increase in core thickness parameter, power law index and temperature of top face of FGM layer. The frequency of the beam also decreases with increase in core thickness parameter, power law index and temperature of top face of FGM layer. Linear and non-linear temperature variation along the thickness has negligible effect on buckling load as well as on natural frequency. The probability of instability of the beam increases with increase in core thickness parameter, power law index and temperature of top face of FGM layer.