Thermal Buckling and Free Vibration Analysis of Heated Functionally Graded Material Beams

Abstract

The effect of temperature dependency of material properties on thermal buckling and free vibration of functionally graded material (FGM) beams is studied. The FGM beam is assumed to be at a uniform through thickness temperature, above the ambient temperature. Finite element system of equations based on the first order shear deformation theory is developed. FGM beam with axially immovable ends having the classical boundary conditions is analysed. An exhaustive set of numerical results, in terms of buckling temperatures and frequencies, is presented, considering the temperature independent and temperature dependent material properties. The buckling temperature and fundamental frequency obtained using the temperature independent material properties is higher than that obtained by using the temperature dependent material properties, for all the material distributions, geometrical parameters in terms of length to thickness ratios and the boundary conditions considered. It is also observed that the frequencies of the FGM beam will reduce with the increase in temperature. This observation is applicable for the higher modes of vibration also. The necessity of considering the temperature dependency of material properties in determining thermal buckling and vibration characteristics of FGM beams is clearly demonstrated.

Perfis Perfurados Submetidos À Flambagem Térmica E Mecânica

“…Segundo Anandrao et al (2013), no caso de flambagem do elemento, com extremidades imóveis, sujeitos a um aumento de temperatura uniforme, acima da temperatura ambiente, o problema de autovalores é resolvido através da Eq. (1).…”