Stochastic Nonlinear Free Vibration Analysis of Functionally Graded Beam Subjected to Thermal Loading with Random Material Properties

Abstract:

This paper deals with the stochastic nonlinear free vibration response of functionally graded materials (FGMs) beam subjected to thermal loadings with uncertain material properties subjected to uniform and nonuniform temperature changes with temperature independent (TID) and dependent (TD) material properties. System properties such as material properties of each constituents material and volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strains using modified C⁰ continuity. A direct iterative based nonlinear finite element method in conjunction with first order perturbation technique (FOPT) is used for FGMs beam to compute the second order statistics (mean and coefficient of variation) of the nonlinear fundamental frequency. The present outlined approach has been validated with the results available in literatures and independent Monte Carlo simulation (MCS).

• Periodical: Advanced Materials Research (Volume 747)
• Pages: 551-554
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.747.551
• Online since: August 2013
• Authors: Niranjan L. Shegokar, Achchhe Lal
• Keywords: FGMs Beam, Finite Element Method (FEM), HSDT, Stochastic Response

References

[1] Sina SA, Navazi HM, Haddadpour H , An analytical method for free vibration analysis of functionally graded beams, Mater Des 30 (2009) 741–7.

DOI: 10.1016/j.matdes.2008.05.015

[2] Simsek M, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories., Nucl Eng Des 240 (2010) 697–705.

DOI: 10.1016/j.nucengdes.2009.12.013

[3] Wattanasakulpong Nuttawit, Gangadhara Prusty B, Donald W. Kelly, Thermal buckling and elastic vibration of third-order shear deformable Functionally graded beams, Int. Journal of Mechanical Sciences 53 (2011)734–743.

DOI: 10.1016/j.ijmecsci.2011.06.005

[4] Thai Huu-Tai, Vo P. Thuc, Bending and vibration of functionally graded beam using various higher-orders shear deformation theories, Int J Mech Sci doi: 10. 1016/j. ijmecsci. 2012. 05. 014.

DOI: 10.1016/j.ijmecsci.2012.05.014

[5] Jagtap KR, Achchhe Lal, Singh BN, Stochastic nonlinear free vibration analysis of elastically supported functionally graded materials plate with system randomness in thermal environment, Compost Structures 93 (2011) 3185–3199.

DOI: 10.1016/j.compstruct.2011.06.010

[6] Heyliger PR, Reddy JN, A higher order beam finite element for bending and vibration problems, J. Sound Vibration 126 (1988) 309–326.

DOI: 10.1016/0022-460x(88)90244-1