%0 Journal Article
%T Free vibration behavior of tapered functionally graded material beam in thermal environment considering geometric non
%A Amlan Paul
%A Debabrata Das
%J Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications
%@ 2041-3076
%D 2019
%R 10.1177/1464420718759376
%X An improved mathematical model is presented to investigate the free vibration behavior of post-buckled tapered functionally graded material beam, subjected to uniform temperature rise and steady-state heat conduction. The material properties including the thermal conductivity are considered to be temperature-dependent and an iterative algorithm for solving temperature-dependent steady-state heat conduction equation is presented to get the correct temperature profile. The initial static post-buckling problem is formulated using minimum potential energy principle and the subsequent free vibration problem is formulated using Hamilton＊s principle by employing the tangent stiffness of the post-buckled configuration. The solution of the governing equations is obtained using Ritz method. Following Timoshenko beam theory, a geometrically non-linear mathematical model is developed by employing the non-linear strain每displacement relationships for both normal and shear strains. The study is carried out for both hinged每hinged and clamped每clamped beams. Non-dimensional load每frequency behaviors are presented for different gradation indices, taperness parameters, and length每thickness ratios. Static post-buckling equilibrium path for clamped每clamped beams is also presented. The significant effects of shear non-linearity and temperature-dependent thermal conductivity on dynamics of tapered functionally graded material beam are shown in the paper
%K Tapered beam
%K functionally graded
%K post-buckling
%K free vibration
%K thermal loading
%U https://journals.sagepub.com/doi/full/10.1177/1464420718759376