Nonlinear Aero-Thermo Elastic Oscillation of Inextensible Functionally Graded Beams Subject to Concentrated Harmonic Load Based on the Nonlinear Piston Theory

Abstract

PurposeThis paper presents nonlinear aero-thermo elastic oscillation of inextensible functionally graded (FG) beams with temperature dependent properties subject to concentrated harmonic point load with viscous aerodynamic heating by using nonlinear piston theory.MethodsGoverning nonlinear equations are derived based on Euler-Bernoulli-inextensible beam theory. Properties of FG material are considered as temperature dependent and expressed by nonlinear equation of thermoplastic material. Galerkin's method is utilized to discretize governing nonlinear partial differential equation in form of a nonlinear ordinary differential equation. Then, obtained nonlinear differential equation is solved analytically by using method of multiple time scales.ResultsNonlinear dynamic behavior of three different material constituent for FG beam includes combinations of Stainless Steel with Silicon , Stainless Steel with Zirconia and Titanium alloy with Zirconia is investigated.ConclusionsThis investigation can be helpful for mechanical analysis of structural elements under aero-thermal conditions.