Size-dependent flutter analysis of a nanobeam made of metal-ceramic functionally graded materials subjected to supersonic fluid flow

Abstract

In the presented paper, the size-dependent flutter analysis of a nanobeam made of metal-ceramic functionally graded (FG) materials subjected to supersonic fluid flow is examined. The volume fractions of metal and ceramic vary along both longitudinal and thickness directions. The size effects are modeled based on the nonlocal strain gradient theory (NSGT) and the surface effects are included according to the Gurtin-Murdoch surface elasticity theory. The mathematical modeling of nanobeam is performed in the framework of Reddy's third-order shear deformation beam theory (TSDBT), and the aerodynamic pressure is modeled according to the linear approximation of the piston theory. The governing equations and boundary conditions are obtained utilizing Hamilton's principle and are solved approximately via the differential quadrature method (DQM). Convergence and precision of the presented work are proved and the effects of several parameters on the flutter boundaries are inspected such as material gradation indexes, nonlocal and strain gradient parameters, thickness-to-length ratio, and incorporation of surface effects. It is discovered that the incorporation of the surface effects has a remarkable impact on the flutter boundaries of nanobeams and increases both critical aerodynamic pressure and flutter frequency of the nanobeam. The aim of this work is to examine how the aeroelastic stability characteristics of an FG nanobeam can be affected by the nonlocal and strain gradient parameters and the variations in the volume fractions of the metal and ceramic in the longitudinal and thickness directions. © 2025 The Authors