On large deformation and stability of microcantilevers under follower load

Abstract

In the present study, a novel geometrically exact nonlinear beam model based on the nonlinear displacement field, centerline-inextensibility condition, Euler-Bernoulli beam hypothesis, and modified couple stress theory is established to investigate the extremely large deformations and stability characteristics of size-dependent microcantilevers subjected to a tip-concentrated non-conservative (follower type) load with arbitrary inclination angle. The newly developed mathematical formulation explains the size effect phenomenon in the microcantilevers with only one material length scale parameter. The nonlinear shooting method for two-point boundary value problems is utilized to assess the deformed configuration of microsystem based on the quasistatic form of nonlinear mathematical model. Afterwards, the linearized dynamical mathematical model around the nonlinear deformed configurations of microsystem is numerically solved using the Galerkin technique to examine the stability of obtained responses. A comprehensive investigation is then conducted to highlight the role of size-dependency in the critical follower force at which the microsystem undergoes a flutter instability, as well as the nonlinear large deformation of microsystem in the pre-flutter region.