Nonlinear micromechanically analysis of forced vibration of the rectangular-shaped atomic force microscopes incorporating contact model and thermal influences

Abstract

The linear and nonlinear forced vibrations of microprobe in contact-mode atomic force microscopes are presented based on a rectangular beam model of modified couple stress theory. The Hamilton principle is employed to derive governing PDEs for the first and second modes transformed into nonlinear ODEs by the Galerkin procedure coupled with time multiple scales method. The important effect of linear tip inertia is regarded despite of others. The impact of damping, thermal loading, and constant contact stiffness on the amplitude and phase angle-frequencies are investigated. Location of a concentrated tip mass with tip-sample interaction are modeled by delta Dirac functions.

Communicated by Francesco Tornabene.

Keywords:

• Atomic force microscopes
• contact-mode
• forced–vibrating
• nonlinear micromechanical model