Reduced Order Model Analysis for Two-Dimensional Molecular Dynamic Chain Structure Attached to an Atomic Force Microscope

Abstract

Dynamic analysis and numerical simulation of a protein-ligand chain structure connected to a moving atomic force microscope (AFM) has been conducted. The elements of the chain are free to extend and rotate relative to each other in a two-dimensional plane. Sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. Reduced order (dynamic) models are constructed using global modes for both linear and nonlinear dynamic systems with and without the “nearest neighbor assumption.” The agreement between the original and reduced order models (ROM) is very good even when only one global mode is included in the ROM for either the linear case or for the nonlinear case, provided the excitation frequency is lower than the fundamental natural frequency of the linear system. For higher excitation frequencies, more global modes are required. The computational advantage of the reduced order model is clear from the results presented.