Reduced order dynamic model for polysaccharides molecule attached to an atomic force microscope

A dynamic analysis and numerical simulation has been conducted of a polysaccharides molecular structure (a ten (10) single-α-d-glucose molecule chain) connected to a moving atomic force microscope (AFM). Sinusoidal base excitation of the AFM cantilevered beam is considered. First a linearized perturbation model is constructed for the complex polysaccharides molecular structure. Then reduced order (dynamic) models based upon a proper orthogonal decomposition (POD) technique are constructed using global modes for both the linearized perturbation model and for the full nonlinear model. The agreement between the original and reduced order models (ROM/POD) is very good even when only a few global modes are included in the ROM for either the linear case or for the nonlinear case. The computational advantage of the reduced order model is clear from the results presented.