tailieunhanh - Nonlinear Dynamics Part 5

Tham khảo tài liệu 'nonlinear dynamics part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions in Atomic Force Microscopy 93 r -acc -ass tan-1 Ys c x - tan-1------------------------ 65 ks F z0 kcn F z0 - mcra2 where acc and ass are obtained from Eqs. 45 and 46 respectively. To the same extent that r may be approximated by Eq. 65 we may also approximate Gn given by Eq. 57 as Gn - F Z0 DcsQccQss. 66 2 Rcs Important features of the solution set The present derivation is based on the assumption that the cantilever tip-sample surface interaction force is a multiply differentiable nonlinear function of the tip-surface separation distance as indicated in Fig. 2. Points on the curve below the separation distance zA in Fig. 2 correspond to a repulsive interaction force while points above zA in Fig. 2 correspond to an attractive interaction force. The force-separation curve has a minimum at a separation distance zB corresponding to the maximum nonlinearity of the curve and that point lies in the attractive force portion of the curve. Cantilever oscillations result in continuous oscillatory changes in the tip-surface separation distance about the quiescent tip-surface separation distance z0 see Fig. 4 . Since the cantilever oscillations are constrained to follow the force-separation curve the fractions of the cantilever oscillation cycle in the repulsive and attractive portions of the force-separation curve depend on the quiescent tip-surface separation distance and the amplitude of the oscillations. The cantilever oscillations are known to be bi-stable with the particular mode of oscillation being determined by the initial conditions that includes the tip-surface separation distance Garcia Perez 2002 . Unless some extraneous perturbation changes the mode of oscillation the cantilever continues to oscillate in a given bi-stable mode for a given set of initial conditions. For large oscillation amplitudes the bi-stability coalesces to a single stable mode. In the present model the bi-stable mode of .