The Influence of Nonlinear Air Drag on Microbeam Response for Noncontact Atomic Force Microscopy

2007 ◽  
Author(s):  
O. Gottlieb ◽  
A. Hoffman ◽  
W. Wu ◽  
R. Maimon ◽  
R. Edrei ◽  
...  
Keyword(s):  
Free Vibration ◽  
Frequency Response ◽  
Forced Vibration ◽  
Continuum Model ◽  
Viscoelastic Damping ◽  
Nonlinear Frequency ◽  
Amplitude Response ◽  
Atomic Force ◽  
Backbone Curves ◽  
Nonlinear Geometric

In this paper we formulate and analyze a continuum model for the vibration of a noncontacting atomic force microscope (AFM) microbeam in air that consistently incorporates nonlinear geometric and inertia effects, localized atomic interaction, viscoelastic damping and quadratic drag. We investigate a controlled set of experiments that include both free vibration decay of a large Silicon beam and forced vibration response of an AFM Silicon microbeam mapping a Silicon sample for various initial interaction distances. Nonlinear frequency and damping backbone curves are obtained from free vibration decay data and equivalent damping ratios are deduced from forced vibration frequency response. Estimation of the system linear viscoelastic parameters and nonlinear drag parameters is enabled by comparison of the experimental backbone curves with those of a nonlinear modal dynamical system deduced from the continuum model. The calibration results without sample interaction include both a slight softening effect for small amplitude response due to nonlinear inertia and viscoelastic damping and a hardening effect for large amplitude response governed by nonlinear geometric effects and drag. Validation of the nonlinear model is enabled by comparison with the measured forced vibration AFM frequency response below the dynamic jump-to-contact threshold.

Modal parameter identification of a long-span footbridge by forced vibration experiments

2017 ◽  
Vol 20 (5) ◽  
pp. 661-673 ◽  
Author(s):  
Q Wen ◽  
XG Hua ◽  
ZQ Chen ◽  
JM Guo ◽  
HW Niu
Keyword(s):  
Free Vibration ◽  
Frequency Response ◽  
Forced Vibration ◽  
Ambient Vibration ◽  
Modal Parameters ◽  
Response Functions ◽  
Modal Parameter ◽  
Modal Parameter Identification ◽  
Cable Stayed Bridge ◽  
Vibration Tests

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.

scholarly journals Nonlinear transverse steady-state periodic forced vibration of 2-dof discrete systems with cubic nonlinearities

2011 ◽  
pp. 143-166
Author(s):  
Ahmed Eddanguir ◽  
Zitouni Beidouri ◽  
Rhali Benamar
Keyword(s):  
Spectral Analysis ◽  
Steady State ◽  
Frequency Response ◽  
Forced Vibration ◽  
Transverse Vibration ◽  
Frequency Response Function ◽  
Discrete Systems ◽  
Nonlinear Frequency ◽  
Transverse Vibrations ◽  
Nonlinear Frequency Response

A method based on Hamilton’s principle and spectral analysis has been applied recently to nonlinear transverse vibrations of discrete systems with cubic nonlinearities, leading to calculation of the nonlinear free modes of transverse vibration and their associated nonlinear frequencies. The objective of the present work was the extension of this method to the nonlinear forced transverse steady-state periodic response of 2-dof system leading to nonlinear frequency response function in the neighbourhood of the two modes

Non-Linear Frequency Response of Atomic Force Microscope Cantilevers at the Solid-Liquid Interface

2012 ◽  
Author(s):  
Daniel R. Kiracofe ◽  
Arvind Raman
Keyword(s):  
Frequency Response ◽  
Primary Resonance ◽  
Liquid Interface ◽  
Nonlinear Frequency ◽  
Quality Factors ◽  
Atomic Force ◽  
Non Linear ◽  
Nonlinear Frequency Response ◽  
Solid Liquid Interface ◽  
Solid Liquid

One significant advantage of atomic force microscopy (AFM) over other microscopy methods is its ability to characterize surfaces in liquid environments. However, operation in liquid is complicated by the large hydrodynamic loading, which leads to low quality factors, and in turn leads to many changes in the dynamics as opposed to air/vacuum environments. A thorough understanding of the dynamics is necessary for properly interpreting data from experiments. In this work, we study the non-linear dynamics of AFM micro-cantilevers interacting with hard surfaces in liquids. In comparison to prior works that have mostly examined the dynamics at a single drive frequency, we examine the full nonlinear frequency response. Two important results are highlighted. First, in addition to the primary resonance, there are also superharmonic resonances, which can distort tapping mode approach curves. Secondly, we point out that the layering (hydration forces) of liquid molecules at the solid-liquid interface, traditionally detected using small amplitude (linear) AFM, in fact has a significant effect on the nonlinear response. These results are shown by experiments and examined analytically. The effects of parameters such as cantilever stiffness and quality factors are studied using numerical simulation.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

On the Frequency Response of a Spinning Disk With Large Deformations

2010 ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Nonlinear Frequency ◽  
Response Characteristics ◽  
Geometrical Nonlinear ◽  
Oscillation Frequencies ◽  
Multi Mode ◽  
Different Levels

In this paper, the effect of geometrical nonlinear terms, caused by a space fixed point force, on the frequencies of oscillations of a rotating disk with clamped-free boundary conditions is investigated. The nonlinear geometrical equations of motion are based on Von Karman plate theory. Using the eigenfunctions of a stationary disk as approximating functions in Galerkin’s method, the equations of motion are transformed into a set of coupled nonlinear Ordinary Differential Equations (ODEs). These equations are then used to find the equilibrium positions of the disk at different discrete blade speeds. At any given speed, the governing equations are linearized about the equilibrium solution of the disk under the application of a space fixed external force. These linearized equations are then used to find the oscillation frequencies of the disk considering the effect of large deformation. Using multi mode approximation and different levels of nonlinearity, the frequency response of the disk considering the effect of geometrical nonlinear terms are studied. It is found that at the linear critical speed, the nonlinear frequency of the corresponding mode is not zero. Results are presented that illustrate the effect of the magnitude of disk displacement upon the frequency response characteristics. It is also found that for each mode, including the effect of the geometrical nonlinear terms due to the applied load causes a separation in the frequency responses of its backward and forward traveling waves when the disk is stationary. This effect is similar to the effect of a space fixed constraint in the linear problem. In order to verify the numerical results, experiments are conducted and the results are presented.

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