Dynamic Responses of an Atomic Force Microscope Interacting with Samples

2004 ◽  
Vol 127 (4) ◽  
pp. 705-709 ◽  
Author(s):  
Jih-Lian Ha ◽  
Rong-Fong Fung ◽  
Yi-Chan Chen
Keyword(s):  
Atomic Force Microscope ◽  
Cantilever Beam ◽  
Contact Region ◽  
Equations Of Motion ◽  
Dynamic Responses ◽  
Governing Equations ◽  
External Voltage ◽  
Atomic Force ◽  
Repulsive Forces ◽  
Tip Mass

The objective of this paper is to formulate the equations of motion and to analyze the vibrations of an atomic force microscope (AFM), which contains a piezoelectric rod coupling with a cantilever beam, and the tip mass interacting with samples. The governing equations of the AFM system are formulated completely by Hamilton’s principle. The piezoelectric rod is treated as an actuator to excite the cantilever beam via an external voltage. The repulsive forces between the tip and samples are modeled by the Hertzian, the Derjaguin-Müller-Toporov, and Johnson-Kendall-Roberts models in the contact region. Finally, numerical results are provided to illustrate the coupling effects between the piezoelectric actuator and the cantilever beam and the interaction effects between the tip and samples on the dynamic responses.

Dynamic Modeling and Vibration Analysis of the Atomic Force Microscope

2001 ◽  
Vol 123 (4) ◽  
pp. 502-509 ◽  
Author(s):  
Rong-Fong Fung ◽  
Shih-Chien Huang
Keyword(s):  
Atomic Force Microscope ◽  
Piezoelectric Actuator ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Repulsive Force ◽  
Dynamic Responses ◽  
Governing Equations ◽  
External Voltage ◽  
Atomic Force ◽  
Vdw Force

The objective of this paper is to formulate the equations of motion and to investigate the vibrations of the atomic force microscope (AFM), which is divided into the contact and noncontact types. First, the governing equations of the AFM including both base oscillator and piezoelectric actuator are obtained using Hamilton’s principle. In the dynamic analysis, the piezoelectric layer is treated as a sensor to measure the deflection and as an actuator to excite the AFM via an external voltage. The repulsive force and van der Waals (vdW) force are considered in the contact and noncontact types of the AFM, respectively. Some important observations are made from the governing equations and boundary conditions. Finally, numerical results using a finite element method are provided to illustrate the excitation effects of base oscillator and piezoelectric actuator on the dynamic responses.

Free and Forced Vibration of a Kinked Cantilever Beam

1999 ◽  
Author(s):  
B. S. Reddy ◽  
K. R. Y. Simha ◽  
A. Ghosal
Keyword(s):  
Cantilever Beam ◽  
Mode Shape ◽  
Forced Vibration ◽  
Equations Of Motion ◽  
Element Formulation ◽  
Kink Angle ◽  
Order Polynomial ◽  
Relationship Of ◽  
Tip Mass ◽  
Beam Mode

Abstract In this paper we use the assumed modes method to derive an analytical model of a kinked cantilever beam of unit mass carrying a kink mass (mk) and a tip mass (mt). The model is used to study the free and forced vibration of such a beam. For the free vibration, we obtain the mode shape of the complete beam by solving an eight order polynomial whose coefficients are functions of the kink mass, kink angle and tip mass. A relationship of the form f(mk,mt,δ)=mk+mt(4+103cosδ+23cos2δ)=constant appears to give the same fundamental frequency for a given kink angle, δ, and different combinations of kink mass and tip mass. To derive the dynamic equations of motion, the complete kinked beam mode shape is used in a Lagrangian formulation. The equations of motion are numerically integrated with a torque applied at the base and the tip response for various kink angles are presented. The results match those obtained from a traditional finite element formulation.

Design and Construction of Low Temperature Attachment for Commercial AFM

2013 ◽  
Vol 209 ◽  
pp. 137-142
Author(s):  
Abrarkhan M. Pathan ◽  
Dhawal H. Agrawal ◽  
Pina M. Bhatt ◽  
Hitarthi H. Patel ◽  
U.S. Joshi
Keyword(s):  
Atomic Force Microscope ◽  
Cryogenic Temperature ◽  
Low Cost ◽  
Perovskite Manganite ◽  
Atomic Force ◽  
Structure Of Nanomaterials ◽  
Negative Bending ◽  
Set Up ◽  
Free Environment ◽  
Repulsive Forces

With the rapid advancements in the field of nanoscience and nanotechnology, scanning probe microscopy has become an integral part of a typical R&D lab. Atomic force microscope (AFM) has become a familiar name in this category. The AFM measures the forces acting between a fine tip and a sample. The tip is attached to the free end of a cantilever and is brought very close to a surface. Attractive or repulsive forces resulting from interactions between the tip and the surface will cause a positive or negative bending of the cantilever. The bending is detected by means of a laser beam, which is reflected from the backside of the cantilever. Atomic force microscopy is currently applied to various environments (air, liquid, vacuum) and types of materials such as metal semiconductors, soft biological samples, conductive and non-conductive materials. With this technique size measurements or even manipulations of nano-objects may be performed. An experimental setup has been designed and built such that a commercially available Atomic Force Microscope (AFM) (Nanosurf AG, Easyscan 2) can be operated at cryogenic temperature under vacuum and in a vibration-free environment. The design also takes care of portability and flexibility of AFM i.e. it is very small, light weight and AFM can be used in both ambient and cryogenic conditions. The whole set up was assembled in-house at a fairly low cost. It is used to study the surface structure of nanomaterials. Important perovskite manganite Pr0.7Ca0.3MnO3thin films were studied and results such as morphology, RMS area and line roughness as well as the particle size have been estimated at cryogenic temperature.

The Influence of Excitation Frequency on Dynamical Behaviors of Atomic Force Microscope

2012 ◽  
Vol 518-523 ◽  
pp. 3891-3895
Author(s):  
Ran Hui Liu ◽  
Qing Quan Hu
Keyword(s):  
Atomic Force Microscope ◽  
Numerical Solutions ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Bifurcation Diagrams ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Atomic Force ◽  
Dynamical Behaviors ◽  
Amplitude Decrease

This paper deals with dynamical behaviors of Atomic Force Microscope in the different excitation frequency. By using Poincare maps, phase trajectory, Lyapunov exponent, bifurcation diagram, the dynamical behaviors are identified based on the numerical solutions of the governing equations. Bifurcation diagrams are presented in the case that the excitation amplitude increases while other parameters are fixed. Numerical simulations indicate that periodic and chaotic motions occur in the system. At the same, when chaotic motions occur, the excitation amplitude decrease as the excitation frequency increases.

scholarly journals Nonlinear Vibration of the Blade with Variable Thickness

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaobo Jie ◽  
Wei Zhang ◽  
Jiajia Mao
Keyword(s):  
Variable Thickness ◽  
Conical Shell ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Dynamic Responses ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Relationship ◽  
Governing Equations ◽  
First Order

In this paper, the nonlinear dynamic responses of the blade with variable thickness are investigated by simulating it as a rotating pretwisted cantilever conical shell with variable thickness. The governing equations of motion are derived based on the von Kármán nonlinear relationship, Hamilton’s principle, and the first-order shear deformation theory. Galerkin’s method is employed to transform the partial differential governing equations of motion to a set of nonlinear ordinary differential equations. Then, some important numerical results are presented in terms of significant input parameters.

Response variations of a cantilever beam–tip mass system with nonlinear and linearized boundary conditions

2018 ◽  
Vol 25 (3) ◽  
pp. 485-496 ◽  
Author(s):  
Vamsi C. Meesala ◽  
Muhammad R. Hajj
Keyword(s):  
Boundary Conditions ◽  
Cantilever Beam ◽  
Nonlinear Boundary ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Boundary Conditions ◽  
Distributed Parameter ◽  
Governing Equations ◽  
Mass System ◽  
Tip Mass

The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.

Quantifying Attractor Morphing for High-Sensitivity Detection of Parameter Variations by Point Cloud Averaging

2005 ◽  
Author(s):  
Ali I. Hashmi ◽  
Bogdan I. Epureanu
Keyword(s):  
Atomic Force Microscope ◽  
Point Cloud ◽  
Time Series Data ◽  
Equations Of Motion ◽  
High Sensitivity ◽  
Series Data ◽  
Optimal Basis ◽  
Atomic Force ◽  
Nominal Parameter ◽  
Parameter Values

A novel method of damage detection for systems exhibiting chaotic dynamics is presented. The algorithm reconstructs variations of system parameters without the need for explicit system equations of motion, or knowledge of the nominal parameter values. The concept of a Sensitivity Vector Field (SVF) is developed. This construct captures geometrical deformations of the dynamical attractor of the system in state space. These fields are collected by the means of Point Cloud Averaging (PCA) applied to discrete time series data from the system under healthy (nominal parameter values) and damaged (variations of the parameters) conditions. Test variations are reconstructed from an optimal basis of the SVF snapshots which is generated by means of proper orthogonal decomposition. The method is applied to two system models, a magneto-elastic oscillator and an atomic force microscope. The method is shown to be highly accurate, and capable of identifying multiple simultaneous variations. The success of the method as applied to an atomic force microscope (AFM) and a magneto-elastic oscillator (MEO) indicates a potential for highly accurate sample readings by exploiting recently observed chaotic vibrations.

Closed-Form Solution of Natural Frequencies of a Cantilever Beam Under Longitudinal Rotation of the Support

2005 ◽  
Author(s):  
Mehdi Esmaeili ◽  
Mohammad Durali ◽  
Nader Jalili
Keyword(s):  
Closed Form ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Longitudinal Direction ◽  
Form Solution ◽  
Governing Equations ◽  
Well Drilling ◽  
General Base ◽  
Tip Mass

This paper presents the modeling steps towards development of frequency equations for a cantilever beam with a tip mass under general base excitations. More specifically, the beam is considered to vibrate in all the three directions, while subjected to a base rotational motion around its longitudinal direction. This is a common configuration utilized in many vibrating beam gyroscopes and well drilling systems. The governing equations are derived using Extended Hamilton’s Principle with general 6-DOF base motion. The natural frequency equations are then extracted in closed-form for the case where the base undergoes longitudinal rotation. For validation purposes, the resulting natural frequencies are compared with two example case studies; one with a beam on a stationary base and the other one with a rotor having flexible shaft.

Nonlinear dynamic responses of electrically actuated dielectric elastomer-based microbeam resonators

2021 ◽  
pp. 1045389X2110235
Author(s):  
Amin Alibakhshi ◽  
Hamidreza Heidari
Keyword(s):  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time History ◽  
Nonlinear Resonance ◽  
Multiple Scale ◽  
Dielectric Elastomer ◽  
Constitutive Law ◽  
Dynamic Responses ◽  
Governing Equations

This paper aims to investigate the chaotic and nonlinear resonant behaviors of a dielectric elastomer-based microbeam resonator, incorporating material and geometric nonlinearities. The von Kármán strain-displacement equation is utilized to model the geometric nonlinearity. Material nonlinearity is described via the hyperelastic Gent model and Neo-Hookean constitutive law. The applied electrical loading to the elastomer includes both static and sinusoidal voltages. The governing equations of motion are formulated based on an energy approach and generalized Hamilton’s principle. Employing a single-mode Galerkin technique, the governing equations are obtained only in terms of time derivatives. The governing ordinary differential equations are solved by means of the multiple scale method and a time-integration-based solver. The nonlinear resonance characteristics are explored through the frequency-amplitude plots. The nonlinear oscillations of the system are analyzed making use of visual techniques such as phase plane diagram, Poincaré section and time history, and fast Fourier transform. Based on the results obtained, the resonant behavior is the hardening type. The vibration of the dielectric elastomer based-microbeam is the quasiperiodic response.

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