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.

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.

scholarly journals Redesigned Sensor Holder for an Atomic Force Microscope with an Adjustable Probe Direction

2021 ◽  
Author(s):  
Janik Schaude ◽  
Maxim Fimushkin ◽  
Tino Hausotte
Keyword(s):  
Atomic Force Microscope ◽  
Piezoelectric Actuator ◽  
High Speed ◽  
Closed Loop ◽  
Coefficient Of Thermal Expansion ◽  
Measuring System ◽  
Contact Mode ◽  
Loop Control ◽  
Atomic Force ◽  
Measuring Machine

AbstractThe article presents a redesigned sensor holder for an atomic force microscope (AFM) with an adjustable probe direction, which is integrated into a nano measuring machine (NMM-1). The AFM, consisting of a commercial piezoresistive cantilever operated in closed-loop intermitted contact-mode, is based on two rotational axes, which enable the adjustment of the probe direction to cover a complete hemisphere. The axes greatly enlarge the metrology frame of the measuring system by materials with a comparatively high coefficient of thermal expansion. The AFM is therefore operated within a thermostating housing with a long-term temperature stability of 17 mK. The sensor holder, connecting the rotational axes and the cantilever, inserted one adhesive bond, a soldered connection and a geometrically undefined clamping into the metrology circle, which might also be a source of measurement error. It has therefore been redesigned to a clamped senor holder, which is presented, evaluated and compared to the previous glued sensor holder within this paper. As will be shown, there are no significant differences between the two sensor holders. This leads to the conclusion, that the three aforementioned connections do not deteriorate the measurement precision, significantly. As only a minor portion of the positioning range of the piezoelectric actuator is needed to stimulate the cantilever near its resonance frequency, a high-speed closed-loop control that keeps the cantilever within its operating range using this piezoelectric actuator further on as actuator was implemented and is presented within this article.

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.

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.

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.

Vibration Analysis of Single Lap Adhesive Joint with Non-Uniform Adhesive Thickness: Experimental and Analytical Investigation

2011 ◽  
Vol 418-420 ◽  
pp. 1312-1319
Author(s):  
Wei Dong Li ◽  
Jin Xiang Gu ◽  
Ping Hu ◽  
Kun Yue Wu
Keyword(s):  
Epoxy Resin ◽  
Adhesive Joint ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Analytical Investigation ◽  
Dynamic Responses ◽  
Axial Deformation ◽  
Test Technique ◽  
Slant Angle ◽  
Adhesive Thickness

This paper deals with the analytical and experimental vibration analysis of the single lap adhesive joint with non-uniform adhesive thickness . In the theoretical part, an analytical modal is described and a motion equation is built. A joint consists of two different adherends are bonded over a certain length by a viscoelastic material, epoxy resin. Adherends are modeled as Euler-Bernoulli beams. Both ransverse and axial deformation of adherends are considered in deriving the equations of motion. In the experimental part, the steel use Q235, the aluminium use 6016-T4 and the adhesive use ESP110 and AV138, epoxy resin. Dynamic responses of the joints are investigated using the hammer test technique, natural frequencies and model shapes obtained by using an accelerometer depended on the accelerometer location in the system, which is attributed to its mass contribution to the overall system mass. The investigates are also carried out using the finite element method(FEM) and simulated with ABAQUS. Both results show that resonant frequencies decrease with the slant angle increase.

scholarly journals On the Modeling of Periodic Sandwich Structures with the Use of the Broken Line Hypothesis

2020 ◽  
Vol 22 (3) ◽  
pp. 761-774 ◽  
Author(s):  
Jakub Marczak
Keyword(s):  
Vibration Analysis ◽  
Sandwich Plate ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
System Of Equations ◽  
Governing Equations ◽  
Fem Model ◽  
Constant Coefficients ◽  
Plate Strip ◽  
Periodic Plate

AbstractIn this paper a dynamic analysis of sandwich plate with a certain periodic microstructure is considered. The initial system of governing equations is derived basing on the classic broken line hypothesis. As a result of transformations one can obtain a system of three differential equations of motion with periodic, highly oscillating and non-continuous coefficients. In order to derive a system of equations with constant coefficients tolerance averaging technique is applied. Eventually, in the calculation example a free vibration analysis of certain periodic plate strip is performed with the use of both the derived model and a FEM model. It can be observed that the consistency of obtained results is highly dependent on the calculation assumptions.

On the Free Vibration Analysis of a Sandwich Beam With Tip Mass

2018 ◽  
Author(s):  
E. F. Joubaneh ◽  
O. R. Barry
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Sandwich Beam ◽  
Free Vibration Analysis ◽  
Design Parameters ◽  
Governing Equations ◽  
Tip Mass

This paper presents the free vibration analysis of a sandwich beam with a tip mass using higher order sandwich panel theory (HSAPT). The governing equations of motion and boundary conditions are obtained using Hamilton’s principle. General Differential Quadrature (GDQ) is employed to solve the system governing equations of motion. The natural frequencies and mode shapes of the system are presented and Ansys simulation is performed to validate the results. Various boundary conditions are also employed to examine the natural frequencies of the sandwich beam without tip mass and the results are compared with those found in the literature. Parametric studies are conducted to examine the effect of key design parameters on the natural frequencies of the sandwich beam with and without tip mass.

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