scholarly journals Design of Harmonic AFM Probe Subjected to van der Waals Force in the Modified Couple Stress Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shueei-Muh Lin ◽  
Ching-Yao Chang ◽  
Chihng-Tsung Liauh ◽  
Wen-Rong Wang
Keyword(s):  
Couple Stress Theory ◽  
Classical Model ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Size Dependency ◽  
Two Factors ◽  
Modified Couple Stress ◽  
Afm Probe ◽  
Sample Distance ◽  
Probe Geometry

The conventional design of harmonic AFM probe geometry is made in neglect of the effects of the size-dependency factor and the tip-sample interacting force. Obviously, the effect of these two factors on the natural frequencies of a probe is significant. In this study, the effects of the two factors on the integer-multiples relation among frequencies are investigated. In this study, the effects of the two factors on the integer-multiples relation among frequencies are investigated. It is discovered that, in general, the integer-multiples relations of the probe’s frequencies in the classical model does not be kept as the same as that in the system with the effect of the size-dependency factor under the same material and geometry properties of probe. In addition, when the probe is used to measure the sample, the deviation of the relations will happen. The smaller the tip-sample distance is, the larger the deviation of integer-multiples frequencies is. The analytical method is presented here such that during scanning a sample at some tip-sample distance, the material and geometry properties of the probe can be tuned to the integer-multiples relation of resonant frequencies. Moreover, five similarity conditions among the systems with and without the effects of size-dependency and the tip-sample interacting force are discovered. According to these conditions, the integer-multiples relation is kept in different systems.

A NONLOCAL CURVED BEAM MODEL BASED ON A MODIFIED COUPLE STRESS THEORY

2011 ◽  
Vol 11 (03) ◽  
pp. 495-512 ◽  
Author(s):  
Y. P. LIU ◽  
J. N. REDDY
Keyword(s):  
Couple Stress Theory ◽  
Classical Model ◽  
Modified Couple Stress Theory ◽  
Curved Beam ◽  
Beam Model ◽  
Stress Theory ◽  
Material Length Scale Parameter ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length

A nonlocal Timoshenko curved beam model is developed using a modified couple stress theory and Hamilton's principle. The model contains a material length scale parameter that can capture the size effect, unlike the classical Timoshenko beam theory. Both bending and axial deformations are considered, and the Poisson effect is incorporated in the model. The newly developed nonlocal model recovers the classical model when the material length scale parameter and Poisson's ratio are both taken to be zero and the straight beam model when the radius of curvature is set to infinity. In addition, the nonlocal Bernoulli–Euler curved beam model can be realized when the normal cross-section assumption is restated. To illustrate the new model, the static bending and free vibration problems of a simply supported curved beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko curved beam model. Also, the differences in both the deflection and rotation predicted by the current and classical Timoshenko model are very large when the beam thickness is small, but they diminish with the increase of the beam height. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the nonlocal model is higher than that by the classical model, and the difference between them is significantly large only for very thin beams. These predicted trends of the size effect at the micron scale agree with those observed experimentally.

Investigating the Size-Dependent Static and Dynamic Behavior of Circular Micro-Plates Subjected to Capillary Force

2015 ◽  
Author(s):  
M. H. Kahrobaiyan ◽  
I. Vardi ◽  
M. T. Ahmadian ◽  
S. Henein
Keyword(s):  
Elasticity Theory ◽  
Capillary Force ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Size Dependency ◽  
Size Dependent ◽  
Modified Couple Stress

The size-dependent static deflection, pull-in instability and resonant frequency of a circular microplate under capillary force have been studied using modified couple stress elasticity theory. Size-dependency is a phenomenon in which the normalized quantities that classical elasticity theory predicts to be independent of the structure size, such as normalized deflection or normalized frequency, vary significantly as the structure size changes. This phenomenon has been observed in micro-scale structures such as micro-electro-mechanical-systems (MEMS). Since classical elasticity theory is unable to predict the size-dependency, non-classical elasticity theories such as modified couple stress theory have been developed recently. In this paper, modified couple stress theory is used for the first time to develop the governing equation and boundary conditions of circular microplates when subjected to capillary force. Consideration of capillary force is important since it is has a significant role in the mechanical behavior and stability of micro-scale structures in the presence of a liquid bridge. We investigated the static deflection and pull-in instability of microplates using the Galerkin method to assess the effect of size-dependency for static deflection. We observed that, as the ratio of the microplate thickness to length scale parameter (an additional material property suggested in modified couple stress theory to capture the size-dependency) decreases, the normalized deflection of the microplate also decreases. We further observed that the difference between the normalized deflection predicted by classical elasticity theory and the one evaluated using modified couple stress theory is significant when thickness of the microplate is small, but diminishes as thickness increases. Furthermore, we defined a dimensionless number called the dimensionless capillary tension (DCT) as a function of the mechanical, geometrical and size-dependent properties of the microplate as well as the characteristics of the liquid bridge such as the contact angle and the interfacial tension. We showed that for DCT values greater than a threshold evaluated in this paper, pull-in instability happens and the microplate collapses to the substrate. Moreover, we evaluated the size-dependent resonant frequency of the microplate under capillary force as a function of the DCT and obtained the result that the frequency decreases as DCT increases. In addition, our investigation of size-dependency revealed that as the ratio of the microplate thickness to length scale parameter increases, the frequency decreases in a way that for large values of the ratio, it asymptotically approaches the value predicted by classical elasticity theory.

scholarly journals Resonance-Size Parameter Relationship and Dynamics of an AFM Subjected to Multimode Excitation and Based on the Modified Couple Stress Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Shueei-Muh Lin ◽  
Ching-Yao Chang
Keyword(s):  
Couple Stress ◽  
Response Spectrum ◽  
Couple Stress Theory ◽  
Transient Behavior ◽  
Modified Couple Stress Theory ◽  
Size Parameter ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Afm Probe ◽  
Semianalytical Method

The mathematical model of AFM probe subjected to multimode excitation based on the modified couple stress theory is presented. The semianalytical solution of the system is proposed. The transient behavior and response spectrum of AFM probe subjected to multimode excitation are investigated. It is very helpful to predict the nanotopography and surface properties based on the response of multimodes excitation. The effects of the root excitation, size parameter, and interacting distance on the response spectrum and frequency shift are investigated. The resonant frequency relation of the two systems with different size parameters is discovered and expressed in a formula. The natural frequencies predicted via the formula and those determined by the semianalytical method are significantly consistent.

Size-Dependent Postbuckling of Piezoelectric Microbeams Based on a Modified Couple Stress Theory

2017 ◽  
Vol 09 (04) ◽  
pp. 1750053 ◽  
Author(s):  
Xingjia Li ◽  
Ying Luo
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Classical Model ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Postbuckling Behavior ◽  
Stress Theory ◽  
Size Dependent ◽  
Critical Buckling Force ◽  
Modified Couple Stress

This paper aims to investigate the postbuckling behavior of piezoelectric microbeams (PMBs) using a modified couple stress theory (MCST) and a Euler–Bernoulli–von Kármán beam model. The critical buckling force, voltage and the deformation amplitude were calculated for the buckling of the axially compressed microbeams with a clamp–clamp boundary condition. It is found that the stiffness of microbeams considering the MCST is higher than that given by the classical model when the feature size decreases to the microscale. Moreover, the microscale size effect has a strong influence on the critical buckling loads and the amplitude of postbuckling deformation. This study brings an improved understanding of the postbuckling behavior of PMBs, and offers useful guidance for the design of piezobeam-based sensors, actuators and stretchable microelectronics.

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