scholarly journals Size-Dependent Dynamic Behavior of a Microcantilever Plate

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaoming Wang ◽  
Fei Wang
Keyword(s):  
Size Effect ◽  
Dynamic Behavior ◽  
Size Effects ◽  
Numerical Solutions ◽  
Couple Stress Theory ◽  
Differential Quadrature Method ◽  
Modified Couple Stress Theory ◽  
Cantilever Plate ◽  
Size Dependent ◽  
Material Length Scale

Material length scale considerably affects the mechanical properties of microcantilever components. Recently, cantilever-plate-like structures have been commonly used, whereas the lack of studies on their size effects constrains the design, testing, and application of these structures. We have studied the size-dependent dynamic behavior of a cantilever plate based on a modified couple stress theory and the differential quadrature method in this note. The numerical solutions of microcantilever plate equation involving the size effect have been presented. We have also analyzed the bending and vibration of the microcantilever plates considering the size effect and discussed the dependence of the size effect on their geometric dimensions. The results have shown that (1) the mechanical characteristics of the cantilever plate show obvious size effects; as a result, the bending deflection of a microcantilever plate reduces whereas the natural frequency increases effectively and (2) for the plates with the same material, the size effect becomes more obvious when the plates are thinner.

Modeling size-dependent thermal-mechanical behaviors of shape memory polymer Timoshenko micro-beam

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fei Zhao ◽  
Xueyao Zheng ◽  
Shichen Zhou ◽  
Bo Zhou ◽  
Shifeng Xue
Keyword(s):  
Size Effect ◽  
Shape Memory ◽  
Couple Stress Theory ◽  
Shape Memory Polymer ◽  
Modified Couple Stress Theory ◽  
Mechanical Behaviors ◽  
Equilibrium Equations ◽  
Content Type ◽  
Size Dependent ◽  
Beam Height

PurposeIn this paper, a three-dimensional size-dependent constitutive model of SMP Timoshenko micro-beam is developed to describe the micromechanical properties.Design/methodology/approachAccording to the Hamilton's principle, the equilibrium equations and boundary conditions of the model are established and according to the modified couple stress theory, the model is available to capturing the size effect because of the material length scale parameter. Based on the model, the simply supported beam was taken for example to be solved and simulated.FindingsResults show that the size effect of SMP micro-beam is more obvious when the dimensionless beam height is similar or the larger of the value of loading time. The rigidity and strength of the SMP beam decrease with the increasing of the dimensionless beam height or the loading time. The viscous property of SMP micro-beam plays a more important role with the larger dimensionless beam height. And the smaller the dimensionless beam height is, the more obvious the shape memory effect of the SMP micro-beam is.Originality/valueThis work implies prediction of size-dependent thermo-mechanical behaviors of the SMP micro-beam and will provide a theoretical basis for design SMP microstructures in the field of micro/nanomechanics.

scholarly journals Analysis of Bifurcation and Chaos of the Size-dependent Micro–plate Considering Damage

2019 ◽  
Vol 8 (1) ◽  
pp. 461-469 ◽  
Author(s):  
Xiumei Wang ◽  
Jihai Yuan ◽  
Haorui Zhai
Keyword(s):  
Internal State ◽  
Couple Stress Theory ◽  
Damage Model ◽  
Modified Couple Stress Theory ◽  
Damage Effect ◽  
Bifurcation And Chaos ◽  
Stress Theory ◽  
Size Dependent ◽  
Material Length Scale ◽  
Plate System

Abstract In this research, nonlinear dynamics and characteristics of a micro–plate system under electrostatic forces on both sides are studied. A novel model, which takes micro-scale effect and damage effect into account, is established on the basis of the Talreja’s tensor valued internal state damage model and modified couple stress theory. According to Hamilton principle, the dynamic governing equations of the size-dependent micro–plate are derived by variational method and solved via Galerkin method and the fourth order Runge-Kutta method. The effects of damage variable and material length scale parameter on bifurcation and chaos of the micro–plate system are presented with numerical simulations using the bifurcation diagram, Poincare map. Results provide a theoretical basis for the design of dynamic stability of electrically actuated micro- structures.

Size-Dependent Dynamic Behavior and Instability Analysis of Nano-Scale Rotational Varactor in the Presence of Casimir Attraction

2016 ◽  
Vol 08 (02) ◽  
pp. 1650018 ◽  
Author(s):  
Hamid M. Sedighi ◽  
Meisam Moory-Shirbani ◽  
Mohammad Shishesaz ◽  
Ali Koochi ◽  
Mohamadreza Abadyan
Keyword(s):  
Dynamic Behavior ◽  
Casimir Force ◽  
Scale Parameter ◽  
Dynamic Instability ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Stress Theory ◽  
Size Dependent ◽  
Casimir Attraction

When the size of structures approaches to the sub-micron scale, physical responses of such systems become size-dependent, hence, classic theories may not be able to predict the behavior of the miniature structures. In the present article, the modified couple stress theory (MCST) is employed to account for the effect of the size-dependency on the dynamic instability of torsional nano-electromechanical systems (NEMS) varactor. By incorporating the Coulomb, Casimir and damping forces, the dimensionless governing equations are derived. The influences of Casimir force, applied voltage and length scale parameter on the dynamic behavior and stability of fixed points are investigated by plotting the phase portrait and bifurcation diagrams. It is found that the Casimir force reduces the instability threshold of the systems and the small-scale parameter enhances the torsional stability. The pull-in instability phenomenon shows the saddle-node bifurcation for torsional nano-varactor.

Nonlinear Analysis of Microswitches Considering Nonclassical Theory

2017 ◽  
Vol 09 (08) ◽  
pp. 1750113 ◽  
Author(s):  
S. Hakamiha ◽  
M. Mojahedi
Keyword(s):  
Classical Theory ◽  
Couple Stress ◽  
Numerical Solutions ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Size Dependent ◽  
Modified Couple Stress ◽  
Dependent Model ◽  
Analytical Approaches

This paper introduces a new nonlinear model for microswitches based on the modified couple stress theory. The microswitch includes a microbeam which is connected to the clamped support from one side and attached to an electrostatically driven proof mass with a large gap from the other side. The microswitch operates in the pull-in instability with large deformation. The effects of fringing field and large curvature as well as size dependency are considered in the modeling. With regard to the size-dependent model, the equations of motion are obtained using Hamilton’s principle and solved by both numerical and analytical approaches. Consequently, dynamic pull-in instability is investigated based on the analytical and numerical solutions for dynamic conditions. The results depict that the dynamic deflection predicted by the modified couple stress theory is smaller than that obtained by the classical theory. The classical theory underestimates the pull-in instability voltage of the microswitches especially when the beam’s thickness is in the order of material length scale parameter. Furthermore, it is shown that neglecting nonlinearity due to large deflection leads to significant errors in the pull-in instability of the microstructures and these errors are calculated. The novelty of this paper is to provide a nonlinear size-dependent model for microswitches and to investigate the nonlinearity and instability of microswitches based on this model using the analytical and numerical methods.

Size Effect on Pull-In Behaviors of Electrostatically Actuated Cantilever Micro-Beams

2013 ◽  
Vol 300-301 ◽  
pp. 889-892
Author(s):  
Sheng Li Kong
Keyword(s):  
Size Effect ◽  
Couple Stress Theory ◽  
Ritz Method ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Electrostatically Actuated ◽  
Size Dependent ◽  
Deformation Problem ◽  
Approximate Analytical Solutions ◽  
Modified Couple Stress

For the deformation problem of an electrostatically actuated cantilever micro-beam, size effect on pull-in behaviors of the micro-beams have been studied based on modified couple stress theory. The approximate analytical solutions to the pull-in voltage and pull-in displacement of the micro-beam are derived by using the Rayleigh-Ritz method. The results show that the normalized pull-in voltage of the cantilever micro-beam is size-dependent and the normalized pull-in displacement of the micro-beam is size independence.

Size-Dependent Dynamic Behavior of Electrostatically Actuated Microaccelerometers Under Mechanical Shock

2017 ◽  
Vol 17 (04) ◽  
pp. 1750042 ◽  
Author(s):  
M. Rahaeifard ◽  
M. Mojahedi
Keyword(s):  
Dynamic Response ◽  
Dynamic Behavior ◽  
Classical Theory ◽  
Couple Stress Theory ◽  
Perturbation Technique ◽  
Finite Difference Methods ◽  
Modified Couple Stress Theory ◽  
Mechanical Shock ◽  
Electrostatically Actuated ◽  
Size Dependent

This paper studies the size-dependent dynamic behavior of electrostatically actuated microaccelerometers using the modified couple stress theory. The device is modeled as a cantilevered microbeam with an electrostatically actuated proof mass attached to its free end. The equation of motion is derived based on the Hamilton’s principle and solved both numerically (using the finite element and finite difference methods) and analytically (using the perturbation technique) and the dynamic response and pull-in instability of the device is studied. The results of these methods are compared and the source of error in the analytical results at high values of external acceleration is discussed. Furthermore, the results are compared with those evaluated based on the classical theory. It is found that for cantilevered accelerometers with a beam thickness of the order of the material length scale parameter, the classical theory gives a rough estimation of the dynamic response of the system. In this situation, the error of using the classical theory may change the prediction of the system behavior from unstable to stable.

scholarly journals Analytic solution for size-dependent behaviors of micro-beam under forced vibration

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Shuai WANG ◽  
Zhiyong WANG ◽  
Feifei WANG ◽  
Bo ZHOU ◽  
Shifeng XUE
Keyword(s):  
Forced Vibration ◽  
Couple Stress Theory ◽  
Separation Of Variables ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Mechanical Behaviors ◽  
Governing Equations ◽  
Euler Beam ◽  
Size Dependent ◽  
Material Length Scale

This paper focuses on the size-dependently mechanical behaviors of a micro-beam under forced vibration. Governing equations of a micro-beam under forced vibration are established by using the modified couple stress theory, Bernoulli-Euler beam theory and D’Alembert’s principle together. A simply supported micro-beam under forced vibration is solved according to the established governing equations and the method of separation of variables. The dimensionless deflection, amplitude mode and period mode are defined to investigate the size-dependently mechanical behaviors of a micro-beam under forced vibration. Results show that the performance of a micro-beams under forced vibration is distinctly size-dependent when the ratio of micro-beam height to material length-scale parameter is small enough. Both frequency ratio and loading location are the important factors that determine the size-dependent performance of a micro-beams under forced vibration.

Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage

2013 ◽  
Vol 228 (5) ◽  
pp. 896-906 ◽  
Author(s):  
Masoud Rahaeifard ◽  
Mohammad Taghi Ahmadian ◽  
Keikhosrow Firoozbakhsh
Keyword(s):  
Dynamic Behavior ◽  
Classical Theory ◽  
Couple Stress ◽  
Multiple Scales ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Dc Voltage ◽  
Size Dependent ◽  
Modified Couple Stress

This paper investigates the dynamic behavior of microcantilevers under suddenly applied DC voltage based on the modified couple stress theory. The cantilever is modeled based on the Euler–Bernoulli beam theory and equation of motion is derived using Hamilton’s principle. Both analytical and numerical methods are utilized to predict the dynamic behavior of the microbeam. Multiple scales method is used for analytical analysis and the numerical approach is based on a hybrid finite element/finite difference method. The results of the modified couple stress theory are compared with those from the literature as well as the results predicted by the classical theory. It is shown that the modified couple stress theory predicts size-dependent normalized dynamic behavior for the microbeam while according to the classical theory the normalized behavior of the microbeam is independent of its size. When the thickness of the beam is in order of its material length scale, the difference between the results given by the modified couple stress theory and those predicted by the classical theory is considerable. As the beam thickness increases, the results of the modified couple stress theory converge to those of the classical theory.

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