Static Analysis of Electrically Actuated Nano to Micron Scale Beams Using Nonlocal Theory

2011 ◽  
Author(s):  
Y. Alizadeh Vaghasloo ◽  
Abdolreza Pasharavesh ◽  
M. T. Ahmadian ◽  
Ali Fallah
Keyword(s):  
Size Effect ◽  
Algebraic Equation ◽  
Bending Moment ◽  
Nonlocal Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Beam Deflection ◽  
Electrostatically Actuated ◽  
Size Dependent ◽  
Electrically Actuated ◽  
The One

In this paper, size dependent static behavior of micro and nano cantilevers actuated by a static electric field including deflection and pull-in instability, is analyzed implementing nonlocal theory. Euler-bernoulli assumptions are made to model the relation between deflection of the beam and bending moment. Differential form of the constitutive equation of nonlocal theory is used to find the revised equation for bending moment and substituting in the equilibrium equation of electrostatically actuated beams final nonlinear ordinary differential equation is arrived. Also the boundary conditions for solving the equation are revised and to analyze the size effect better governing equation is nondimetionalized. The one parameter Galerkin method is used to transform this equation to a nonlinear algebraic equation. Arrived algebraic equation is solved utilizing Newton-Raphson method. Size effect on the maximum deflection and deflection shape for various applied voltages is studied. Also effect of beam size on the static pull-in voltage is studied. Results indicate that the dimensionless beam deflection decreases as size decreases while the pull-in voltage increases and specially change of deflection and pull-in voltage is significant for nanobeams.

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.

Effect of Microbeam Electrical Resistivity on Dynamic Pull-In Voltage of an Electrostatically Actuated Microbeam

2010 ◽  
Author(s):  
Abdolreza Pasharavesh ◽  
M. T. Ahmadian ◽  
Y. Alizadeh Vaghasloo ◽  
A. Assempour
Keyword(s):  
Electrical Resistivity ◽  
Differential Equations ◽  
Differential Quadrature Method ◽  
Nonlinear Partial Differential Equations ◽  
System Stability ◽  
Beam Deflection ◽  
Quadrature Method ◽  
Electrostatically Actuated ◽  
Voltage Application ◽  
The One

The dynamic pull-in voltage as a criterion for the system stability is one of the most important effects considered with the dynamics of microstructures. In this study effect of microbeam electrical resistivity on the pull-in voltage of an electrostatically actuated microbeam is investigated. Assuming Euler-Bernoulli theory for the microbeam, two coupled nonlinear partial differential equations are derived for the beam deflection and voltage. The one parameter Galerkin method is implemented to transform the equations to a set of nonlinear coupled ordinary differential equations. Obtained equations are solved implementing the differential quadrature method (DQM). Variation of dynamic pull-in voltage with changing the microbeam electrical resistivity with different boundary conditions and different configurations of voltage application, is investigated. Considering effect of resistivity on the deflection of the beam, it is observed that at a certain resistivity called critical resistivity there exists a jump in frequency with a peak in damping of the beam. Results indicate that the dynamic pull-in voltage increases when the microbeam electrical resistivity is increased and reaches the static pull-in voltage for resistivities higher than this critical resistivity.

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.

Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
J. Awrejcewicz ◽  
A. V. Krysko ◽  
S. P. Pavlov ◽  
M. V. Zhigalov ◽  
V. A. Krysko
Keyword(s):  
Differential Equations ◽  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Stability Loss ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Timoshenko Beams ◽  
Size Dependent ◽  
Rigid Layer ◽  
Graded Material

The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state.

Microarray-assisted size-effect study of amorphous silica nanoparticles on human bronchial epithelial cells

Nanoscale ◽  
2019 ◽  
Vol 11 (47) ◽  
pp. 22907-22923 ◽  
Author(s):  
Yang Li ◽  
Junchao Duan ◽  
Xiangyuan Chai ◽  
Man Yang ◽  
Ji Wang ◽  
...  
Keyword(s):  
Gene Expression ◽  
Epithelial Cells ◽  
Size Effect ◽  
Toxic Effect ◽  
Silica Nanoparticles ◽  
Amorphous Silica ◽  
Effect Study ◽  
Human Bronchial Epithelial Cells ◽  
Bronchial Epithelial ◽  
Size Dependent

Silica nanoparticles produced size-dependent toxic effect on the gene expression profile of BEAS-2B cells.

Investigation of the Oscillatory Behavior of Electrostatically-Actuated Microbeams

2010 ◽  
Author(s):  
Mahdi Mojahedi ◽  
Mahdi Moghimi Zand ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Axial Stress ◽  
Nonlinear Partial Differential Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Oscillatory Behavior ◽  
Electrostatically Actuated ◽  
Homotopy Analysis ◽  
Analytic Expressions ◽  
Good Agreement

Vibrations of electrostatically-actuated microbeams are investigated. Effects of electrostatic actuation, axial stress and midplane stretching are considered in the model. Galerkin’s decomposition method is utilized to convert the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. Homotopy perturbation method (i.e. a special and simpler case of homotopy analysis method) is utilized to find analytic expressions for natural frequencies of predeformed microbeam. Effects of increasing the voltage, midplane stretching, axial force and higher modes contribution on natural frequency are also studied. The anayltical results are in good agreement with the numerical results in the literature.

scholarly journals Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jihai Yuan ◽  
Xiangmin Zhang ◽  
Changping Chen
Keyword(s):  
Size Effect ◽  
Frequency Response ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Couple Stress Theory ◽  
Harmonic Balance Method ◽  
Damage Effect ◽  
Physical Parameters ◽  
Response Curves ◽  
Electrically Actuated

Since microplates are extensively used in MEMS devices such as microbumps, micromirrors, and microphones, this work aims to study nonlinear vibration of an electrically actuated microplate whose four edges are clamped. Based on the modified couple stress theory (MCST) and strain equivalent assumption, size effect and damage are taken into consideration in the present model. The dynamic governing partial differential equations of the microplate system were obtained using Hamilton’s principle and solved using the harmonic balance method after they are transformed into ordinary differential equation with regard to time. Size effect and damage effect on nonlinear free vibration of the microplate under DC voltage are discussed using frequency-response curve. In the forced vibration analysis, the frequency-response curves were also employed for the purpose of highlighting the influence of different physical parameters such as external excitation, damping coefficient, material length scale parameter, and damage variable when the system is under AC voltage. The results presented in this study may be helpful and useful for the dynamic stability of a electrically actuated microplate system.

Coupled Interfacial Energy and Temperature Effects on Size-Dependent Yield Strength and Strain Hardening of Small Metallic Volumes

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Rashid K. Abu Al-Rub ◽  
Abu N. M. Faruk
Keyword(s):  
Yield Strength ◽  
Size Effect ◽  
Strain Hardening ◽  
Interfacial Energy ◽  
Thermal Loading ◽  
Temperature Sensitive ◽  
Gradient Plasticity ◽  
Energy Effect ◽  
Size Dependent ◽  
Film Substrate

Plasticity in heterogeneous metallic materials with small volumes is governed by the interactions of dislocations at interfaces. In particular, interfaces of a material confined in a small volume can strongly affect the mechanical properties of micro and nanosystems. In this paper, the framework of higher-order strain gradient plasticity theory with interfacial energy effect is used to investigate the coupling of interfacial energy with temperature and how it affects the initial yield strength (i.e., onset of plasticity) and the strain hardening rates of confined small metallic volumes. It is postulated that the interfacial energy decreases as temperature increases such that size effect decreases as temperature increases. As an application, the size effect of thermal loading of a film-substrate system is investigated. It is shown that the temperature at which the film starts to yield plastically is size-dependent, which is attributed to the size-dependent yield strength. Furthermore, the flow stress is more temperature sensitive as the size decreases.

Synthesis of Self-Assembly Au Nano-Particles Based on Sodium Citrate-Tannin Reduction Method

2011 ◽  
Vol 311-313 ◽  
pp. 461-465
Author(s):  
Dau Chung Wang ◽  
Shinn Hwa Chen ◽  
Gen You Chen ◽  
Ken Yen Chen ◽  
Cheng Hsien Tsai
Keyword(s):  
Particle Size ◽  
Self Assembly ◽  
Reduction Method ◽  
Low Cost ◽  
Trisodium Citrate ◽  
Nano Particles ◽  
Size Dependent ◽  
Biological Toxicity ◽  
The One ◽  
Au Nano Particles

Recently, self-assembly synthesis of metal nano-particles has attracted great interest due to its unique size dependent properties. In this study, an easy synthesis would be developed to form Au nano-particles which are without toxicity. The Au particles could be applied in biological and biological toxicity experiments. Some phenomena could be discovered in this paper. First, the concentration ratio of Au and trisodium citrate would be adjusted to control the Au nano-particles size. And the particle size is limited because of the size dependent energy would be discovered in this paper. The minimum particle size is also found. The one phase liquid reduction method is easy and without toxicity, it is low-cost, high-throughput, and suitable to be applied in biological and biological toxicity studies.

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