Size-Dependent Pull-In Instability of Hydrostatically and Electrostatically Actuated Circular Microplates

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
V. Mohammadi ◽  
M. Faghih Shojaei
Keyword(s):  
Boundary Conditions ◽  
Governing Equation ◽  
Couple Stress Theory ◽  
Gradient Elasticity ◽  
Modified Couple Stress Theory ◽  
Distributed Model ◽  
Length Scale ◽  
Scale Parameters ◽  
Various Boundary Conditions ◽  
Size Dependent

This article is concerned with the development of a distributed model based on the modified strain gradient elasticity theory (MSGT), which enables us to investigate the size-dependent pull-in instability of circular microplates subjected to the uniform hydrostatic and nonuniform electrostatic actuations. The model developed herein accommodates models based on the classical theory (CT) and modified couple stress theory (MCST), when all or two material length scale parameters are set equal to zero, respectively. On the basis of Hamilton's principle, the higher-order nonlinear governing equation and corresponding boundary conditions are obtained. In order to linearize the nonlinear equation, a step-by-step linearization scheme is implemented, and then the linear governing equation is discretized along with different boundary conditions using the generalized differential quadrature (GDQ) method. In the case of CT, it is indicated that the presented results are in good agreement with the existing data in the literature. Effects of the length scale parameters, hydrostatic and electrostatic pressures, and various boundary conditions on the pull-in voltage and pull-in hydrostatic pressure of circular microplates are thoroughly investigated. Moreover, the results generated from the MSGT are compared with those predicted by MCST and CT. It is shown that the difference between the results from the MSGT and those of MCST and CT is considerable when the thickness of the circular microplate is on the order of length scale parameter.

scholarly journals Electroelastic biaxial compression of nanoplates considering piezoelectric effects

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Mohammad Malikan
Keyword(s):  
Scale Parameter ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Theoretical Work ◽  
Modified Couple Stress Theory ◽  
Length Scale Parameter ◽  
Biaxial Compression ◽  
Length Scale ◽  
Stress Theory ◽  
Various Boundary Conditions

In the present theoretical work, it is assumed that a piezoelectric nanoplate is connected to the voltage meter which voltages have resulted from deformation of the plate due to in-plane compressive forces whether they are critical buckling loads or arbitrary forces. In order to derive governing equations, a simplified four-variable shear deformation plate theory has been employed using Hamilton’s principle and Von-Kármán assumptions. Modified couple stress theory has been applied to considering size-dependent effects in nano size. In order to compare the results, a validation has been done with the results of macroscopic. Results have been presented by changing some parameters, such as aspect ratio, various boundary conditions and length scale parameter influence on the produced voltage by the piezoelectric nanoplate. The most important outcomes show that an increase in length scale parameter leads to decreasing the produced voltage at constant in-plane arbitrary forces.

A modified couple stress theory for buckling analysis of higher order inhomogeneous microbeams with porosities

2018 ◽  
Vol 233 (8) ◽  
pp. 2855-2866 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Fateme Mahmoodi
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Stress Theory ◽  
Various Boundary Conditions ◽  
Modified Couple Stress

In this paper, buckling behavior of a higher order functionally graded microbeam with porosities is investigated based on the modified couple stress theory and the exact position of the neutral axis. Porosities are evenly and unevenly distributed inside the functionally graded microbeam. Material properties of the functionally graded microbeam are assumed to vary in the thickness direction through a modified form of power-law distribution in which the volume fraction of porosities is considered. The governing equations are derived by using Hamilton's principle and an analytical method is employed to solve these equations for various boundary conditions. The present formulation and numerical results demonstrate a good agreement with some available cases in the literature. Influences of several important parameters such as power-law exponent, porosity distributions, porosity volume fraction, slenderness ratio, and various boundary conditions on buckling loads of porous functionally graded microbeams are investigated and discussed in detail.

Free vibration and buckling analysis of laminated composites and sandwich microbeams using a transverse shear-normal deformable beam theory

2019 ◽  
Vol 26 (3-4) ◽  
pp. 214-228 ◽  
Author(s):  
Armagan Karamanli ◽  
Metin Aydogdu
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transverse Shear ◽  
Couple Stress Theory ◽  
Laminated Composite ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Arbitrary Boundary ◽  
Various Boundary Conditions ◽  
Aspect Ratios

In this paper, the free vibration and buckling responses of laminated composite and sandwich microbeams with arbitrary boundary conditions are investigated. The governing equations based on the modified couple stress theory are derived by using the total potential energy of a microbeam and employing a transverse shear-normal deformable beam theory. Extensive analysis results in terms of dimensionless fundamental frequencies and dimensionless critical buckling loads are introduced for various boundary conditions, aspect ratios, orthotropy ratios, fiber orientation angles, thickness to material length scale parameter ratios, and core thickness to face layer thickness ratios.

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.

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