USE OF STRAIN GRADIENT THEORY FOR MODELING THE SIZE-DEPENDENT PULL-IN OF ROTATIONAL NANO-MIRROR IN THE PRESENCE OF MOLECULAR FORCE

Experiments reveal that mechanical behavior of nanostructures is size-dependent. Herein, the size dependent pull-in instability of torsional nano-mirror is investigated using strain gradient nonclassic continuum theory. The governing equation of the mirror is derived taking the effect of electrostatic Coulomb and molecular van der Waals (vdW) forces into account. Variation of the rotation angle of the mirror as a function of the applied voltage is obtained and the instability parameters i.e., pull-in voltage and pull-in angle are determined. Nano-mirrors with square and circular cross-sectional beams are investigated as case studies. It is found that when the thickness of the torsional nano-beam is comparable with the intrinsic material length scales, size effect can substantially increase the instability parameters of the rotational mirror. Moreover, the effect of vdW forces on the size-dependent pull-in instability of the system is discussed. The proposed model is able to predict the experimental results more accurately than the previous classic models and reduce the gap between experiment and previous theories.

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On size-dependent bending behaviors of shape memory alloy microbeams via nonlocal strain gradient theory

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x20986993 ◽

2021 ◽

pp. 1045389X2098699

Author(s):

Bo Zhou ◽

Zetian Kang ◽

Xiao Ma ◽

Shifeng Xue

Keyword(s):

Shape Memory Alloy ◽

Shape Memory ◽

Functionally Graded ◽

Strain Gradient Theory ◽

Gradient Theory ◽

Size Dependent ◽

Material Length Scale Parameter ◽

Material Length Scale ◽

Material Length ◽

Nonlocal Strain Gradient

This paper focuses on the size-dependent behaviors of functionally graded shape memory alloy (FG-SMA) microbeams based on the Bernoulli-Euler beam theory. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus and critical transformation stresses vary continuously along the longitudinal direction. According to the simplified linear shape memory alloy (SMA) constitutive equations and nonlocal strain gradient theory, the mechanical model was established via the principle of virtual work. Employing the Galerkin method, the governing differential equations were numerically solved. The functionally graded effect, nonlocal effect and size effect of the mechanical behaviors of the FG-SMA microbeam were numerically simulated and discussed. Results indicate that the mechanical behaviors of FG-SMA microbeams are distinctly size-dependent only when the ratio of material length scale parameter to the microbeam height is small enough. Both the increments of material nonlocal parameter and ratio of material length-scale parameter to the microbeam height all make the FG-SMA microbeam become softer. However, the stiffness increases with the increment of FG parameter. The FG parameter plays an important role in controlling the transverse deformation of the FG-SMA microbeam. This work can provide a theoretical basis for the design and application of FG-SMA microstructures.

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On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220965611 ◽

2020 ◽

pp. 095440622096561

Author(s):

Amir-Reza Asghari Ardalani ◽

Ahad Amiri ◽

Roohollah Talebitooti ◽

Mir Saeed Safizadeh

Keyword(s):

Wave Propagation ◽

Strain Gradient ◽

Surface Elasticity ◽

Shear Deformation Theory ◽

Wave Dispersion ◽

Strain Gradient Theory ◽

Wave Number ◽

Gradient Theory ◽

Specific Domain ◽

Size Dependent

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

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