scholarly journals On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

2021 ◽  
Author(s):  
Mohammad Malikan ◽  
Tomasz Wiczenbach ◽  
Victor A. Eremeyev
Keyword(s):  
Thermal Loading ◽  
Effective Properties ◽  
Thermal Environment ◽  
Variational Formula ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Beam Model ◽  
Elastic Solids ◽  
Size Dependent ◽  
Euler Bernoulli Beam

AbstractBy relying on the Euler–Bernoulli beam model and energy variational formula, we indicate critical temperature causes in the buckling of piezo-flexomagnetic microscale beams. The corresponding size-dependent approach is underlying as a second strain gradient theory. Small deformations of elastic solids are assessed, and the mathematical discussion is linear. Regardless of the pyromagnetic effects, the thermal loading of the thermal environment varies in three states along with the thickness, which is linear, uniform, and parabolic forms. We then establish the results by developing consistent shape functions that independently evaluate boundary conditions. Next, we analytically develop and explore the effective properties of the studied beam concerning vital factors. It was achieved that piezomagnetic-flexomagnetic microbeams are more affected by the thermal environment while the thermal loading is parabolically distributed across the thickness, particularly when the boundaries involve simple supports.

Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory

2016 ◽  
Vol 231 (23) ◽  
pp. 4457-4469 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad R Barati
Keyword(s):  
Stress Field ◽  
Elastic Medium ◽  
Strain Gradient ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Beam Model ◽  
Simply Supported ◽  
Size Dependent ◽  
Nonlocal Strain Gradient

In this paper, size-dependent free vibration analysis of curved functionally graded nanobeams embedded in Winkler–Pasternak elastic medium is carried out via an analytical solution method. Three kinds of boundary condition namely, simply supported-simply supported, simply supported-clamped and clamped-clamped are investigated. Material properties of curved functionally graded beam change in thickness direction according to the Mori–Tanaka model. Nonlocal strain gradient elasticity theory is adopted to capture the size effects in which the stress is considered for not only the nonlocal stress field but also the strain gradients stress field. Nonlocal governing equations of curved functionally graded nanobeam are obtained from Hamilton’s principle based on Euler–Bernoulli beam model. Finally, the influences of length scale parameter, nonlocal parameter, opening angle, elastic medium, material composition, slenderness ratio and boundary conditions on the vibrational characteristics of nanosize curved functionally graded beams are explored.

Exact solution for frequency response of sandwich microbeams with functionally graded cores

2019 ◽  
Vol 25 (19-20) ◽  
pp. 2641-2655 ◽  
Author(s):  
Ehsan Taati ◽  
Famida Fallah
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Frequency Response ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Transverse Load ◽  
Gradient Theory ◽  
Beam Model ◽  
Various Boundary Conditions ◽  
Size Dependent

Based on the Euler–Bernoulli beam model and the modified strain gradient theory, the size-dependent forced vibration of sandwich microbeams with a functionally graded (FG) core is presented. The equation of motion and the corresponding classical and nonclassical boundary conditions are derived using the Hamilton’s principle. An exact solution of the governing equation is developed for sandwich beams with various boundary conditions and subjected to an arbitrarily distributed harmonic transverse load. Finally, parametric studies are presented to investigate the effects of geometric ratios, length scale parameters, power index, boundary conditions, layup, and thickness of the FG layer on the frequency response of clamped and simply supported microbeams. Numerical results show that in the case of clamped microbeams, the essential and natural size-dependent boundary conditions have a significant effect on the resonance frequency and transverse deflection of microbeams. Also, it is seen that an optimal layup (without change in total volume of each material) can significantly improve the frequency characteristics of sandwich microbeams.

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

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.

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

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.

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

2013 ◽  
Vol 27 (18) ◽  
pp. 1350083 ◽  
Author(s):  
Y. TADI BENI ◽  
M. ABADYAN
Keyword(s):  
Strain Gradient ◽  
Continuum Theory ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Cross Sectional ◽  
Size Dependent ◽  
Proposed Model ◽  
Molecular Force ◽  
Intrinsic Material Length ◽  
Material Length

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.

Sign in / Sign up

Export Citation Format

Share Document