A novel size-dependent quasi-3D isogeometric beam model for two-directional FG microbeams analysis

2019 ◽  
Vol 211 ◽  
pp. 76-88 ◽  
Author(s):  
Tiantang Yu ◽  
Jiankang Zhang ◽  
Huifeng Hu ◽  
Tinh Quoc Bui
Keyword(s):  
Beam Model ◽  
Size Dependent

Chaotic dynamics of the size-dependent non-linear micro-beam model

2017 ◽  
Vol 50 ◽  
pp. 16-28 ◽  
Author(s):  
A.V. Krysko ◽  
J. Awrejcewicz ◽  
S.P. Pavlov ◽  
M.V. Zhigalov ◽  
V.A. Krysko
Keyword(s):  
Chaotic Dynamics ◽  
Beam Model ◽  
Size Dependent ◽  
Non Linear

On the size-dependent nonlinear dynamics of viscoelastic/flexoelectric nanobeams

2020 ◽  
pp. 107754632095222
Author(s):  
Rasoul Bagheri ◽  
Yaghoub Tadi Beni
Keyword(s):  
Boundary Conditions ◽  
Viscoelastic Medium ◽  
Medium Effect ◽  
Small Scale ◽  
Beam Model ◽  
Governing Equations ◽  
Size Dependent ◽  
Flexoelectric Effect ◽  
Nonlinear Forced Vibration ◽  
Euler Bernoulli Beam

In this study, size-dependent nonlinear forced vibration of viscoelastic/flexoelectric nanobeams has been investigated. By calculating enthalpy and kinetic energy and using Hamilton’s principle, the coupled governing equations of viscoelastic/flexoelectric nanobeams are derived along with dependent electrical and mechanical boundary conditions. Furthermore, to take the effects of the small scale into account, the nonclassical theory of continuous medium has been used and the Euler–Bernoulli beam model has been adopted to model the nanobeams. Finally, the governing equations are solved using numerical methods for distributed loaded and clamped–clamped boundary conditions. By comparing the results, it is determined that the parameters of the size effect and the viscoelastic medium effect can increase the vibrational frequency of the nanobeams. Also, the results show that the frequency of nanobeams outside of the viscoelastic medium strongly depends on the size-dependent parameters, and the increase in the length and thickness of the nanobeam decreases the frequency. The results also show that with the increasing flexoelectric effect, the amplitude of the nonlinear oscillation increases.

Bernoulli–Euler Dielectric Beam Model Based on Strain-Gradient Effect

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Xu Liang ◽  
Shuling Hu ◽  
Shengping Shen
Keyword(s):  
Electric Field ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Beam Theory ◽  
Field Strain ◽  
Beam Model ◽  
Strain Gradient Elasticity ◽  
Cantilever Beams ◽  
Size Dependent ◽  
Classical Beam Theory

The theoretical investigation of the size dependent behavior of a Bernoulli–Euler dielectric nanobeam based on the strain gradient elasticity theory is presented in this paper. The variational principle is utilized to derive the governing equations and boundary conditions, in which the coupling between strain and electric field, strain gradient and electric field, and strain gradient and strain gradient are taken into account. Different from the classical beam theory, the size dependent behaviors of dielectric nanobeams can be described. The static bending problems of elastic, pure dielectric (nonpiezoelectric), and piezoelectric cantilever beams are solved to show the effects of the electric field-strain gradient coupling and the strain gradient elasticity. Comparisons between the classical beam theory and the strain gradient beam theory are given in this study. It is found that the beam deflection predicted by the strain gradient beam theory is smaller than that by the classical beam theory when the beam thickness is comparable to the internal length scale parameters and the external applied voltage obviously affects the deflection of the dielectric and piezoelectric nanobeam. The presented model is very useful for understanding the electromechanical coupling in nanoscale dielectric structures and is very helpful for designing devices based on cantilever beams.

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.

scholarly journals Nonlinear size-dependent modeling and dynamics of nanocrystalline arc resonators

2021 ◽  
Author(s):  
Amal Z. Hajjaj ◽  
Jonathan Ortiz ◽  
Abdessattar Abdelkefi
Keyword(s):  
Frequency Tuning ◽  
Electrostatic Force ◽  
Couple Stress Theory ◽  
Material Structure ◽  
Successful Implementation ◽  
Beam Model ◽  
Stress Theory ◽  
Size Dependency ◽  
Size Dependent ◽  
Resonance Frequencies

AbstractThe adequate modeling of the micro/nano arc resonators' dynamics is vital for their successful implementation. Here, a size-dependent model, wherein material structure, porosity, and micro-rotation effects of the grains are considered, is derived by combining the couple stress theory, multi-phase model, and the classical Euler–Bernoulli beam model, aiming to characterize the frequency tunability of micro/nano arc resonators as monitoring either the axial load or the electrostatic force for the first time. The arc dimensions are optimized to show various phenomena in the same arc, namely snap-through, crossing, and veering. The first three natural frequencies are monitored, showing the size dependency on the frequency tuning, snap-through/back, and pull-in instability as shrinking the scale from micro- to nano-scale. Significant changes in the static snap-through and pull-in voltages and the resonance frequencies were shown as scale shrinks. A dynamic analysis of the resonator's vibration shows a dramatic effect of the size-dependency as shrinking dimensions around the veering zone.

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