Size-dependent continuum-based model of a flexoelectric functionally graded cylindrical nanoshells Asghar Faramarzi Babadi, Yaghoub Tadi Beni Mathematical Methods in the Applied Sciences, 2026 Flexoelectricity is dependent on the strain gradient, which is high in microscale and nanoscale, leading to its considerable effect on the electromechanical behavior of structures in microscale and nanoscale. Using the Love's theory for thin shells and the modified flexoelectricity theory, governing coupled equations of the functionally graded magneto‐electro‐elastic (FGMEE) cylindrical nanoshells were formulated along with their boundary conditions using the Hamilton's principle and variation method. It is worth noting that the governing coupled equations of FGMEE cylindrical nanoshell with an electric potential‐independent polarization parameter, where the polarization is independent of the electric potential, are considered the major novelty of this study. To show the ability and uniqueness of the formulation, free vibrations of the shell were examined in a specific state, regardless of the magnetic field effect under the clamped–clamped boundary condition. The effects of different parameters including geometry, size effect, and external voltage on the vibration frequency of the nanoshell were investigated. According to the results, the vibration behavior of the flexoelectric nanoshell is largely dependent on the size effect. Given the application of this structure in sensors and actuators, the external voltage has a considerable effect on the electromechanical behavior of the structure in the presence of the flexoelectric effect.
Vibration analysis of shell-like curved carbon nanotubes using nonlocal strain gradient theory Jamal Zare, Alireza Shateri, Yaghoub Tadi Beni, Afshin Ahmadi Mathematical Methods in the Applied Sciences, 2026 The performance of nanotube‐based resonators is significantly affected by the variation of their natural frequencies. In reality, nanotubes may have some levels of initial imperfection, which definitely changes their vibrational characteristics. In the present article, the vibrational behavior of initially curved nanotubes is investigated on the basis of thin shell theory incorporating the nonlocal strain gradient theory. The three‐dimensional governing equations of motion are derived by adopting the curvilinear coordinate system through Hamilton's principle. A new formulation of Eringen's model containing the higher‐order strain gradients is employed to capture the effects of nonlocality and small scale parameter. Galerkin decomposition method is employed to acquire a bi‐cubic relation for the natural frequency of the considered nanoshell. The effects of different parameters like the ratio of radius of curvature to the cross section radius, small scale and nonlocality, and length‐to‐radius ratio on the variation of the natural frequency are presented. Excellent agreements are found in some comparative studies between the results of this work and those obtained by molecular dynamics and experimental findings in the literature. Finally, some interesting results are found by plotting the variation of natural frequency of the system versus the length‐to‐radius ratio. It is exhibited that by increasing the ratio L / r , the natural frequencies associated with different values of wavenumber m converge to the lower one and the convergence speed is highly dependent to the circumferential wavenumber n.
Vibration Analysis of Rotating Annular Flexoelectric Microplate S. M. H. Hosseini, Y. Tadi Beni, Y. Kiani International Journal of Structural Stability and Dynamics, 2025 This research investigates the free vibration of a rotating annular microplate under the flexoelectric effect. Initially, the Kirchhoff plate theory assumptions are used to express the displacement fields. After considering the displacement field, strains and their gradients are derived and substituted into the electric enthalpy and kinetic energy expressions. Subsequently, by applying Hamilton’s principle to the aforementioned equations, the electric and mechanical equations are computed. To derive the equations of motion, initially, the polarization vectors and their gradients are derived from the electric equations and associated boundary conditions. Subsequently, these are incorporated into the mechanical equations, which also encompass electric components. It is notable that by removing the time-dependent terms from the in-plane equations of motion, the static displacement due to rotation at each speed is obtained. After deriving the equations of motion and boundary conditions, these equations are non-dimensionalized using non-dimensionalizing relations. In the next step, Hamilton’s principle is used to discretize the equations and boundary conditions. Consequently, by applying the generalized differential quadrature method and extracting the stiffness and mass matrices resulting from the transverse equation of motion and boundary conditions, the natural transverse frequency of the rotating annular microplate under the flexoelectric effect is calculated. The results of this research are useful for promoting the use of rotating annular microplants under flexoelectric effect for microelectromechanical systems designers with high efficiency.
Free vibration analysis of microtubules as orthotropic elastic shells using stress and strain gradient elasticity theory Journal of Solid Mechanics, 2016
USING ALE-FEM to simulate the instability of beam-type nano-Actuator in the presence of electrostatic field and dispersion forces Iranian Journal of Science and Technology Transactions of Mechanical Engineering, 2013
Use of augmented continuum theory for modeling the size dependent material behavior of nano-actuators Iranian Journal of Science and Technology Transactions of Mechanical Engineering, 2012
A complete treatment of thermo-mechanical ale analysis; Part 2: Finite element equations and applications Iranian Journal of Science and Technology Transaction B Engineering, 2010
A complete treatment of thermo-mechanical ale analysis; Part I: Formulation Iranian Journal of Science and Technology Transaction B Engineering, 2010
Green-Lindsay based generalized flexothermoelasticity of a microstructure F Kheibari, YT Beni Applied Physics A 132 (6), 533 , 2026 2026
Green-Lindsay thermoelasticity model in two-dimensional bounded micro-media YT Beni, S Sadeghi Iranian Journal of Science and Technology, Transactions of Mechanical … , 2026 2026 Citations: 1
Electromechanical dynamic behavior of the three-layered porous functionally graded flexoelectric microshell under moving load: Electromechanical Dynamic Behavior of the Three … AF Babadi, YT Beni, KK Żur Acta Mechanica 237 (1), 473-509 , 2026 2026
Size dependent generalized thermoelasticity: Green-Lindsay theory with modified strain gradient theory J Alihemmati, Y Tadi Beni Waves in Random and Complex Media 35 (5), 9567-9591 , 2025 2025 Citations: 11
Developing an Efficient Three-Dimensional Hermite-Family Element for Gradient Elasticity Analysis S Sadeghi, YT Beni Iranian Journal of Science and Technology, Transactions of Civil Engineering … , 2025 2025 Citations: 1
Size-dependent torsional wave propagation in FG flexoelectric micro/nanotubes YT Beni Waves in Random and Complex Media 35 (4), 8220-8242 , 2025 2025 Citations: 22
Vibration analysis of rotating annular flexoelectric microplate SMH Hosseini, Y Tadi Beni, Y Kiani International Journal of Structural Stability and Dynamics 25 (12), 2550126 , 2025 2025 Citations: 9
Free vibration analysis of piezoelectric nano tube conveying fluid supported by a visco-Pasternak foundation F Kheibari, Y Tadi Beni Advanced Structural Mechanics 1 (3), 174-198 , 2025 2025
Analysis of Electromechanical Behavior of the Piezoelectric Micro Multi Layered Sandwich Plate on the Basis of the Modified Unified Formulation using the Modified Couple Stress … N Ebrahimi, M Botshekanan Dehkordi, Y Tadi Beni Iranian Journal of Mechanical Engineering Transactions of ISME 27 (1), 98-128 , 2025 2025
Free vibrations and dynamic behavior of the three layered flexoelectric functionally graded microbeam under moving load AF Babadi, YT Beni, KK Żur European Journal of Mechanics-A/Solids 109, 105464 , 2025 2025 Citations: 17
Size-dependent generalized piezothermoelasticity of microlayer M Pakdaman, Y Tadi Beni Journal of Applied and Computational Mechanics 11 (1), 223-238 , 2025 2025 Citations: 13
On the coupled bending–torsional analysis of flexoelectric microbeams HRB Dehkordi, YT Beni, H Arvin Archives of Civil and Mechanical Engineering 25 (1), 53 , 2024 2024 Citations: 6
On the nonlocal nonlinear vibration of electro-magneto piezoelectric porous visco-microbeam reinforced with agglomerated CNTs considering surface effects M Botshekanan Dehkordi, YT Beni, A Cheraghbak Applied Physics A 130 (12), 910 , 2024 2024 Citations: 10
Lord-Shulman based generalized thermoelasticity of piezoelectric layer using finite element method F Kheibari, YT Beni, Y Kiani Structural Engineering and Mechanics 92 (1), 81-88 , 2024 2024 Citations: 4
Size-dependent coupled bending-torsional analysis of piezoelectric micro beams HR Balali Dehkordi, Y Tadi Beni Mechanics Based Design of Structures and Machines 52 (9), 6484-6506 , 2024 2024 Citations: 9
On the size-dependent electromechanical layered beam-type porous functionally graded flexoelectric energy harvesters SF Dehkordi, YT Beni Engineering Analysis with Boundary Elements 165, 105801 , 2024 2024 Citations: 8
On the generalized flexothermoelasticity of a microlayer. F Kheibari, YT Beni, H Golestanian Acta Mechanica 235 (6) , 2024 2024 Citations: 10
Size-dependent electro-thermal buckling analysis of flexoelectric microbeams YT Beni International Journal of Structural Stability and Dynamics 24 (08), 2450093 , 2024 2024 Citations: 38
Generalized piezothermoelasticity of hollow spheres under thermal shock using Lord–Shulman theory SMH Jani, Y Kiani, Y Tadi Beni Journal of Thermal Stresses 47 (3), 347-362 , 2024 2024 Citations: 15
Free vibration behaviour of composite laminated skew cylindrical shells reinforced with graphene platelets R Jahanbazi, Y Kiani, YT Beni Structures 61, 106074 , 2024 2024 Citations: 18
MOST CITED SCHOLAR PUBLICATIONS
Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory YT Beni, F Mehralian, H Razavi Composite Structures 120, 65-78 , 2015 2015 Citations: 265
Cylindrical thin-shell model based on modified strain gradient theory H Zeighampour, YT Beni International Journal of Engineering Science 78, 27-47 , 2014 2014 Citations: 210
Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams Y Tadi Beni Journal of Intelligent Material Systems and Structures 27 (16), 2199-2215 , 2016 2016 Citations: 161
Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS YT Beni, A Koochi, M Abadyan Physica E: Low-dimensional Systems and Nanostructures 43 (4), 979-988 , 2011 2011 Citations: 155
Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes F Mehralian, YT Beni, MK Zeverdejani Physica B: Condensed Matter 514, 61-69 , 2017 2017 Citations: 144
Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory H Razavi, AF Babadi, Y Tadi Beni Composite Structures 160, 1299–1309 , 2017 2017 Citations: 138
Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory H Zeighampour, YT Beni, MB Dehkordi Thin-Walled Structures 122, 378-386 , 2018 2018 Citations: 127
The modified couple stress functionally graded cylindrical thin shell formulation Y Tadi Beni, F Mehralian, H Zeighampour Mechanics of Advanced Materials and Structures 23 (7), 791-801 , 2016 2016 Citations: 117
Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory H Zeighampour, YT Beni Physica E: Low-dimensional Systems and Nanostructures 61, 28-39 , 2014 2014 Citations: 114
Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell F Mehralian, YT Beni, R Ansari Composite Structures 152, 45-61 , 2016 2016 Citations: 108
Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method A Koochi, AS Kazemi, YT Beni, A Yekrangi, M Abadyan Physica E: Low-dimensional Systems and Nanostructures 43 (2), 625-632 , 2010 2010 Citations: 106
Size-dependent torsional buckling analysis of functionally graded cylindrical shell F Mehralian, YT Beni Composites Part B: Engineering 94, 11-25 , 2016 2016 Citations: 101
Free vibration analysis of axially functionally graded nanobeam with radius varies along the length based on strain gradient theory H Zeighampour, YT Beni Applied Mathematical Modelling 39 (18), 5354-5369 , 2015 2015 Citations: 101
Size dependent electro-mechanical vibration of single-walled piezoelectric nanotubes using thin shell model F Kheibari, Y Tadi Beni Materials & Design 114, 572–583 , 2017 2017 Citations: 99
Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling YT Beni Mechanics Research Communications 75, 67-80 , 2016 2016 Citations: 99
Wave propagation in double-walled carbon nanotube conveying fluid considering slip boundary condition and shell model based on nonlocal strain gradient theory H Zeighampour, YT Beni, I Karimipour Microfluidics and Nanofluidics 21 (5), 85 , 2017 2017 Citations: 98
Investigating the effects of resin cross-linking ratio on mechanical properties of epoxy-based nanocomposites using molecular dynamics Farshid Aghadavoudi, Hossein Golestanian, Yaghoub Tadi Beni Polymer Composites , 2016 2016 Citations: 87
Analysis of conical shells in the framework of coupled stresses theory H Zeighampour, YT Beni International Journal of Engineering Science 81, 107-122 , 2014 2014 Citations: 87
On the size-dependent nonlinear thermo-electro-mechanical free vibration analysis of functionally graded flexoelectric nano-plate A Ghobadi, H Golestanian, YT Beni, KK Żur Communications in Nonlinear Science and Numerical Simulation 95, 105585 , 2021 2021 Citations: 86
Electro-mechanical free vibration of single-walled piezoelectric/flexoelectric nano cones using consistent couple stress theory SF Dehkordi, YT Beni International Journal of Mechanical Sciences 128, 125-139 , 2017 2017 Citations: 83
