Article
Engineering, Mechanical
Ali Naderi, Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: In this study, the vibration, buckling, and energy harvesting of piezoelectric nanobeams are investigated using a paradox-free nonlocal theory called two-phase local/nonlocal elasticity. The exact solution and a numerical solution are obtained using the governing equations derived from the two-phase elasticity and Hamilton's principle. A comparison study with common differential nonlocal elasticity shows that differential nonlocal theory is incompetent for reliable results in studying piezoelectric-based materials. This study suggests using other nonlocal theories like two-phase local/nonlocal elasticity for analyzing the mechanics of piezoelectric nanostructures.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Interdisciplinary Applications
Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: Considering the size effects of nanostructures, employing the two-phase local/nonlocal elasticity has recently gained attention in nano-mechanics research. This study provides the exact solution for the vibrations of two-phase Timoshenko nanobeams and investigates the shear-locking problem in the case of two-phase finite-element method (FEM). It aims to create an efficient locking-free local/nonlocal FEM with a simple and efficient beam element.
ENGINEERING WITH COMPUTERS
(2022)
Article
Computer Science, Interdisciplinary Applications
Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: It has been found that the common nonlocal strain gradient theory has inconsistencies, but the local/nonlocal strain gradient (LNSG) theory can solve the transverse vibrations of nanobeams. By introducing a higher order beam element in finite element analysis, numerical and exact solutions for LNSG nanobeams are obtained.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mechanics
Fan Yang, Xianlai Song, Xuyang Wang, Weilin Yang, Zengtao Chen
Summary: This study analyzes the post-buckling behavior of porous piezoelectric nanobeams by considering surface effects. The results show that the surface effects can increase the effective elastic modulus and critical load of the nanobeams, while reducing the post-buckling configuration, path, and induced charge. Additionally, the mechanical properties of the nanobeams can be improved by optimizing the pore distribution.
Article
Physics, Multidisciplinary
Shahin Behdad, Mahmood Fakher, Ali Naderi, Shahrokh Hosseini-Hashemi
Summary: The dynamics of cracked nanobeams surrounded by size-dependent Winkler-Pasternak medium were studied using two-phase local/nonlocal elasticity theory. The results showed significant changes in vibration frequencies of intact and defected nanobeams when size dependency was applied to the medium. The impact of nonlocal effects on defected nanobeams varied depending on crack characteristics. This research can provide more accurate predictions in vibration analysis of defected nanostructures embedded in two-parameter medium.
WAVES IN RANDOM AND COMPLEX MEDIA
(2021)
Article
Chemistry, Multidisciplinary
Daniela Scorza, Sabrina Vantadori, Raimondo Luciano
Summary: This study extends the two-phase stress-driven integral model to nanobeams with internal discontinuities, addressing the issue by introducing a mixture parameter. The analysis of various case studies and a centrally-cracked nanobeam demonstrates the strong dependency of fracture properties on characteristic length and mixture parameter values.
Article
Mechanics
Pei Zhang, Peter Schiavone, Hai Qing
Summary: This article presents a hygro-thermal-damping vibration analysis of two-variable shear deformation beams supported by a visco-Pasternak foundation. The effects of simultaneously applying stress-driven nonlocal assumptions on the foundation and hygro-thermal load in the undamped and damping vibration of the shear deformation beams are examined.
COMPOSITE STRUCTURES
(2023)
Article
Mechanics
Hossein Darban, Raimondo Luciano, Andrea Caporale, Michal Basista
Summary: This paper formulates a novel buckling model for nanobeams resting on the Pasternak elastic foundation based on the local-nonlocal stress-driven gradient elasticity theory. The model accurately predicts the buckling loads and mode shapes of the nanobeams, and captures both stiffening and softening behaviors at small scales.
COMPOSITE STRUCTURES
(2022)
Article
Mathematics, Applied
Pei Zhang, P. Schiavone, Hai Qing
Summary: A nonlocal study of vibration responses of FG beams supported by a viscoelastic Winkler-Pasternak foundation is conducted, considering the damping responses of both the Winkler and Pasternak layers of the foundation. The bending deformation of the beams and the elastic and damping responses of the foundation are comprehensively considered by uniting differential formulations of strain-driven and stress-driven two-phase local/nonlocal integral models, addressing the stiffness softening and toughening effects. The GDQM is used to solve the complex eigenvalue problem, and benchmark results for vibration frequency are obtained.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2023)
Article
Materials Science, Multidisciplinary
Shahin Behdad, Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: The study demonstrates that using two-phase local/nonlocal elasticity theory is more suitable for analyzing the dynamic stability and damping vibration of Timoshenko nanobeams subjected to an axial load, compared to the fully nonlocal elasticity theory. This approach allows for studying the size-dependent vibration and stability under various boundary conditions.
MECHANICS OF MATERIALS
(2021)
Article
Engineering, Civil
Ashraf M. Zenkour
Summary: In this study, the thermal vibrational behavior of a nanoplate placed on a three-factor foundation is investigated using nonlocal elasticity and Mindlin's first-order shear deformation plate theory. A three-parameter viscoelastic model is obtained by connecting the Winkler-Pasternak elastic foundation with viscous damping. The differential equations of motion are derived and solved to obtain the natural frequencies of simply-supported nanoplates. The influences of the nonlocal index, viscous damping index, and temperature changes are investigated. Additional thermal vibration results of nanoplates resting on the viscoelastic foundation are presented for future comparisons.
STRUCTURAL ENGINEERING AND MECHANICS
(2022)
Article
Mechanics
Andrea Caporale, Raimondo Luciano, Daniela Scorza, Sabrina Vantadori
Summary: Exact closed-form solutions for multi-cracked Euler-Bernoulli nanobeams are provided through two equivalent approaches. Both approaches involve integral and differential equations for modeling the nanobeams with isolated damaged sections. The first approach uses the integral definition of a local-nonlocal stress-driven model, while the second approach shows that this integral definition is equivalent to a differential equation with constitutive boundary conditions. Both approaches yield the same solution, but the second approach is computationally faster. Interesting results show that local beams have a jump in rotation at the damaged sections, while pure nonlocal nanobeams do not have such singularity.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Mechanics
Pei Zhang, Peter Schiavone, Hai Qing
Summary: The buckling and free vibration of functionally graded sandwich Timoshenko beams resting on an elastic foundation are studied using a nonlocal stress-driven strategy and the generalized differential quadrature method (GDQM) for numerical solution. Comparative studies are conducted to validate the effectiveness of the solution and investigate the influence of size-dependency of the elastic foundation.
COMPOSITE STRUCTURES
(2022)
Article
Acoustics
Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: It has been shown that using pure nonlocal elasticity can lead to inconsistent and unreliable results, prompting researchers to utilize Eringen's two-phase local/nonlocal elasticity to consider the nonlocal size dependency of nanostructures. This article investigates the size-dependent nonlinear free vibration of nanobeams within the two-phase elasticity framework, introducing the proper use of the Galerkin method for studying nonlinear vibration. The study highlights the importance of considering integral form of two-phase elasticity in the Galerkin method and the potential errors in using classic mode shapes.
JOURNAL OF VIBRATION AND CONTROL
(2021)
Article
Mathematics, Applied
Mustafa Arda, Metin Aydogdu
Summary: The paper investigates the flexural dynamics of carbon nanotubes under a longitudinal magnetic field using a nonlocal strain gradient model, taking into account the effects of Lorentz force and nonlocal strain gradient parameters on the vibration response of the nanobeam. The study shows that the softening nonlocal strain gradient model provides physically consistent results and that the magnetic field effect shifts the mode shapes of the nanobeam. The research could be useful for designing magnetically actuated nanomotors.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Physics, Multidisciplinary
Shahrokh Hosseini-Hashemi, Shahin Behdad, Mahmood Fakher
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
Article
Engineering, Mechanical
Mahmood Fakher, Shahin Behdad, Ali Naderi, Shahrokh Hosseini-Hashemi
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2020)
Article
Materials Science, Multidisciplinary
Shahin Behdad, Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: The study demonstrates that using two-phase local/nonlocal elasticity theory is more suitable for analyzing the dynamic stability and damping vibration of Timoshenko nanobeams subjected to an axial load, compared to the fully nonlocal elasticity theory. This approach allows for studying the size-dependent vibration and stability under various boundary conditions.
MECHANICS OF MATERIALS
(2021)
Article
Engineering, Mechanical
Ali Naderi, Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: In this study, the vibration, buckling, and energy harvesting of piezoelectric nanobeams are investigated using a paradox-free nonlocal theory called two-phase local/nonlocal elasticity. The exact solution and a numerical solution are obtained using the governing equations derived from the two-phase elasticity and Hamilton's principle. A comparison study with common differential nonlocal elasticity shows that differential nonlocal theory is incompetent for reliable results in studying piezoelectric-based materials. This study suggests using other nonlocal theories like two-phase local/nonlocal elasticity for analyzing the mechanics of piezoelectric nanostructures.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Physics, Multidisciplinary
Shahin Behdad, Mahmood Fakher, Ali Naderi, Shahrokh Hosseini-Hashemi
Summary: The dynamics of cracked nanobeams surrounded by size-dependent Winkler-Pasternak medium were studied using two-phase local/nonlocal elasticity theory. The results showed significant changes in vibration frequencies of intact and defected nanobeams when size dependency was applied to the medium. The impact of nonlocal effects on defected nanobeams varied depending on crack characteristics. This research can provide more accurate predictions in vibration analysis of defected nanostructures embedded in two-parameter medium.
WAVES IN RANDOM AND COMPLEX MEDIA
(2021)
Article
Mechanics
Shahin Behdad, Mohammad Arefi
Summary: This paper discusses the application of a mixed model in small-scale structural mechanics, providing a more comprehensive research perspective by simultaneously considering stiffening and softening effects, and covering all previous theories through various proposed small scales.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Chemistry, Physical
Ali Naderi, Tran Quoc-Thai, Xiaoying Zhuang, Xiaoning Jiang
Summary: For the first time, this study investigates the vibrational responses of a unimorph nanobeam with a functionally graded base and a dielectric layer that exhibits both piezoelectricity and flexoelectricity. The study applies the paradox-free local/nonlocal elasticity and utilizes Hamilton's principle to determine the formulation and boundary conditions. Additionally, the generalized differential quadrature method (GDQM) is implemented to solve complex partial differential equations. The results show that small-scale flexoelectricity dominates the electromechanical coupling, indicating the importance of studying the effect of dielectric materials in smart structures.
Article
Physics, Multidisciplinary
Mahmood Fakher, Shahin Behdad, Shahrokh Hosseini-Hashemi
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
Article
Engineering, Mechanical
Ali Naderi, Shahin Behdad, Mahmood Fakher, Shahrokh Hosseini-Hashemi
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2020)