Article
Mechanics
H. M. Numanoglu, H. Ersoy, O. Civalek, A. J. M. Ferreira
Summary: This article examines the free thermal vibration analysis of nanobeams surrounded by an elastic matrix using nonlocal elasticity and Timoshenko beam theories. The equation of motion for free vibration is solved by analytical method, and a weighted residue-based finite element formulation is developed for boundary conditions other than simply supported nano beams. Numerical results show the high accuracy of the nonlocal finite element formulation and the effects of size dependency and environmental factors on the dynamic behavior of nanobeams are discussed in detail.
COMPOSITE STRUCTURES
(2021)
Article
Engineering, Civil
Moustafa S. Taima, Tamer A. El-Sayed, Michael I. Friswell
Summary: This study presents a novel approach to investigate the thermal lateral vibration of cracked nanobeams using Reddy beam analysis-based solutions. The effects of various factors on the natural frequencies are explored, and the outcomes are compared with prior findings, showing a strong level of agreement.
THIN-WALLED STRUCTURES
(2023)
Article
Construction & Building Technology
Mahsa Najafi, Isa Ahmadi
Summary: A nonlocal Layerwise theory is proposed for free vibration analysis of nanobeams resting on an elastic foundation, considering small-scale effects and predicting more accurate results. Effects of nonlocal parameter, Pasternak shear coefficient, Winkler spring coefficient, and boundary conditions on the vibration of nanobeams are studied. The theory can be applied to analyze the mechanical behavior of various nanostructures with different loading and boundary conditions.
STEEL AND COMPOSITE STRUCTURES
(2021)
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
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
Mahsa Najafi, Isa Ahmadi
Summary: In this paper, an efficient method based on nonlocal elasticity theory and Layerwise theory is proposed for the analysis of bending, buckling, and vibration of functionally graded nanobeam. The method takes into account the transverse shear and normal strains of nanobeam and the small-scale effect. The proposed theory is validated by comparing with other theories and shows accurate results in predicting vibration, buckling, and bending of nanobeams.
ENGINEERING WITH COMPUTERS
(2023)
Article
Engineering, Mechanical
Tran Van Lien, Tran Binh Dinh, Nguyen Tat Thang
Summary: This study presents exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams, and provides a detailed analysis of the factors influencing their free vibration.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE
(2023)
Article
Mathematics, Applied
Hayri Metin Numanoglu, Hakan Ersoy, Bekir Akgoz, Omer Civalek
Summary: This study investigates the size-dependent thermo-mechanical vibration analysis of nanobeams by implementing Hamilton's principle and the stress equation of nonlocal elasticity theory. The finite element method is used to solve the eigenvalue problem and derive stiffness and mass matrices. Nonlocal finite element method is emphasized for analyzing the vibration behavior of nanobeams under different boundary conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Engineering, Mechanical
Buesra Uzun, Mustafa Oezguer Yayli
Summary: This study aims to solve the free vibrations of embedded functionally graded porous and non-porous nanobeams with different material distributions (power-law and sigmoid) under general elastic boundary conditions. The proposed models are effective for studying arbitrary boundary conditions.
JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES
(2023)
Article
Mechanics
Busra Uzun, Omer Civalek, Mustafa Ozgur Yayli
Summary: This study presents an efficient solution method based on the Stokes' transformation to investigate the effects of deformable boundary conditions and axial point load on the transverse vibration of a nanobeam. The eigenvalue problem obtained by using Fourier sine series and Stokes' transform can be used to analyze the frequencies of nanobeam applications subjected to vibration and axial force at both rigid and non-rigid boundaries. This analytical method can be applicable to various nanotechnology structures and machines.
Article
Engineering, Multidisciplinary
Farzad Ebrahimi, Mahsa Karimiasl, Vinyas Mahesh
Summary: This study verifies the bending analysis of flexoelectric functionally graded (FG) microbeams according to nonlocal elasticity theory. It presents a parametric study on the effects of nonlocal parameter, power-law hygro-thermal loadings, flexoelectric effect, transverse external loading on the bending characteristics of FG microbeam. The research finds that boundary conditions, flexoelectric effect, nonlocal parameter, power-law index, and beam geometrical parameters have notable effects on the dimensionless deflection of FG microscale beams.
SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES
(2021)
Article
Physics, Multidisciplinary
Chinika Dangi, Roshan Lal
Summary: A nonlocal model has been proposed to study the vibration behavior of bi-directional functionally graded nanobeam, considering surface and size effects. The results show that the surface effect plays an important role in such material.
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
Mechanics
C. Chr Koutsoumaris, K. G. Eptaimeros
Summary: This study explores the analysis of static engineering problems of a nanobeam using nonlocal integral elasticity models. The results show that the integral models exhibit a flexible behavior compared to classic and nonlocal differential models, demonstrating good physical robustness and promising applications in the field of nanomaterials and beyond.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Engineering, Mechanical
J. A. Loya, J. Aranda-Ruiz, R. Zaera
Summary: This study analyzes the dynamic behavior of cracked Timoshenko beams immersed in a Winkler elastic medium and obtains their natural frequencies of bending vibration. By modeling the beam as two segments connected by springs and considering the discontinuity of displacement and rotation due to bending, the differential equations for free vibration are solved. The proposed methodology allows for calculating the natural frequencies as a function of support type, soil stiffness, crack position, and initial crack length. The results are compared to other simplified models, highlighting the interaction and importance of the parameters considered in the system's natural frequencies.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2022)
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
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
Instruments & Instrumentation
Ali Naderi, Shahin Behdad, Mahmood Fakher
Summary: This paper studies the mechanics of nonlocal piezo-magnetic nanobeams embedded in a local/nonlocal viscoelastic medium. An exact solution and an efficient approach of generalized differential quadrature method (GDQM) are introduced. The results show that the size-dependency of the viscoelastic medium, external electric, and magnetic loads play significant roles in the vibration characteristics and should be considered based on two-phase theory.
SMART MATERIALS AND STRUCTURES
(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)
