Article
Mechanics
Somnath Karmakar, S. Chakraverty
Summary: This paper aims to investigate the influence of different elastic foundations on the free vibrations of piezoelectric sandwich Euler nanobeam with flexoelectricity based on nonlocal strain gradient theory. Three different types of elastic foundations: constant, linear, and quadratic, were considered. The vibration frequencies under three different classical boundary conditions (S-S, C-S, and C-C) were obtained using the Adomian decomposition method. Additionally, the effects of piezoelectricity and flexoelectricity on the vibrations were discussed in detail.
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
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
Materials Science, Multidisciplinary
Yicong Zheng, Liangliang Chu, Guansuo Dui, Xiang Zhu
Summary: Direct flexoelectricity in dielectrics, as a coupling effect of electric field and elastic strain gradient, is size-dependent and effective in nanostructures. This paper utilizes the flexoelectric theory and mixed finite element method to study the mechanical properties of two-dimensional functionally graded flexoelectric nanobeam and discovers the phenomenon of the deflection platform. The influence of geometric parameters, length scale, and material distribution on the deflection platform is discussed by applying various loads to the nanobeam.
JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
(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, Civil
Burak E. Yapanmi, Necla Togun, Suleyman M. Bagdatli, Sevki Akkoca
Summary: The history of modern humanity is moving towards making technological equipment as small as possible for convenience. This study focuses on the linear and nonlinear vibration of nanobeams, commonly used in nanostructures, under various conditions. Results show that an increase in magnetic field and elastic foundation coefficient leads to a decrease in vibration amplitudes, with higher frequency values observed in clamped-clamped support conditions.
STRUCTURAL ENGINEERING AND MECHANICS
(2021)
Article
Mathematics, Applied
Roshan Lal, Chinika Dangi
Summary: This article introduces a nonlocal model based on the Timoshenko beam theory for vibration response of bi-directional functionally graded moderately thick nanobeam under surface effect. The study considers surface and nonlocal effects using the Gurtin-Murdoch surface elasticity theory and Eringen's nonlocal theory, and numerical results are obtained using the differential quadrature method.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Engineering, Civil
Fateme Shayestenia, Majid Ghadiri
Summary: This study presents a size-dependent electromechanical Euler-Bernoulli micro/nanobeam based on nonlocal strain gradient theory and von-Karman hypothesis. The results show that the flexoelectric and piezoelectric parameters have a significant influence on the amplitude response and dynamic instability regions.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Engineering, Multidisciplinary
Subrat Kumar Jena, S. Chakraverty, Vinyas Mahesh, Dineshkumar Harursampath
Summary: This article investigates the vibration characteristics of a nanobeam embedded in an elastic foundation using the Haar Wavelet Method (HWM) and the Higher Order Haar Wavelet Method (HOHWM). Various parameters, such as small scale, length scale, magnetic field intensity, hygroscopic and thermal effects, are studied for different boundary conditions. The convergence rate of the wavelet methods is determined using Richardson's formula, and the extrapolated HWM is shown to have comparable convergence rate with the higher order Haar wavelet method. The effectiveness of the higher order Haar wavelet method is demonstrated, and the results are cross-validated with previously published literature, showing excellent agreement.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Engineering, Multidisciplinary
Zhu XiaoWu, Li Li
Summary: This study demonstrates how both cross-sectional nonlocal interactions and axial nonlocality affect the tensile behaviors of nanobars. When the length-to-height ratio is small, nonlocal interactions become significant, while in slender bars, the main nonlocal effect stems from the nonlocal cross-sectional effect. Overcoming the ill-posed problem of pure nonlocal integral elasticity can be achieved by employing both pure nonlocal integral elasticity and surface elasticity.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2021)
Article
Nanoscience & Nanotechnology
Zhenhai Liu, Peng Wang, Jiawei Xu
Summary: The aim of this study is to investigate the coupling responses of a functionally graded piezoelectric cantilever nanobeam under concentrated load, where the material properties follow an exponential distribution in the thickness direction. The governing equations and boundary conditions of the Euler-Bernoulli FG beam are derived using variational principle, and analytical expressions for deflection, polarization intensity, and induced potential are obtained. The results show that the flexoelectric effect significantly affects the deflection, polarization intensity, and induced potential of the FG cantilever nanobeam.
Article
Materials Science, Multidisciplinary
Pengfei Yu, Weifeng Leng, Liming Peng, Yaohong Suo, Jinquan Guo
Summary: This study investigates the dynamic flexoelectric effect in functional gradient piezoelectric nanobeams, showing that it plays a significant role in the investigation of higher-order vibration modes. The gradient index affects the dimensionless frequency of each mode, and the effective stiffness is influenced by factors such as the gradient index, piezoelectricity, and flexoelectricity. The modified electric field equilibrium equation provides valuable insights for designing energy harvesting devices at the nanometer scale.
RESULTS IN PHYSICS
(2021)
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
Mathematics, Applied
Ali Koochi, Masoud Goharimanesh, Mohammad Reza Gharib
Summary: This paper investigates the electromagnetic dynamic instability of a doubly clamped CNT-based nano-sensor considering external magnetic field, structural damping, and van der Waals force. The results show that the magnetic flux has a significant impact on the nano-sensor's dynamic instability voltage.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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)
