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
Acoustics
Santanu Manna, Rahul Som
Summary: In this article, the characteristics of flexural edge waves on a piezoelectric structure are studied using an elastic foundation. The microscale effect on edge wave propagation is investigated using nonlocal elasticity theory. The analysis shows significant differences in dispersion curves for piezoelectric plates with different foundations and nonlocal parameters.
JOURNAL OF VIBRATION AND CONTROL
(2022)
Article
Engineering, Civil
Mouayed H. Z. Al-Toki, Hayder A. K. Ali, Nadhim M. Faleh, Raad M. Fenjan
Summary: In this research, the dynamic stability behavior of nonlocal beams on an elastic foundation has been numerically assessed. The beams are made of functional graded porous material and are exposed to thermal and humid environments. The study also considers the beams subjected to axial periodic mechanical load, which leads to instability behavior. The governing equations are established using nonlocal elasticity and solved using the Chebyshev-Ritz-Bolotin method. The stability boundaries of the beams are significantly influenced by temperature and moisture variation, as well as the amount of porosities inside the material.
GEOMECHANICS AND ENGINEERING
(2022)
Article
Mechanics
T. Gortsas, D. G. Aggelis, D. Polyzos
Summary: Strain gradient elasticity and nonlocal elasticity are two enhanced elastic theories used to explain phenomena that classical elasticity cannot explain. This study aims to derive all the strain gradient elastic theories appearing in the literature via the nonlocal definitions of energy densities and Hamilton's principle.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Thermodynamics
Quoc-Hoa Pham, Van Ke Tran, Trung Thanh Tran, Trung Nguyen-Thoi, Phu-Cuong Nguyen, Van Dong Pham
Summary: This article presents a finite element method based on a quasi-3D nonlocal theory to study the free vibration of functionally graded material nanoplates on an elastic foundation in a thermal environment. The study compares numerical results with previous research to verify accuracy and investigates the effects of various parameters on the free vibration of nanoplates.
CASE STUDIES IN THERMAL ENGINEERING
(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
Mechanics
Yu-fang Zheng, De-yong Qu, Li-chuan Liu, Chang-ping Chen
Summary: In this study, a nonlinear bending model of the nonlocal three-layer magneto-electro-elastic (MEE) laminated nanobeam resting on elastic foundation is established using Reddy's third-order shear deformation theory (RTSDT) and nonlocal elasticity theory. The model considers the geometrically nonlinear equations proposed by von Karman and also takes into account the effects of electric and magnetic potentials in the laminated nanobeam through Maxwell's magnetic-electro equations and boundary conditions. The governing equations are re-expressed in a dimensionless form and simplified using the Galerkin method. The study explores the effects of foundation parameters, nonlocal parameter, stacking sequence, external electric voltage and external magnetic potential on the bending behaviors of MEE laminated nanobeams.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2023)
Article
Acoustics
Moustafa S. Taima, Tamer A. El-Sayed, Said H. Farghaly
Summary: The free vibration of multistepped nanobeams was studied using the dynamic stiffness matrix method, based on Bernoulli-Euler theory for beam analysis and Eringen's nonlocal elasticity theory for nanoscale analysis. The impact of nonlocal parameters, boundary conditions, and step ratios on the nanobeam natural frequency was investigated. Validation of results was achieved by comparing selected cases with literature, showing consistent results.
JOURNAL OF VIBRATION AND CONTROL
(2021)
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
Acoustics
Deshui Xu, Jun Lu, Kun Zhang, Pengzhou Li, Lei Sun
Summary: This manuscript presents an exact solution for the longitudinal vibrating characteristics of generally restrained nanorod structures with multiple internal elastic supports. By introducing artificial springs and setting restrained stiffness accordingly, the general boundary restraints are formulated. The study provides an effective method for predicting the longitudinal vibration characteristics of nanorods with complex boundary and coupling conditions.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Engineering, Civil
Iwona Wstawska, Krzysztof Magnucki, Piotr Kedzia
Summary: The main objective of this paper is the stability analysis of an axially compressed three-layered beam on an elastic foundation. The authors propose an analytical model of the beam on the elastic foundation and present a new approach to structures on the elastic foundation by adopting variable properties. The assumption proposed by the authors allows for a continuous description of the interaction of the beam with the foundation, unlike the discrete Winkler model. Critical loads as a function of geometric and mechanical properties are calculated, and original shape functions and deflection functions are proposed. Numerical analysis is also performed, showing good agreement with the analytical results.
THIN-WALLED STRUCTURES
(2022)
Article
Mechanics
Francesco Paolo Pinnola, Marzia Sara Vaccaro, Raffaele Barretta, Francesco Marotti de Sciarra, Giuseppe Ruta
Summary: A challenging task in nonlocal continuum mechanics is to formulate constitutive relations for well-posed structural problems. Strategies such as using local/nonlocal mixtures of elasticity and integral models have been adopted to overcome the limitations of Eringen's pure nonlocal theory in nanostructures. This paper proposes a consistent formulation of a nonlocal elastic foundation for a Bernoulli-Euler beam, where the transverse displacements are a convex combination of reaction-driven local and nonlocal phases governed by Winkler and Wieghardt laws, respectively. The proposed integral mixture is proven to be equivalent to a more convenient differential problem with nonlocal boundary conditions, which can effectively solve nonlocal problems of beams on mixture reaction-driven continuous foundation.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Engineering, Mechanical
Andrea Francesco Russillo, Giuseppe Failla
Summary: This paper focuses on the elastic wave propagation analysis of small-size planar beam lattices, proposing two novel computational approaches and comparing their advantages. Dispersion curves for a typical lattice are calculated to highlight the role of nonlocality.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Engineering, Mechanical
Ahmad Mamandi
Summary: In this paper, the PDEs and BCs governing the large deflection of an Euler-Bernoulli cantilever nano-beam on a nonlinear Winkler-Pasternak elastic foundation and under uniformly distributed lateral load have been derived and solved using finite difference method. The effect of different parameters on the deflection, bending slope angle, and length change of the nano-beam have been investigated. Results show that increasing the nonlocal parameter decreases the bending slope angle and deflection of the nano-beam, and reduces the dimensionless ratio of its final length. The effect of nonlocal parameter on the nonlinear large deflection is more significant at higher values of the applied lateral load.
JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY
(2023)
Article
Mathematical & Computational Biology
Sung Woo Choi
Summary: This paper investigates the boundary value problem of finite beam deflection on an elastic foundation with two point boundary conditions. The authors explicitly compute the fundamental boundary matrices for specific boundary conditions and demonstrate that the matrices for all boundary conditions can be derived from those for the specific ones.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mechanics
R. Artan, R. C. Batra
Article
Mechanics
Reha Artan, Ayse Toksoz
ARCHIVE OF APPLIED MECHANICS
(2013)
Article
Chemistry, Multidisciplinary
Aysegul Tepe, Reha Artan
JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE
(2009)
Article
Chemistry, Multidisciplinary
Ayseguel Tepe
JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE
(2010)
Article
Chemistry, Multidisciplinary
Reha Artan, Ayseguel Tepe, Ayse Toksoz
JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE
(2010)
Article
Materials Science, Multidisciplinary
Reha Artan, Aysegul Tepe
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2011)
Article
Engineering, Civil
Erol Demirkan, Reha Artan
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2019)
Article
Construction & Building Technology
Abdulgazi Gedik, Ertugrul Bilgin, Abdullah Hilmi Lav, Reha Artan
SUSTAINABLE CITIES AND SOCIETY
(2019)
Article
Engineering, Electrical & Electronic
Ceyda Nur, Reha Artan
MICROSYSTEM TECHNOLOGIES-MICRO-AND NANOSYSTEMS-INFORMATION STORAGE AND PROCESSING SYSTEMS
(2020)
Article
Mathematics, Applied
Gokhan Guclu, Reha Artan
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2020)
Article
Engineering, Civil
Murat Celik, Reha Artan
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2020)
Article
Engineering, Electrical & Electronic
Murat Celik, Reha Artan
MICROSYSTEM TECHNOLOGIES-MICRO-AND NANOSYSTEMS-INFORMATION STORAGE AND PROCESSING SYSTEMS
(2020)
