Article
Mechanics
YanMing Ren, Hai Qing
Summary: This paper investigates the bending and buckling behavior of functionally graded piezoelectric Timoshenko nanobeams. It is found that the purely nonlocal piezoelectric integral model leads to an ill-posed mathematical model and inconsistent size-dependent response. The numerical results show a consistent softening response.
COMPOSITE STRUCTURES
(2022)
Article
Mathematics, Applied
Hai Qing, Lu Wei
Summary: This study performs linear and nonlinear free vibration analysis of functionally graded porous nanobeams with four different porous distribution patterns using the stress-driven two-phase local/nonlocal integral model. Analytical and numerical methods are employed to investigate the influence of nonlocal parameters and vibration amplitude on the vibration frequencies. The results indicate that the accuracy of prediction depends on the magnitude of vibration, with nonlocal linear vibration mode shape providing more accurate results at small amplitudes but becoming less suitable for strong nonlinear vibrations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(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
Mechanics
Yan-Ming Ren, Peter Schiavone, Hai Qing
Summary: In this paper, a nonlocal gradient piezoelectric model capable of distinguishing softening and toughening size-effects due to elasticity and piezoelectricity is proposed. The model is applied to study the static bending of functionally graded piezoelectric nanobeams. The results show that bending deflections increase consistently with the increase of nonlocal parameter and the decrease of gradient parameter for strain-driven model and the decrease of nonlocal parameter and the increase of gradient parameter for stress-driven model.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
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
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
Construction & Building Technology
Jia-Qin Xu, Gui-Lin She, Yin-Ping Li, Lei-Lei Gan
Summary: This paper fills the gap in the existing literature by considering the influences of geometric nonlinearity and initial geometric imperfection in the resonance problem of nanoplates. Nonlinear resonances of functionally graded nanoplates with initial geometric imperfection under different boundary conditions are established based on the nonlocal strain gradient theory. The equations of motion are derived using the Euler-Lagrange principle and solved with the perturbation method, and the effects of various factors on the nonlinear forced vibration behavior of nanoplates are discussed.
STEEL AND COMPOSITE STRUCTURES
(2023)
Article
Engineering, Civil
Zheng Lyu, Ming Ma
Summary: This work focuses on the nonlinear dynamic response of a functionally graded magneto-electro-elastic (MEE) nanobeam. The interaction between the imperfect nanobeam and its multi-physical stimulus is numerically solved via a differential quadrature method. Simulation results demonstrate the significance of the MEE coupling effect for designing smart and advanced devices in aerospace and industrial applications.
THIN-WALLED STRUCTURES
(2023)
Article
Acoustics
Ahmed E. Abouelregal, Rakhi Tiwari
Summary: Functionally graded materials are widely used in various industries due to their exceptional properties. This study introduces a new mathematical model to analyze the interaction of functionally gradient thermoelastic nanobeams with abrupt heat. Analytical solutions for the system were obtained using Laplace transform, and numerical methods were used to study the distributions of temperature, displacement, deflection, and flexural moment. The effects of kernel functions, time delay, and nonlocal quantum on the system were discussed based on the computational results and graphical figures. A comparison with existing thermal conductivity models confirmed the validity of the proposed model.
JOURNAL OF VIBRATION AND CONTROL
(2023)
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
Manjur Alam, Sudib K. Mishra
Summary: This study investigates the geometrically nonlinear vibration of NL-SG beams on a nonlinear substrate with shear interactions. It includes higher-order curvature, von Karman nonlinearity, and a nonlinear Pasternak model for the substrate. The research shows that nonlinear bending and substrate stiffness play a dominant role in influencing the vibration behavior, while the NL and SG interactions significantly affect the vibration behavior with the effect of functional gradation of material being minor.
COMPOSITE STRUCTURES
(2021)
Article
Mechanics
S. El-Borgi, P. Rajendran, M. Trabelssi
Summary: This paper investigates the free and forced vibration of a graded geometrically nonlinear Timoshenko nanobeam supported by a nonlinear foundation. By combining nonlocal and surface elasticity and using the physical neutral axis method, a new formulation for the dynamic response of the beam is proposed. The effects of various parameters on the vibration response are thoroughly studied.
ARCHIVE OF APPLIED MECHANICS
(2023)
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
Pei-Liang Bian, Hai Qing, Tiantang Yu
Summary: A new finite element method framework is developed in this paper to analyze the mechanical responses of nanobeams made of axially functionally-graded material (FGM) under different boundary conditions, with the introduction of size effects. A series of numerical examples demonstrate the flexibility of this framework in handling complex distribution patterns, boundary conditions, and loads.
COMPOSITE STRUCTURES
(2022)
Article
Mechanics
Wentao Xu, Genji Pan, Zohre Moradi, Navvab Shafiei
Summary: This research investigates the linear and nonlinear forced vibration response of axially functionally graded microbeams under dynamic harmonic loads, considering the impact of various parameters such as cross-section shape and porosity on the dynamic behavior. The study utilizes modified couple stress theory and numerical methods to derive governing equations and analyze the effects of different parameters on the dynamic response of microscale tubes and beams.
COMPOSITE STRUCTURES
(2021)
Article
Engineering, Electrical & Electronic
Mohamed Trabelssi, Heike Ebendorff-Heidepriem, Kathleen A. Richardson, Tanya M. Monro, Paul F. Joseph
JOURNAL OF LIGHTWAVE TECHNOLOGY
(2015)
Article
Mechanics
S. El-Borgi, P. Rajendran, M. I. Friswell, M. Trabelssi, J. N. Reddy
COMPOSITE STRUCTURES
(2018)
Article
Materials Science, Ceramics
Mohamed Trabelssi, Paul F. Joseph
JOURNAL OF NON-CRYSTALLINE SOLIDS
(2018)
Article
Materials Science, Ceramics
Mohamed Trabelssi, Paul F. Joseph
JOURNAL OF NON-CRYSTALLINE SOLIDS
(2018)
Article
Engineering, Multidisciplinary
M. Trabeissia, S. El-Borgi, R. Fernandes, L. -L. Ke
COMPOSITES PART B-ENGINEERING
(2019)
Article
Materials Science, Ceramics
Mohamed Trabelssi, Heike Ebendorff-Heidepriem, Kathleen C. Richardson, Tanya M. Monro, Paul F. Joseph
JOURNAL OF THE AMERICAN CERAMIC SOCIETY
(2014)
Article
Materials Science, Ceramics
Mohamed Trabelssi, Paul F. Joseph
JOURNAL OF THE AMERICAN CERAMIC SOCIETY
(2014)
Article
Mechanics
S. El-Borgi, P. Rajendran, M. Trabelssi
Summary: This paper investigates the free and forced vibration of a graded geometrically nonlinear Timoshenko nanobeam supported by a nonlinear foundation. By combining nonlocal and surface elasticity and using the physical neutral axis method, a new formulation for the dynamic response of the beam is proposed. The effects of various parameters on the vibration response are thoroughly studied.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Mechanics
M. Trabelssi, S. El-Borgi
Summary: In this paper, a locally adaptive weak quadrature element method is proposed to develop elements for nonlinear graded strain gradient nanobeams. The method ensures full integration of the variational statement by using Gauss quadrature points and constructs matrices based on the differential quadrature method using Lagrange-based polynomials. These matrices can be modified to accommodate any number of extra derivative degrees of freedom. The performance of the method is evaluated by comparing linear and nonlinear frequencies for various configurations and boundary conditions, showing improved accuracy and convergence speed compared to existing methods.
Article
Nanoscience & Nanotechnology
M. Trabelssi, S. El-Borgi
Summary: This paper proposes a novel method to derive Differential Quadrature Method matrices with multiple degrees of freedom at the boundaries to solve fourth and higher-order equations of motion. The method is applied to nonlinear nanobeams and achieves good accuracy and convergence speed.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART N-JOURNAL OF NANOMATERIALS NANOENGINEERING AND NANOSYSTEMS
(2022)
Article
Mechanics
M. Trabelssi, S. El-Borgi, L. -L. Ke, J. N. Reddy
COMPOSITE STRUCTURES
(2017)