Article
Engineering, Multidisciplinary
Pham Toan Thang, Phuong Tran, T. Nguyen-Thoi
Summary: This research paper investigates the vibrational responses of functionally graded carbon nanotube-reinforced composite nanoplates considering the effect of nonlocal parameter and strain gradient coefficient. By studying four types of CNT distribution under small length scale effects, the study aims to estimate the fundamental natural frequencies in FG-CNTRC nanoplates. The mathematical modeling and analytical solutions provide insights into how the small length-scale influences the vibrational behavior of nanoplates.
APPLIED MATHEMATICAL MODELLING
(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
M. Esmaeilzadeh, M. E. Golmakani, M. Sadeghian
Summary: This article utilizes the nonlocal strain gradient theory to investigate the dynamic properties of bi-directional functionally graded porous nanoplates. The effects of porosity coefficients, nonlocal and strain gradient parameters, boundary conditions, gradient indexes, and elastic foundations on the deflection are analyzed.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Computer Science, Interdisciplinary Applications
Pham Toan Thang, Dieu T. T. Do, Jaehong Lee, T. Nguyen-Thoi
Summary: This paper presents an in-depth study on the influence of nanoscale parameters on the bending and free vibration responses of functionally graded carbon nanotube-reinforced composite nanoshells. Mathematical formulas and numerical calculations are used to investigate the effect of nanoscale parameters, material properties, and shell shapes on the deflection and fundamental frequency parameters of the nanoshells.
ENGINEERING WITH COMPUTERS
(2023)
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
Materials Science, Multidisciplinary
Mohamed-Ouejdi Belarbi, Li Li, Mohammed Sid Ahmed Houari, Aman Garg, Hanuman Devidas Chalak, Rossana Dimitri, Francesco Tornabene
Summary: This work studies the size-dependent free vibration response of functionally graded nanoplates using a layerwise theory. The proposed model has a fixed number of variables and adopts the nonlocal elasticity theory to capture the small size effects. The developed finite element model has been demonstrated to be robust and reliable, and a detailed parametric analysis has been conducted.
MATHEMATICS AND MECHANICS OF SOLIDS
(2022)
Article
Engineering, Civil
Hossein B. Khaniki, Mergen H. Ghayesh
Summary: This paper presents a novel investigation of nonlinear forced vibrations and internal resonance in nonlocal strain gradient nanoplates. The study comprehensively models the nanoplate structure and discusses the influence of nonlocal and strain gradient parameters on the nonlinear vibration response. Specific combinations of these parameters lead to various types of internal resonance, significantly affecting the nonlinear frequency responses of the nanoplate. This study contributes to the understanding of the complex dynamics of nanoplates and offers valuable insights for the design of diverse nanoplate systems.
THIN-WALLED STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
Yuan Tang, Hai Qing
Summary: This work investigates the elastic buckling and free vibration response of functionally graded Timoshenko beams using a nonlocal strain gradient integral model. By deriving governing equations and boundary conditions via Hamilton's principle and utilizing Laplace transform technique to solve integral-differential equations, explicit expressions for bending deflections, moments, cross-sectional rotation, and shear force are obtained with eight unknown constants. The nonlinear characteristic equations for determining buckling load and vibration frequency are explicitly derived, and the results are validated against existing literature.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mechanics
Yucheng Zhou, Kefu Huang
Summary: This paper presents an effective analytical elastic general solution to the inhomogeneous spatial axisymmetric problem and studies the axisymmetric bending problem of functionally graded circular plates based on this general solution, obtaining analytical solutions consistent with existing numerical results. The explicit elastic field distributions related to the inhomogeneous parameter demonstrate the influence of inhomogeneity on stress and displacement in FGM circular plates.
Article
Mechanics
Chang Li, Hai Qing
Summary: In this work, a nonlocal strain gradient integral model is used to study the free damping vibration analysis of functionally graded viscoelastic Timoshenko microbeams with immovable boundary conditions in thermal environment. The microbeams are modeled using the Kelvin-Voigt model and the differential governing equations and corresponding boundary conditions are derived using Hamilton's principle. By combining the nonlocal strain gradient integral model and Kelvin-Voigt viscoelastic model, the integral constitutive equations of nonlocal stress with thermal effect are derived and converted into a differential form with constitutive constraints. The size-dependent axial force due to thermal expansion is explicitly derived and the bending deflection, moment, cross-sectional rotation, and shear force are computed using Laplace transformation for linear thermo-elastic vibration. A two-step numerical method is proposed to solve the elastic vibration frequency and damping ratio, and numerical investigations are conducted to explore the influences of various parameters on the vibration frequencies and damping ratio.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Materials Science, Multidisciplinary
Mohammad Shishesaz, Mojtaba Shariati, Reza Mosalmani
Summary: In this study, the stress-driven method and strain gradient theory were used to investigate the vibrational behavior of functionally graded circular nanoplates. The results show that considering the small-scale effect and using nonlinear behavior are important. The material size parameter and aspect ratio have significant effects on the frequency ratios.
JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES
(2023)
Article
Chemistry, Physical
Rabab A. A. Alghanmi
Summary: This paper presents a static analysis of functionally graded nanoplates with porosities by combining nonlocal strain gradient theory and four-variable shear deformation theory. The proposed model captures the effects of both nonlocal and strain gradient on the nanoplate structures by incorporating corresponding factors into the elastic constants of the nanoplate.
Article
Engineering, Mechanical
Nikola Nesic, Milan Cajic, Danilo Karlicic, Aleksandar Obradovic, Julijana Simonovic
Summary: This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both the elastic stress gradient field considering the nonlocal parameter and the strain gradient stress field considering the material length scale parameter. The study demonstrates that the application of the incremental harmonic balance method in analyzing nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems.
NONLINEAR DYNAMICS
(2022)
Article
Mechanics
Chien H. Thai, A. M. J. Fereira, H. Nguyen-Xuan, P. Phung-Van, P. T. Hung
Summary: In this study, a nonlocal strain gradient isogeometric model for free vibration analysis of magneto-electro-elastic (MEE) nanoplates made of functionally graded (FG) materials is presented. The model takes into account higher-order shear deformation theory, nonlocal strain gradient theory, and isogeometric analysis method. The stiffness of MEE-FG nanoplates is shown to be influenced by two scale parameters. The natural frequency of the nanoplates is evaluated by considering the power-law scheme, geometrical parameter, nonlocal parameter, strain gradient parameter, electric voltage, and magnetic potential. The results obtained using nonlocal strain gradient theory (NSGT) are compared to those obtained using classical theory.
COMPOSITE STRUCTURES
(2023)
Article
Engineering, Civil
Chien H. Thai, P. T. Hung, H. Nguyen-Xuan, P. Phung-Van
Summary: In this paper, a new size-dependent meshfree method is introduced to analyze the free vibrations of magneto-electro-elastic (MEE) functionally graded (FG) nanoplates. The method combines the nonlocal strain gradient theory (NSGT), the higher-order shear deformation theory (HSDT), and meshfree method for the first time. The effective material properties of MEE-FG nanoplates are expressed using a power-law scheme. Numerical examples are given to investigate the effect of various parameters on the natural frequency of MEE-FG nanoplates.
ENGINEERING STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
Suihan Sui, Ling Chen, Cheng Li, Xinpei Liu
MATHEMATICAL PROBLEMS IN ENGINEERING
(2015)
Article
Nanoscience & Nanotechnology
C. Li, N. Zhang, S. Li, L. Q. Yao, J. W. Yan
JOURNAL OF NANOMATERIALS
(2019)
Article
Engineering, Mechanical
L. Q. Yao, C. J. Ji, J. P. Shen, C. Li
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING
(2020)
Article
Physics, Applied
C. Li, P. Y. Wang, Q. Y. Luo
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2020)
Article
Acoustics
Chengxiu Zhu, Jianwei Yan, Pingyuan Wang, Cheng Li
Summary: This study presents vibration analyses on axially moving functionally graded nanoplates exposed to hygrothermal environments. The results show that factors like nonlocal parameter, gradient index, temperature changing, moisture concentration, axial speed, material characteristic scale parameter, and aspect ratio significantly affect the vibration frequencies of functionally graded nanoplates.
SHOCK AND VIBRATION
(2021)
Article
Engineering, Multidisciplinary
Chengxiu Zhu, Yingting Chen, Jingbo Zhao, Cheng Li, Zuxiang Lei
Summary: This study investigates the vertical and horizontal bending behavior of micro-beams subjected to axial compressive and transverse concentrated loadings using nonlocal theory. A mathematical model is developed and the effects of external load, external size, structural stiffness, and internal characteristic scale on the bending deformation are analyzed. The results show a decrease in critical compression with increasing internal characteristic scale and significant variation in midpoint deflection due to various factors. Additionally, a nonlocal scale effect is observed, emphasizing the importance of internal characteristic scale compared to external size.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Multidisciplinary Sciences
Ying-Ting Chen, Cheng Li, Lin-Quan Yao, Yang Cao
Summary: This paper proposes a new hybrid radial basis function collocation method (HRBF-CM) for solving two-dimensional elastostatic symmetric problems. The method combines infinitely smooth RBF and piecewise smooth RBF, with two parameters (the shape parameter and the weight parameter). Discretization schemes are presented in detail. Numerical results using MATLAB show that the proposed method has higher accuracy compared to traditional methods, especially with a larger number of nodes. The effectiveness of the new method compared to widely used traditional RBF is discussed, as well as the effect of parameters on the method's performance.
Article
Multidisciplinary Sciences
Liulin Kong, Bo Zhang, Cheng Li
Summary: This study analyzed the thermal buckling and postbuckling characteristics of functionally graded carbon nanotube-reinforced nanobeams, showing that considering couple stress or surface energy could significantly increase postbuckling stability, impacting the thermal buckling and postbuckling behaviors of nanobeams.
Article
Multidisciplinary Sciences
Bo Zhang, Cheng Li, Limin Zhang, Feng Xie
Summary: This paper analyzes the free vibration of isotropic gradient elastic thick non-rectangular microplates. A negative second-order gradient elastic theory with symmetry is used to capture the microstructure-dependent effects. The equations of motion and boundary conditions are obtained using the energy variational principle. Analytical solutions are presented for simply supported free-vibrational rectangular microplates, and a differential quadrature finite element method is applied to solve the free vibration of thick microplates. Numerical examples are validated against existing literature, and the impact of various parameters on the free vibration characteristics of annular and triangular microplates is shown.
Article
Multidisciplinary Sciences
Limin Guo, Cheng Li, Jingbo Zhao
Summary: This paper investigates numerical solutions and approximate solutions of fractional differential equations using various methods such as Lie symmetry, variational method, and the optimal ADM method. The author obtains positive solutions by iterative methods for sum operators and deduces Green's function and its properties. Based on the properties of Green's function, the existence of iterative positive solutions for a nonlinear Caputo-Hadamard infinite-point fractional differential equation is derived. An example is provided to illustrate the main result.
Article
Engineering, Civil
H. N. Li, W. Wang, S. K. Lai, L. Q. Yao, C. Li
Summary: This paper investigates the nonlinear vibration and stability analysis of rotating functionally graded (FG) piezoelectric nanobeams using the nonlocal strain gradient theory. The study derives nonlinear equations of motion and discretizes them to determine the vibration frequencies and buckling loads of the nanobeams. The results show that increasing the nonlocal parameter and material length parameter can result in a stiffness-hardening effect, and incorporating the effect of geometric nonlinearity is crucial for accurate analysis.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Engineering, Multidisciplinary
Chengxiu Zhu, Yingting Chen, Jingbo Zhao, Cheng Li, Zuxiang Lei
Summary: This study investigates the vertical and horizontal bending of micro-beams subjected to axial compressive and transverse concentrated loadings using the nonlocal theory. A simplified mathematical model and nonlocal differential constitutive equation are developed for this purpose. The results show that the critical compression decreases with increasing internal characteristic scale, and the midpoint deflection varies with respect to various factors including loadings, stiffness, and size. The study highlights the nonlocal scale effect and the mutual restriction between structural stiffness and external loadings in micro-/nano-scaled mechanics.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)