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Keywords = generalized differential quadrature method (GDQM)

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18 pages, 12446 KiB  
Article
Dynamic Behavior of Carbon Nanotube-Reinforced Polymer Composite Ring-like Structures: Unraveling the Effects of Agglomeration, Porosity, and Elastic Coupling
by Hossein Mottaghi T., Moein A. Ghandehari and Amir R. Masoodi
Polymers 2025, 17(5), 696; https://doi.org/10.3390/polym17050696 - 5 Mar 2025
Viewed by 825
Abstract
This research examines the free vibration characteristics of composite ring-like structures enhanced with carbon nanotubes (CNTs), taking into account the effects of CNT agglomeration. The structural framework comprises two concentric composite rings linked by elastic springs, creating a coupled beam ring (CBR) system. [...] Read more.
This research examines the free vibration characteristics of composite ring-like structures enhanced with carbon nanotubes (CNTs), taking into account the effects of CNT agglomeration. The structural framework comprises two concentric composite rings linked by elastic springs, creating a coupled beam ring (CBR) system. The first-order shear deformation theory (FSDT) is applied to account for transverse shear deformation, while Hamilton’s principle is employed to formulate the governing equations of motion. The effective mechanical properties of the composite material are assessed with regard to CNT agglomeration, which has a significant impact on the elastic modulus and the overall dynamic behavior of the structure. The numerical analysis explores the influence of porosity distribution, boundary conditions (BCs), and the stiffness of the springs on the natural vibration frequencies (NVFs). The results demonstrate that an increase in CNT agglomeration leads to a reduction in the stiffness of the composite, consequently decreasing the NVFs. Furthermore, asymmetric porosity distributions result in nonlinear fluctuations in NVFs due to irregularities in mass and stiffness, whereas uniform porosity distributions display a nearly linear relationship. This study also emphasizes the importance of boundary conditions and elastic coupling in influencing the vibrational response of CBR systems. These findings offer significant insights for the design and optimization of advanced composite ring structures applicable in aerospace, nanotechnology, and high-performance engineering systems. Full article
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22 pages, 5668 KiB  
Article
Nonlinear Dynamic Analysis of a Curved Sandwich Beam with a Time-Dependent Viscoelastic Core Using the Generalized Differential Quadrature Method (GDQM)
by Mehmet Mert Serveren, Ozgur Demir and Aytac Arikoglu
Symmetry 2024, 16(2), 238; https://doi.org/10.3390/sym16020238 - 15 Feb 2024
Cited by 1 | Viewed by 1470
Abstract
This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibration are derived by using Hamilton’s principle. The first-order [...] Read more.
This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibration are derived by using Hamilton’s principle. The first-order shear deformation theory is used to obtain kinematic relations. The spatial discretization of the equations is achieved using the generalized differential quadrature method (GDQM), and the Newmark-Beta algorithm is used to solve the time variation of the equations. The Newton–Raphson method is used to transform nonlinear equations into linear equations. The validation of the proposed model and the GDQM solution’s reliability are provided via comparison with the results that already exist in the literature and finite element method (FEM) analyses using ANSYS. Then, a series of parametric studies are carried out for a curved sandwich beam with aluminum face layers and a time-dependent viscoelastic core. The resonance and cancellation phenomena for the nonlinear moving-load problem of curved sandwich beams with a time-dependent viscoelastic core are performed using the GDQM for the first time, to the best of the authors’ knowledge. Full article
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25 pages, 4714 KiB  
Article
Vibration Analysis of a Unimorph Nanobeam with a Dielectric Layer of Both Flexoelectricity and Piezoelectricity
by Ali Naderi, Tran Quoc-Thai, Xiaoying Zhuang and Xiaoning Jiang
Materials 2023, 16(9), 3485; https://doi.org/10.3390/ma16093485 - 30 Apr 2023
Cited by 4 | Viewed by 2158
Abstract
In this study, for the first time, free and forced vibrational responses of a unimorph nanobeam consisting of a functionally graded base, along with a dielectric layer of both piezoelectricity and flexoelectricity, is investigated based on paradox-free local/nonlocal elasticity. The formulation and boundary [...] Read more.
In this study, for the first time, free and forced vibrational responses of a unimorph nanobeam consisting of a functionally graded base, along with a dielectric layer of both piezoelectricity and flexoelectricity, is investigated based on paradox-free local/nonlocal elasticity. The formulation and boundary conditions are attained by utilizing the energy method Hamilton’s principle. In order to set a comparison, the formulation of a model in the framework of differential nonlocal is first presented. An effective implementation of the generalized differential quadrature method (GDQM) is then utilized to solve higher-order partial differential equations. This method can be utilized to solve the complex equations whose analytic results are quite difficult to obtain. Lastly, the impact of various parameters is studied to characterize the vibrational behavior of the system. Additionally, the major impact of flexoelectricity compared to piezoelectricity on a small scale is exhibited. The results show that small-scale flexoelectricity, rather than piezoelectricity, is dominant in electromechanical coupling. One of the results that can be mentioned is that the beams with higher nonlocality have the higher voltage and displacement under the same excitation amplitude. The findings can be helpful for further theoretical as well as experimental studies in which dielectric material is used in smart structures. Full article
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28 pages, 3583 KiB  
Article
Deflection Analysis of a Nonlocal Euler–Bernoulli Nanobeam Model Resting on Two Elastic Foundations: A Generalized Differential Quadrature Approach
by Ramzy M. Abumandour, Mohammed A. El-Shorbagy, Islam M. Eldesoky, Mohamed H. Kamel, Hammad Alotaibi and Ahmed L. Felila
Symmetry 2022, 14(11), 2342; https://doi.org/10.3390/sym14112342 - 7 Nov 2022
Cited by 2 | Viewed by 1997
Abstract
This paper provides a general formularization of the nonlocal Euler–Bernoulli nanobeam model for a bending examination of the symmetric and asymmetric cross-sectional area of a nanobeam resting over two linear elastic foundations under the effects of different forces, such as axial and shear [...] Read more.
This paper provides a general formularization of the nonlocal Euler–Bernoulli nanobeam model for a bending examination of the symmetric and asymmetric cross-sectional area of a nanobeam resting over two linear elastic foundations under the effects of different forces, such as axial and shear forces, by considering various boundary conditions’ effects. The governing formulations are determined numerically by the Generalized Differential Quadrature Method (GDQM). A deep search is used to analyze parameters—such as the nonlocal (scaling effect) parameter, nonuniformity of area, the presence of two linear elastic foundations (Winkler–Pasternak elastic foundations), axial force, and the distributed load on the nanobeam’s deflection—with three different types of supports. The significant deductions can be abbreviated as follows: It was found that the nondimensional deflection of the nanobeam was fine while decreasing the scaling effect parameter of the nanobeams. Moreover, when the nanobeam is not resting on any elastic foundations, the nondimensional deflection increases when increasing the scaling effect parameter. Conversely, when the nanobeam is resting on an elastic foundation, the nondimensional deflection of the nanobeam decreases as the scaling effect parameter is increased. In addition, when the cross-sectional area of the nanobeam varies parabolically, the nondimensional deflection of the nonuniform nanobeam decreases in comparison to when the cross-sectional area varies linearly. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Optics: Topics and Advances)
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31 pages, 4794 KiB  
Article
Critical Temperature and Frequency Characteristics of GPLs-Reinforced Composite Doubly Curved Panel
by Armen Adamian, Keivan Hosseini Safari, Mehdi Sheikholeslami, Mostafa Habibi, M. S. H. Al-Furjan and Guojin Chen
Appl. Sci. 2020, 10(9), 3251; https://doi.org/10.3390/app10093251 - 7 May 2020
Cited by 121 | Viewed by 3011
Abstract
In this study, critical temperature and frequency characteristics of a doubly curved panel are reinforced by graphene nanoplatelets (GPLs) with the aid of a two-dimensional generalized differential quadrature method (2D-GDQM) are investigated. The size effects are included using nonlocal strain gradient theory (NSGT) [...] Read more.
In this study, critical temperature and frequency characteristics of a doubly curved panel are reinforced by graphene nanoplatelets (GPLs) with the aid of a two-dimensional generalized differential quadrature method (2D-GDQM) are investigated. The size effects are included using nonlocal strain gradient theory (NSGT) that has two length scale parameters, and the panel is modeled as a panel using high order shear deformation theory (HSDT). The mechanical properties of GPLs are calculated based on the rule of mixtures and the modified Halpin–Tsai model. The novelty of the current study is in considering the effects of the thermal environment, various boundary conditions, and size effects on the frequency and critical temperature of the GPLRC panel. The validation is performed through the comparison of the numerical results for the frequency of the GPLRC panel and the literature. For more verification, a finite element model is presented using the finite element package to simulate the response of the current structure. The results created from a finite element simulation illustrate a close agreement with the numerical method results. The results demonstrate that GPLs’ weight function, the ratio of panel curvature (R1/R2), GPLs’ pattern, and size-dependent parameters have noticeable effects on the frequency and critical temperature characteristics of the GPLs-reinforced composite (GPLRC) curved panel. The favorable suggestion of this survey is that when designing the GPLRC structure, special attention should be paid to size-dependent parameters because the nonlocal and length scale parameters have an essential role in the static and dynamic behaviors of the GPLRC panel. Full article
(This article belongs to the Section Mechanical Engineering)
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24 pages, 3566 KiB  
Article
Frequency Characteristics of Multiscale Hybrid Nanocomposite Annular Plate Based on a Halpin–Tsai Homogenization Model with the Aid of GDQM
by Mehran Safarpour, Alireza Rahimi, Omid Noormohammadi Arani and Timon Rabczuk
Appl. Sci. 2020, 10(4), 1412; https://doi.org/10.3390/app10041412 - 19 Feb 2020
Cited by 32 | Viewed by 3415
Abstract
In this article, we study the vibration performance of multiscale hybrid nanocomposite (MHC) annular plates (MHCAP) resting on Winkler–Pasternak substrates exposed to nonlinear temperature gradients. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, [...] Read more.
In this article, we study the vibration performance of multiscale hybrid nanocomposite (MHC) annular plates (MHCAP) resting on Winkler–Pasternak substrates exposed to nonlinear temperature gradients. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. The annular plate is modeled based on higher-order shear deformation theory (HSDT). We present a modified Halpin–Tsai model to predict the effective properties of the MHCAP. Hamilton’s principle was employed to establish the governing equations of motion, which is finally solved by the generalized differential quadrature method (GDQM). In order to validate the approach, numerical results were compared with available results from the literature. Subsequently, a comprehensive parameter study was carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, outer temperature, volume fraction and orientation angle of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio, and inner radius to thickness ratio on the response of the plate. The results show that applying a sinusoidal temperature rise and locating more CNTs in the vicinity of the bottom surface yielded the highest natural frequency. Full article
(This article belongs to the Section Materials Science and Engineering)
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15 pages, 3867 KiB  
Article
Irreversibility Analysis of Dissipative Fluid Flow Over A Curved Surface Stimulated by Variable Thermal Conductivity and Uniform Magnetic Field: Utilization of Generalized Differential Quadrature Method
by Muhammad Idrees Afridi, Abderrahim Wakif, Muhammad Qasim and Abid Hussanan
Entropy 2018, 20(12), 943; https://doi.org/10.3390/e20120943 - 7 Dec 2018
Cited by 37 | Viewed by 3793
Abstract
The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the [...] Read more.
The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the energy equation. Appropriate transformations are used to develop the self-similar equations from the governing equations of momentum and energy. The resulting self-similar equations are then solved by the Generalized Differential Quadrature Method (GDQM). For the validation and precision of the developed numerical solution, the resulting equations are also solved numerically using the Runge-Kutta-Fehlberg method (RKFM). An excellent agreement is found between the numerical results of the two methods. To examine the impacts of emerging physical parameters on velocity, temperature distribution and entropy generation, the numerical results are plotted against the various values of physical flow parameters and discussed physically in detail. Full article
(This article belongs to the Special Issue Entropy Generation and Heat Transfer)
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