Article
Physics, Multidisciplinary
Ahmad Haghani, Mehdi Jahangiri, Reza Ghaderi
Summary: Due to the introduction of particular responses not present in linear systems, properties of nonlinear systems can lead to inaccurate or misleading results from linear models. Therefore, studying nonlinear vibrations is crucial in structural vibration analysis. This study utilized the stress driven nonlocal theory (SDM) and the strain gradient theory (SGT) to analyze the nonlinear vibrations of a Timoshenko nanobeam. By solving the nonlinear equations of motion using the homotopy analysis method, it was found that the nonlinear natural frequency increased as the dimensionless characteristic parameter increased. The results also showed a high level of agreement with previous research using a linear frequency of Timoshenko beam model based on the SGT.
Article
Engineering, Civil
Xiao-Jian Xu
Summary: This study addresses the paradox of abnormal frequencies in the free vibration of nonlocal cantilever beams within the framework of nonlocal strain gradient theory. By updating the inconsistencies of reported boundary conditions and proposing a method for calibrating size-effect parameters, the numerical results demonstrate the model's capability in capturing the size-dependent mechanical properties of materials, whether exhibiting stiffness-hardening or stiffness-softening effects.
THIN-WALLED STRUCTURES
(2021)
Article
Physics, Mathematical
M. R. Elahi, Y. Mahmoudi, A. Salimi Shamloo, M. Jahangiri Rad
Summary: In this study, the Fredholm hypersingular integral equation of the first kind with a singular right-hand function on the interval [-1,1] is solved using a simple and straightforward collocation method. The discontinuous solution on the interval [-1,1] is approximated by a piecewise polynomial, and the unknown coefficients are evaluated accurately. The results demonstrate the accuracy of the proposed method compared to other methods in the literature.
ADVANCES IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
A. Panda, S. Santra, J. Mohapatra
Summary: This article discusses two different methods for solving a time fractional partial integro-differential equation, namely the Adomian decomposition method and homotopy perturbation method. It also proves the convergence analysis of the solution based on these methods and provides numerical evidence to support the theoretical analysis.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Applied
Azzh Saad Alshehry, Naila Amir, Naveed Iqbal, Rasool Shah, Kamsing Nonlaopon
Summary: In this study, we propose a method to study fractional-order shock wave equations and wave equations arising from the motion of gases. The approach combines the Yang transform, the homotopy perturbation method, and He's polynomials, as well as the Yang transform, the decomposition method, and the Adomian polynomials. By manipulating the recurrence relation to generate a series solution in a limited number of iterations, the reliability of the suggested methodologies is demonstrated through graphical behaviors and consistent results.
Article
Mechanics
Amin Vahidi-Moghaddam, Arman Rajaei, Ehsan Azadi Yazdi, Mohammad Eghtesad, Dan Sorin Necsulescu
Summary: This paper investigates the nonlinear forced vibrations of homogeneous Euler-Bernoulli microbeams with clamped-clamped boundary conditions. By incorporating the nonlocal strain gradient theory, the governing nonlinear partial differential equation of motion including mid-plane stretching and damping effects is derived. Through the Galerkin approach, a reduced equation of motion is obtained under a central harmonic force. The perturbation technique is used to examine the nonlinear forced vibration behavior of the microbeam, and the simulation results show the role of size effect on the vibration behavior. Moreover, the effects of different physical parameters on the vibration behavior of the microbeam are studied. Finally, the proposed approach is compared with a numerical solution to validate the accuracy and validity of the presented analytical solution.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Engineering, Mechanical
S. M. J. Hosseini, R. Ansari, J. Torabi, K. Hosseini, A. Zabihi
Summary: The investigation focuses on studying the size-dependent dynamic pull-in instability of nanobeams using NLSGT and the Euler-Bernoulli beam model. The Galerkin method and HAM were employed to solve the governing equation, and the results were validated through comparison with previously published results. The study also explores the effects of different theories on the dynamic behavior of nanobeams and discusses the impacts of electrostatic forces, fringing field, and initial gap under different boundary conditions.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF MECHANICAL ENGINEERING
(2021)
Article
Mechanics
Hamidreza Yademellat, Reza Ansari, Abolfazl Darvizeh, Jalal Torabi, Ali Zabihi
Summary: This study investigates the size-dependent dynamic pull-in instability of piezoelectrically and electrostatically actuated micro/nanobeams using the nonlocal strain gradient theory. The effects of flexoelectricity and piezoelectricity are considered, and various nonlinear forces are taken into account. The analysis method used in this study improves the reliability of the research model by comparing the results with existing literature.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Engineering, Mechanical
Yiyuan Jiang, Li Li, Yujin Hu
Summary: When the external stimuli have a similar length scale to most chain lengths within a polymeric solid, nonlocal and microstructure-dependent strain-gradient effects become significant. This study proposes a physically-based nonlocal strain gradient theory for polymer networks, where the kernel functions and intrinsic length scales have clear physical meanings. The main contribution lies in establishing a general framework that can incorporate various microscopic descriptions and derive a corresponding nonlocal strain gradient constitutive relation.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2023)
Article
Mathematics, Applied
M. Mossa Al-Sawalha, Azzh Saad Alshehry, Kamsing Nonlaopon, Rasool Shah, Osama Y. Ababneh
Summary: In this study, the solution of the time-fractional vibration equation for large membranes is found using effective techniques like the homotopy perturbation approach and the Adomian decomposition method via the Yang transform. Numerical experiments are conducted with various initial conditions, and the findings demonstrate the competence and reliability of this analytical framework. The suggested strategies for different orders of memory-dependent derivative reduce computation size and time, and are helpful for both small and large parameters.
Article
Engineering, Multidisciplinary
Huilong Ren, Xiaoying Zhuang, Nguyen-Thoi Trung, Timon Rabczuk
Summary: A general finite deformation higher-order gradient elasticity theory is proposed in the paper, reducing the material parameters significantly under certain simplifications. A nonlocal operator method is developed and applied to numerical examples, demonstrating the stiffness response of the high gradient solid theory and the capability of the nonlocal operator method in solving higher-order physical problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Civil
S. M. J. Hosseini, J. Torabi, R. Ansari, A. Zabihi
Summary: This paper investigates the size-dependent nonlinear dynamic pull-in instability and vibration of nanobeams, using the nonlocal strain gradient theory and the homotopy analysis method to obtain results. The effects of various factors on the electromechanical behavior of the nanobeams are analyzed.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2021)
Article
Mechanics
Chinika Dangi, Roshan Lal, N. Sukavanam
Summary: A mathematical model for bi-directional functionally graded Euler-Bernoulli nanobeams has been developed, considering nonlocal strain gradient theory and Gurtin-Murdoch surface elasticity theory.
A parametric study shows that the surface effect has a significant impact on the frequencies of nanobeams, especially at lower thicknesses.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Engineering, Civil
Dongchang Hou, Lifeng Wang, Jianwei Yan
Summary: This paper proposes a higher-order nonlocal strain gradient plate model that combines nonlocal elasticity theory with strain gradient theory. The model is derived using Hamilton's principle and introduces two higher-order parameters to explain the size effect and dispersive behavior. The meshfree moving Kriging interpolation method is used to calculate the frequency under complicated boundary conditions. The effectiveness of the model is demonstrated by comparing it with other theories.
ENGINEERING STRUCTURES
(2023)
Article
Mathematics, Applied
Azzh Saad Alshehry, Humaira Yasmin, Rasool Shah, Roman Ullah, Asfandyar Khan
Summary: This paper introduces a novel numerical approach for solving the nonlinear fractional Phi-four equation by combining the Homotopy perturbation method, the Adomian decomposition method, and the Shehu transform. The efficacy of this approach is demonstrated by reducing the complexity of the equation and providing accurate and efficient solutions. It has extensive applications in physics and engineering.
Article
Computer Science, Interdisciplinary Applications
Subrat Kumar Jena, S. Chakraverty, Mohammad Malikan
Summary: This study investigates the applicability of shifted Chebyshev polynomial-based Rayleigh-Ritz method and Navier's technique on the free vibration of functionally graded beams with uniformly distributed porosity, considering varying material properties along the thickness and embedding the beam in an elastic substrate. The use of shifted Chebyshev polynomials as shape functions ensures computational efficiency and avoids ill-conditioning, with various boundary conditions considered for parametric study. Validation through comparison with existing literature and a convergence study on natural frequencies are performed to examine the effectiveness and accuracy of the model.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mechanics
Subrat Kumar Jena, S. Chakraverty, Mohammad Malikan, Francesco Tornabene
Summary: This article investigates the vibration characteristics of three different types of Single-Walled Carbon Nanotubes (SWCNTs) while considering the influences of surface energy and surface residual stresses. A refined beam theory, called one-variable shear deformation beam theory, is combined with Hamilton's principle to formulate the governing equations of the proposed model. The size-dependent behavior of the SWCNTs is addressed using Eringen's nonlocal elasticity theory.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2022)
Article
Mathematics, Interdisciplinary Applications
Rajarama Mohan Jena, Snehashish Chakraverty
Summary: The terms fractional differentiation and fractal differentiation have been combined to form a new fractional differentiation operator in this study. Various kernels, including the power-law and the Mittag-Leffler function, are used to investigate these novel operators. The new operators exhibit both fractional-order and fractal dimensions. They are applied to study chaotic attractors using the Mittag-Leffler and power-law kernels, and the solutions are obtained through numerical procedures.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Physics, Multidisciplinary
Subrat Kumar Jena, S. Chakraverty, Vinyas Mahesh, Dineshkumar Harursampath, Hamid M. Sedighi
Summary: This article investigates the influence of geometrical uncertainties on the free vibration of Euler-Bernoulli Functionally Graded beams on a Winkler-Pasternak elastic foundation. The uncertain model is constructed using Symmetric Gaussian Fuzzy Numbers, and the governing equations of motion for the uncertain model are derived. Natural frequencies are computed using different methods and compared to validate the results of the uncertain model. A comprehensive parametric analysis is also conducted to investigate the fuzziness or spreads of natural frequencies in relation to various uncertain parameters.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Review
Computer Science, Artificial Intelligence
Arup Kumar Sahoo, Snehashish Chakraverty
Summary: This article discusses the impact of machine intelligence methods on dynamical systems in interdisciplinary areas, comparing different types of artificial neural network methods. Neural network model-based methods are more general, continuous, and adaptive, making them more effective in solving nonlinear behavior problems.
WILEY INTERDISCIPLINARY REVIEWS-DATA MINING AND KNOWLEDGE DISCOVERY
(2022)
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
Mathematics, Applied
Dhabaleswar Mohapatra, Snehashish Chakraverty
Summary: This paper introduces a new method to solve type-2 fuzzy linear systems by converting them into different types of linear systems and utilizing arithmetic of interval theory for solution. The effectiveness of the proposed method is demonstrated through numerical examples and applications, showing satisfactory results and in some cases, improved solution bounds.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Mrutyunjaya Sahoo, Snehashish Chakraverty
Summary: This manuscript presents a new hybrid technique for solving one-dimensional shallow water wave equations, aiming to find approximate solutions including fuzzy uncertain initial conditions. The study compares crisp and fuzzy uncertainties, and the proposed method ultimately presents the solution results through Gaussian fuzzy number plots.
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
Computer Science, Interdisciplinary Applications
Dhabaleswar Mohapatra, Snehashish Chakraverty
Summary: This paper focuses on the numerical analysis of the fractional order giving up smoking model, using fuzzy sets to deal with uncertainty and the Legendre wavelet method to solve the model. The findings show that the method is effective in solving the model and demonstrating the existence and uniqueness of the solution.
ENGINEERING COMPUTATIONS
(2023)
Article
Mathematics, Applied
Rajarama Mohan Jena, Snehashish Chakraverty, Kottakkaran Sooppy Nisar
Summary: This paper investigates the time-fractional order rotavirus epidemic model in an uncertain environment defined in the Caputo-Fabrizio (CF) derivative sense. A double parametric form (DPF) of fuzzy numbers has been used in the fuzzy fractional rotavirus model. A semi-analytical approach called the homotopy perturbation Elzaki transform method (HPETM) has been employed to solve the present model with the fuzzy initial condition. Various fuzzy and interval solutions have been computed by considering different values of fractional orders, fuzzy parameters, and parameters involved in the given model.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Perumandla Karunakar, K. Shiva Reddy, Snehashish Chakraverty
Summary: In this paper, an interval solution is constructed for the system of differential equations (SDEs) governing the COVID-19 pandemic with uncertain parameters. The imposition of lockdown on infective is considered as an interval parameter. The resulting interval system of differential equations (ISDEs) is solved using the parametric concept and the 4th order Runge-Kutta method. The obtained results are found to be in good agreement with existing crisp results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Multidisciplinary
T. D. Rao, S. Chakraverty, P. Karunakar, B. K. Sahoo
Summary: This paper investigates the radon transport processes in the earth's crust due to changes in geophysical processes. The study focuses on estimating uncertain bounds for radon concentration to identify anomaly behavior. The role of uncertainty in governing parameters, estimated from experimental measurements, is explored. Fuzzy variables and triangular fuzzy numbers are used to address parameter imprecision, and a fuzzy band for radon concentration is estimated to predict anomaly behavior.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Engineering, Multidisciplinary
Dongliang Ji, Hui Cheng, Hongbao Zhao
Summary: The influence of crystal size on the macroscopic parameters of sandstone samples is studied using a rock model based on the Voronoi tessellated model. It is found that decreasing crystal size results in increased strength and elastic modulus. Strain energy density (SED) is shown to help explain the failure mechanisms of the sandstone samples. A constitutive model that considers the heterogeneity in elastic modulus and rock strength is developed and is in good agreement with experimental results. The study also identifies the triggering of surface damage on slopes by vibration excitation in engineering applications as well as proposes a constitutive model for quantitatively evaluating damage accumulation in mining tunnels.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Francesco Tornabene, Matteo Viscoti, Rossana Dimitri
Summary: This manuscript investigates the dynamic properties of doubly-curved shell structures laminated with innovative materials using the Generalized Differential Quadrature (GDQ) method. The displacement field variable follows the Equivalent Single Layer (ESL) approach, and the geometrical description of the structures is distorted by generalized isogeometric blending functions. Through non-uniform discrete computational grid, the fundamental equations derived from the Hamiltonian principle are solved in strong form. Parametric investigations show the influence of material property variation on the modal response of the structures.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Duy-Khuong Ly, Ho-Nam Vu, Chanachai Thongchom, Nguyen-Thoi Trung
Summary: This paper presents a novel numerical approach for nonlinear analysis and smart damping control in laminated functionally graded carbon nanotube reinforced magneto-electro-elastic (FG-CNTMEE) plate structures, taking into account multiple physical fields. The approach employs a multi-physical coupling isogeometric formulation to accurately capture the nonlinear strain-displacement relationship and the magneto-electro-elastic coupling properties. The smart constrained layer damping treatment is applied to achieve nonlinear damped responses. The formulation is transformed into the Laplace domain and converted back to the time domain through inverse techniques for smart control using viscoelastic materials.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Xiaoyang Xu, Jie Cheng, Sai Peng, Peng Yu
Summary: In this study, a smoothed particle hydrodynamics (SPH) method is developed to simulate viscoelastic fluid flows governed by the Phan-Thien-Tanner (PTT) constitutive equation. The method is validated by comparing its solutions with those obtained by the finite volume method (FVM). The method is also used to simulate the impact behavior and dynamics of a viscoelastic droplet, and the influences of various parameters are investigated. The results demonstrate the accuracy and capability of the SPH method in describing the rheological properties and surface variation characteristics of viscoelastic fluid flows.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Xueying Zhang, Yangjiong Wu
Summary: This paper proposes a high resolution strategy for the localized method of approximate particular solutions (LMAPS). The strategy aims to improve the accuracy and stability of numerical calculation by selecting upwind interpolation templates. Numerical results demonstrate that the proposed high-resolution LMAPS is effective and accurate, especially for solving the Navier-Stokes equations with high Reynolds number.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Yong-Tong Zheng, Yijun Liu, Xiao-Wei Gao, Yang Yang, Hai-Feng Peng
Summary: Structures with holes are common in engineering applications. Analyzing stress concentration effects caused by holes using FEM or BEM is challenging and time-consuming. This paper proposes improved methods for simulating holes and cylinders, reducing the number of nodes while maintaining stress accuracy. Numerical examples demonstrate the accuracy and efficiency of the proposed methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Chein-Shan Liu, Chung-Lun Kuo
Summary: The paper presents two new families of fundamental solutions for the 3D Laplace equation and proposes the methods of pseudo fundamental solutions and anisotropic fundamental solutions, which outperform the traditional 3D MFS.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Sima Shabani, Miroslaw Majkut, Slawomir Dykas, Krystian Smolka, Esmail Lakzian
Summary: This study validates and simulates steam condensing flows using different condensation models and equations of state, identifying the most suitable model. The results highlight the importance of choosing the appropriate numerical model for accurately predicting steam condensation flows.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
D. L. Guo, H. H. Zhang, X. L. Ji, S. Y. Han
Summary: In this study, the mechanical behaviors of 2-D orthotropic composites with arbitrary holes were investigated using the numerical manifold method (NMM). The proposed method was verified and found to have good convergence and accuracy. Additionally, the effects of material principal direction and hole configurations on the mechanical behaviors of the orthotropic composites were revealed.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Giacomo Rosilho de Souza, Rolf Krause, Simone Pezzuto
Summary: In this paper, we propose a boundary element method for accurately solving the cell-by-cell bidomain model of electrophysiology. The method removes the degeneracy in the system and reduces the number of degrees of freedom. Numerical experiments demonstrate the exponential convergence of our scheme in space and several biologically relevant experiments are provided.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Riku Toshimitsu, Hiroshi Isakari
Summary: This study extends a recent paper by Lai et al. (2018) by introducing a novel boundary integral formulation for scalar wave scattering analysis in two-dimensional layered and half-spaces. The modified integral formulation eliminates fictitious eigenvalues and reasonable parameter settings ensure efficient and accurate numerical solutions. The proposed method is demonstrated to be effective through numerical examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Ebutalib Celik, Merve Gurbuz-Caldag
Summary: In this paper, a new meshless method based on domain decomposition for an L-shaped domain is proposed, which uses RBF-FD formulation at interface points and classical FD in sub-regions to improve the solution accuracy. The proposed numerical method is applied to simulate benchmark results for a divided-lid driven cavity and solve Navier-Stokes equations with Lorentz force term in a single-lid L-shaped cavity exposed to inclined magnetic field, and the flow structure is analyzed in terms of streamline topology under different magnetic field rotations and strengths.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Engineering, Multidisciplinary
Hanqing Liu, Fajie Wang, Lin Qiu, Cheng Chi
Summary: This paper presents a novel method that combines the singular boundary method with the Loop subdivision surfaces for acoustic simulation of complex structures, overcoming technical challenges in handling boundary nodes.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
