Article
Computer Science, Artificial Intelligence
Zulqurnain Sabir, Juan L. G. Guirao, Tareq Saeed
Summary: This study presents a new model based on the nonlinear singular second order delay differential equation of Lane-Emden type, which is numerically solved using heuristic technique. Four different examples are solved using artificial neural networks optimized by genetic algorithm (GA), sequential quadratic programming (SQP), and GA-SQP. The numerical results are compared with the exact results to demonstrate performance and correctness, and statistical investigations are presented to assess the accuracy and performance of the designed model implemented with heuristic methodology.
APPLIED SOFT COMPUTING
(2021)
Article
Computer Science, Artificial Intelligence
Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Muhammad Umar, Muhammad Shoaib, Dumitru Baleanu
Summary: The study proposes a neuro-swarm-based intelligent computing solver, FMW-ANN-PSO-SQP, to deal with stiff nonlinear singular models represented with NFLES involving both fractional and integer derivative terms, aiming to provide accurate, reliable, and viable frameworks. The algorithm is tested for six different variants of NFLESs, and the obtained numerical outcomes are compared with the exact results to authenticate the correctness, efficacy, and viability, which are further endorsed by statistical observations.
NEURAL COMPUTING & APPLICATIONS
(2022)
Article
Mathematics
Md. Habibur Rahman, Muhammad I. Bhatti, Nicholas Dimakis
Summary: In this paper, a novel technique for solving nonlinear multidimensional fractional differential equations was proposed using a modified version of the Bernstein polynomials called the Bhatti-fractional polynomials. The method approximated the desired solution and treated the resulting equation as a matrix equation. Experimental results showed higher accuracy and computational efficiency, making it suitable for solving fractional differential equations in various programming languages.
Article
Mathematics, Interdisciplinary Applications
Muath Awadalla, Mohamed Hannabou, Kinda Abuasbeh, Khalid Hilal
Summary: This work investigates the existence and uniqueness of solutions to a sequential fractional (Hybrid) differential equation with hybrid boundary conditions using the generalization of Dhage's fixed point theorem and Banach contraction mapping. Additionally, the stability of the solution is verified using the U-H technique, and two examples are provided to illustrate the theoretical findings.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Muhammad Shoaib, Rafia Tabassum, Kottakkaran Sooppy Nisar, Muhammad Asif Zahoor Raja, Farooq Ahmed Shah, Mohammed S. Alqahtani, C. Ahamed Saleel, H. M. Almohiy
Summary: This study investigates the pine wilt disease model (PWDM) using a hybrid bio-inspired algorithm. The artificial neural networks-based genetic algorithm (ANNs-GA) is used for global search, and sequential quadratic programming (SQP) serves as the local search framework. The model consists of two populations, host (h) and vector (v), each having different classes. The proposed ANNs-GASQP solver shows stability, robustness, and effectiveness with high accuracy.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Applied
Paul Bosch, Jose M. Rodriguez, Jose M. Sigarreta
Summary: In this paper, the authors work with a general formulation of Caputo-type fractional derivative and study oscillatory solutions of differential equations involving these derivatives. They extend the Kamenev-type oscillation criterion proposed by Baleanu et al. in 2015 and prove results on the existence and uniqueness of solutions for many equations. Finally, they provide some examples to enhance their study.
Article
Mathematics, Applied
Kobra Rabiei, Mohsen Razzaghi
Summary: This paper presents an effective method for solving fractional Riccati differential equations by defining FOBW and using hypergeometric functions to transform the problem into a set of algebraic equations. The equations are solved using Newton's iterative method, with error estimation provided. The performance of the method is evaluated through multiple examples, showing very accurate results.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics
Ahmed Salem, Lamya Almaghamsi
Summary: The sequential fractional differential equations at resonance, subject to three-point boundary conditions, are studied. These equations involve fractional derivative operators based on the Caputo derivative of order between 1 and 2. The goal of this study is to investigate the existence of solutions for the boundary value problem using the coincidence degree theory by Mawhin, which relies on Fredholm operators with zero index and two continuous projectors. An example is given to illustrate the theoretical results.
Article
Mathematics, Interdisciplinary Applications
Ymnah Alruwaily, Bashir Ahmad, Sotiris K. Ntouyas, Ahmed S. M. Alzaidi
Summary: This paper investigates the existence of solutions for a fully coupled Riemann-Stieltjes, integro-multipoint, boundary value problem of Caputo-type sequential fractional differential equations. The given system is studied using the Leray-Schauder alternative and contraction mapping principle. A numerical example is also provided to illustrate the abstract results.
FRACTAL AND FRACTIONAL
(2022)
Article
Multidisciplinary Sciences
D. A. Refaai, M. M. A. El-Sheikh, Gamal A. F. Ismail, Mohammed Zakarya, Ghada AlNemer, Haytham M. Rezk
Summary: This article discusses several forms of Ulam stability of nonlinear fractional delay differential equations. The investigation is based on a generalised Gronwall's inequality and Picard operator theory. Implementations are provided to demonstrate the stability results obtained for finite intervals.
Article
Engineering, Multidisciplinary
Li Yan, Zulqurnain Sabir, Esin Ilhan, Muhammad Asif Zahoor Raja, Wei Gao, Haci Mehmet Baskonus
Summary: This study presents a computational heuristic design based on the nonlinear Lienard model, using the efficiency of artificial neural networks (ANNs) and the hybridization procedures of global and local search approaches. The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models. The outcomes of the designed procedures are compared to verify their correctness, viability and efficacy.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Omar Alsayyed, Fadi Awawdeh, Safwan Al-Shara', Edris Rawashdeh
Summary: This study proposes high-order schemes for solving nonlinear fractional initial value problems by approximating the fractional integral into history and local terms. The convergence and stability of the proposed schemes are proved and validated through numerical examples.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
M. Manigandan, Subramanian Muthaiah, T. Nandhagopal, R. Vadivel, B. Unyong, N. Gunasekaran
Summary: In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and new kinds of coupled discrete and fractional integral boundary conditions. The validity of the obtained results is demonstrated by numerical examples.
Article
Mathematics, Applied
Parisa Rahimkhani
Summary: In this work, a new computational scheme called fractional-order Genocchi deep neural network (FGDNN) is introduced to solve a class of nonlinear stochastic differential equations (NSDEs) driven by fractional Brownian motion (FBM) with Hurst parameter H & ISIN; (0, 1). The FGDNN method utilizes the fractional-order Genocchi functions and Tanh function as activation functions of the deep structure, and presents a new approximate function to estimate unknown function by adjusting weights. Illustrative examples show the applicability, accuracy, and efficiency of the new method, comparing with analytical solutions and numerical results obtained through other methods.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Muhammad Umar, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Haci Mehmet Baskonus, Mohamed R. Ali, Nehad Ali Shah
Summary: This study proposes a nonlinear system for hepatitis B virus infection using the artificial neural network (ANN) combined with the genetic algorithm (GA) and sequential quadratic programming scheme (SQPS), referred to as ANN-GA-SQPS. An error function is designed based on the mathematical form of the hepatitis B virus differential model and its initial conditions. The hybrid efficiency of GA-SQPS is used to optimize the error function for the disease model, resulting in good measures of absolute error. Statistical measures are also performed to assess the constancy, reliability, and effectiveness of ANN-GA-SQPS using different indices in 50 independent executions and 30 variables.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Multidisciplinary Sciences
Ammara Mehmood, Muhammad Asif Zahoor Raja
Summary: The application of evolutionary computing paradigm-based heuristics for system modeling and parameter estimation of complex nonlinear systems has been widely explored. This study investigates the use of weighted differential evolution (WDE) in estimating the parameters of Hammerstein-Wiener model (HWM) and compares it with state-of-the-art methods. The HWM parameters are estimated using the WDE and genetic algorithms (GAs) heuristics, and the worth and value of the designed WDE algorithm is demonstrated through extensive graphical and numerical comparisons.
JOURNAL OF ADVANCED RESEARCH
(2023)
Article
Computer Science, Artificial Intelligence
Zulqurnain Sabir, Mohamed R. Ali, Muhammad Asif Zahoor Raja, R. Sadat, Dumitru Baleanu
Summary: The present study introduces a novel heuristic computing design for solving the second kind of Three-point singular boundary value problems (TPS-BVPs) by combining Feed forward Gudermannian neural networks (GNN) with Genetic algorithms (GA) and Active-set method (ASM). The proposed intelligent computing solver, FF-GNN-GAASM, is integrated into the hidden layer structure of FF-GNN systems, optimizing the error based Merit function (MF) with the hybrid-combined heuristics of GAASM. The performance of FF-GNN-GAASM is evaluated through statistical assessments, demonstrating consistent stability, accuracy, and convergence.
EVOLUTIONARY INTELLIGENCE
(2023)
Article
Computer Science, Artificial Intelligence
Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Nadia Mumtaz, Irwan Fathurrochman, R. Sadat, Mohamed R. Ali
Summary: This study presents numerical investigations of a fractional order computer virus propagation mathematical model with kill signals using stochastic procedures. The numerical solutions of the model are obtained using the Levenberg-Marquardt backpropagation scheme and neural networks. The results demonstrate the performance of the scheme for different fractional order values.
NEURAL PROCESSING LETTERS
(2023)
Article
Engineering, Multidisciplinary
Qiliang Chen, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Wei Gao, Haci Mehmet Baskonus
Summary: The purpose of this investigation is to numerically study the fractional order economic and environmental mathematical model (FO-EEMM). The study aims to find more realistic results of the FO-EEMM with non-integer and fractional order derivatives. The FO-EEMM is divided into three aspects: control accomplishment cost, capability of manufacturing elements, and diagnostics cost of technical exclusion. The FO-EEMM's solution is presented numerically using scaled conjugate gradient neural networks (SCGNNs). Three cases based on the FO-EEMM have been examined to evaluate numerical performances.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Chemistry, Physical
Zeeshan Ikram Butt, Iftikhar Ahmad, Hira Ilyas, Muhammad Shoaib, Muhammad Asif Zahoor Raja
Summary: This research investigates the magnetohydrodynamics (MHD) Casson nanofluid flow in a porous medium along a stretchable surface with different slips using artificial neural networks (ANNs) and inverse multiquadric (IMQ) radial basis function (RBF) as an activation function. The effects of various parameters on the velocity, temperature, and nanofluid concentration are analyzed through graphs. The proposed solver is validated through boxplot analysis, histograms, and cumulative distribution function (CDF) plots.
INTERNATIONAL JOURNAL OF HYDROGEN ENERGY
(2023)
Article
Physics, Applied
Syed Ali Asghar, Shafaq Naz, Muhammad Asif Zahoor Raja
Summary: The purpose of this research is to utilize a Bayesian solver with neural networks to determine numerical solutions of functional differential equations arising in quantum calculus models. The difficulty in solving functional differential equations with discrete versions is overcome by converting them into recurrence relations and generating datasets for neural networks. The proposed technique is confirmed to be accurate and stable through comprehensive statistical analysis, including mean squared error and regression analysis. The convergence and reliability of the technique are further supported by histogram, training state, and correlation plots, as well as by comparison with a reference solution and absolute error analysis.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Multidisciplinary
Saeed Ehsan Awan, Muhammad Awais, Muhammad Asif Zahoor Raja, Saeed ur Rehman, Chi-Min Shu
Summary: Artificial intelligence techniques are widely used in engineering and technology to enhance efficiency in business and society. This study explores the application of AI-based numerical computing to investigate the heat and mass transport improvement of nanofluids. Mathematical modeling and numerical simulations are conducted to analyze the effect of various parameters on temperature and velocity fields. Bayesian regularization knack-based networks are designed and evaluated for their accuracy and performance in approximating the solution dynamic of nanofluidic models.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
Zeeshan Khan, Samina Zuhra, Saeed Islam, Muhammad Asif Zahoor Raja, Aatif Ali
Summary: This study explores the computational strength of neural networks based on the Levenberg-Marquardt backpropagation technique to simulate the flow of Maxwell nanofluid past a linear stretchable surface. The model incorporates thermal radiation and Darcy's Forchheimer law. The accuracy of the neural network model is checked through statistical analysis and visual representation of the flow parameters.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Interdisciplinary Applications
Muhammad Shoaib, Rafia Tabassum, Kottakkaran Sooppy Nisar, Muhammad Asif Zahoor Raja, Farooq Ahmed Shah, Mohammed S. Alqahtani, C. Ahamed Saleel, H. M. Almohiy
Summary: This study investigates the pine wilt disease model (PWDM) using a hybrid bio-inspired algorithm. The artificial neural networks-based genetic algorithm (ANNs-GA) is used for global search, and sequential quadratic programming (SQP) serves as the local search framework. The model consists of two populations, host (h) and vector (v), each having different classes. The proposed ANNs-GASQP solver shows stability, robustness, and effectiveness with high accuracy.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Applied
Saeed Ehsan Awan, Faizan Ali, Muhammad Awais, Muhammad Shoaib, Muhammad Asif Zahoor Raja
Summary: The research community is interested in studying nanofluid models involving Aluminum Alloys AA7072 and AA7072 +AA7075 due to their advantageous impact on heat transfer and mechanical characteristics. This paper investigates a hybrid nanomaterial fluidic system based on AA7072-AA7075 using an artificial neural network with Bayesian regularization scheme (ANNs-BRS). The influence of flow on temperature distribution and velocity plot is analyzed. The performance of ANNs-BRS is evaluated using error histogram plots, regression analysis, and MSE based statistics. The results for entropy generation, Eckert number Ec, magnetic interaction parameter M, suction parameter S, and heat generation parameter Q are discussed.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Mathematics
Khizer Mehmood, Naveed Ishtiaq Chaudhary, Khalid Mehmood Cheema, Zeshan Aslam Khan, Muhammad Asif Zahoor Raja, Ahmad H. Milyani, Abdulellah Alsulami
Summary: This study investigates the parameter identification of an input nonlinear autoregressive exogenous (IN-ARX) model using swarm intelligence knacks of the nonlinear marine predators' algorithm (NMPA). A comparative analysis of the NMPA with other recent metaheuristics establishes its superiority in terms of accurate, robust, and convergent performances for different noise and generation variations. The statistics generated through multiple autonomous executions further confirm the reliability and stability of the NMPA for parameter estimation of IN-ARX systems.
Article
Physics, Applied
Muhammad Shoaib, Ghania Zubair, Kottakkaran Sooppy Nisar, Muhammad Asif Zahoor Raja, Iqra Naz, Ahmed Morsy
Summary: This paper examines the influence of activation energy in third-grade nanoparticle flow model (TG-NPFM) using Bayesian Regulation Method with backpropagated Artificial Neural Networks (BRM-BPANN). The nonlinear thermal radiation and viscous dissipation are considered in the model to obtain the numerical solutions. The nonlinear partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs) using the Optimal Homotopy Analysis Method (OHAM). The results of TG-NPFM are obtained through testing, validation, and training processes, and compared with standard solutions using MSE, error histogram, and regression plots for validation. The reliability and accuracy of the technique are demonstrated through the absolute error values and convergence and precision of the algorithm.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Computer Science, Information Systems
Sakda Noinang, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Soheil Salahshour, Wajaree Weera, Thongchai Botmart
Summary: The investigations aim to solve the fractional order HBV differential infection system (FO-HBV-DIS) with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation neural networks (LMBNNs). The FO-HBV-DIS with the response of antibody immune is categorized into five dynamics: healthy hepatocytes, capsids, infected hepatocytes, free virus, and antibodies. Through numerical tests with three different fractional order variants, the nonlinear FO-HBV-DIS with the response of antibody immune is solved. The stochastic LMBNNs procedures in conjunction with the Adams-Bashforth-Moulton approach are utilized for numerical simulations and comparison of the results.
CMC-COMPUTERS MATERIALS & CONTINUA
(2023)
Article
Engineering, Multidisciplinary
Li Yan, Zulqurnain Sabir, Esin Ilhan, Muhammad Asif Zahoor Raja, Wei Gao, Haci Mehmet Baskonus
Summary: This study presents a computational heuristic design based on the nonlinear Lienard model, using the efficiency of artificial neural networks (ANNs) and the hybridization procedures of global and local search approaches. The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models. The outcomes of the designed procedures are compared to verify their correctness, viability and efficacy.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Muhammad Shoaib, Ghania Zubair, Kottakkaran Sooppy Nisar, Muhammad Asif Zahoor Raja, Mohammed S. S. Alqahtani, Mohamed Abbas, H. M. Almohiy
Summary: This paper introduces a new Meyer neuro-evolutionary computational algorithm that combines the hybrid heuristics of Meyer wavelet neural network with the global optimized search efficiency of genetic algorithm and sequential quadratic programming for mathematical modeling of the epidemiological smoking model. According to the World Health Organization, tobacco consumption kills 10% of all adults worldwide. The smoking epidemic is considered the greatest health threat humanity has ever faced, making it crucial to address using the suggested hybrid techniques.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Engineering, Multidisciplinary
A. A. Aganin, A. I. Davletshin
Summary: A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed in this paper. The model equations are more accurate and compact compared to existing analogs. Five problems are considered for validation, and the results show good agreement with experimental data and numerical solutions. The model is also used to analyze the behavior of bubbles in different clusters, providing meaningful insights.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Hao Wu, Jie Sun, Wen Peng, Lei Jin, Dianhua Zhang
Summary: This study establishes an analytical model for the coupling of temperature, deformation, and residual stress to explore the mechanism of residual stress formation in hot-rolled strip and how to control it. The accuracy of the model is verified by comparing it with a finite element model, and a method to calculate the critical exit crown ratio to maintain strip flatness is proposed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shengwen Tu, Naoki Morita, Tsutomu Fukui, Kazuki Shibanuma
Summary: This study aimed to extend the finite element method to cope with elastic-plastic problems by introducing the s-version FEM. The s-version FEM, which overlays a set of local mesh with fine element size on the conventional FE mesh, simplifies domain discretisation and provides accurate numerical predictions. Previous applications of the s-version FEM were limited to elastic problems, lacking instructions for stress update in plasticity. This study presents detailed instructions and formulations for addressing plasticity problems with the s-version FEM and analyzes a stress concentration problem with linear/nonlinear material properties.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bo Fan, Zhongmin Wang
Summary: A 3D rotating hyperelastic composite REF model was proposed to analyze the influence of tread structure and rotating angular speed on the vibration characteristics of radial tire. Nonlinear dynamic differential equations and modal equations were established to study the effects of internal pressure, tread pressure sharing ratio, belt structure, and rotating angular speed on the vibration characteristics.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
X. W. Chen, Z. Q. Yue, Wendal Victor Yue
Summary: This paper examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modeled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The analytical solutions of the stress intensity factors are obtained and numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xumin Guo, Jianfei Gu, Hui Li, Kaihua Sun, Xin Wang, Bingjie Zhang, Rangwei Zhang, Dongwu Gao, Junzhe Lin, Bo Wang, Zhong Luo, Wei Sun, Hui Ma
Summary: In this study, a novel approach combining the transfer matrix method and lumped parameter method is proposed to analyze the vibration response of aero-engine pipelines under base harmonic and random excitations. The characteristics of the pipelines are investigated through simulation and experiments, validating the effectiveness of the proposed method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xiangyu Sha, Aizhong Lu, Ning Zhang
Summary: This paper investigates the stress and displacement of a layered soil with a fractional-order viscoelastic model under time-varying loads. The correctness of the solutions is validated using numerical methods and comparison with existing literature. The research findings are of significant importance for exploring soil behavior and its engineering applications under time-varying loads.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Thuy Dong Dang, Thi Kieu My Do, Minh Duc Vu, Ngoc Ly Le, Tho Hung Vu, Hoai Nam Vu
Summary: This paper investigates the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change using the Ritz energy method. The results show the significant beneficial effects of FG-GRC laminated coatings and corrugated core on the nonlinear buckling responses of structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Zhihao Zhai, Chengbiao Cai, Qinglai Zhang, Shengyang Zhu
Summary: This paper investigates the effect of localized cracks induced by environmental factors on the dynamic performance and service life of ballastless track in high-speed railways. A mathematical approach for forced vibrations of Mindlin plates with a side crack is derived and implemented into a train-track coupled dynamic system. The accuracy of this approach is verified by comparing with simulation and experimental results, and the dynamic behavior of the side crack under different conditions is analyzed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
James Vidler, Andrei Kotousov, Ching-Tai Ng
Summary: The far-field methodology, developed by J.C. Maxwell, is utilized to estimate the effective third order elastic constants of composite media containing random distribution of spherical particles. The results agree with previous studies and can be applied to homogenization problems in other fields.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Kim Q. Tran, Tien-Dat Hoang, Jaehong Lee, H. Nguyen-Xuan
Summary: This study presents novel frameworks for graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates and investigates their performance through static and free vibration analyses. The results show that the mass density framework has potential for comparing different porous cores and provides a low weight and high stiffness-to-weight ratio. Primitive plates exhibit superior performance among thick plates.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bence Hauck, Andras Szekrenyes
Summary: This study explores several methods for computing the J-integral in laminated composite plate structures with delamination. It introduces two special types of plate finite elements and a numerical algorithm. The study presents compact formulations for calculating the J-integral and applies matrix multiplication to take advantage of plate transition elements. The models and algorithms are applied to case studies and compared with analytical and previously used finite element solutions.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Wu Ce Xing, Jiaxing Wang, Yan Qing Wang
Summary: This paper proposes an effective mathematical model for bolted flange joints to study their vibration characteristics. By modeling the flange and bolted joints, governing equations are derived. Experimental studies confirm that the model can accurately predict the vibration characteristics of multiple-plate structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Pingchao Yu, Li Hou, Ke Jiang, Zihan Jiang, Xuanjun Tao
Summary: This paper investigates the imbalance problem in rotating machinery and finds that mass imbalance can induce lateral-torsional coupling vibration. By developing a model and conducting detailed analysis, it is discovered that mass imbalance leads to nonlinear time-varying characteristics and there is no steady-state torsional vibration in small unbalanced rotors. Under largely unbalanced conditions, both resonant and unstable behavior can be observed, and increasing lateral damping can suppress instability and reduce lateral amplitude in the resonance region.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Yong Cao, Ziwen Guo, Yilin Qu
Summary: This paper investigates the mechanically induced electric potential and charge redistribution in a piezoelectric semiconductor cylindrical shell. The results show that doping levels can affect the electric potentials and mechanical displacements, and alter the peak position of the zeroth-order electric potential. The doping level also has an inhibiting effect on the first natural frequency. These findings are crucial for optimizing the design and performance of cylindrical shell-shaped sensors and energy harvesters.
APPLIED MATHEMATICAL MODELLING
(2024)
