Article
Engineering, Mechanical
N. Menga, F. Bottiglione, G. Carbone
Summary: The paper evaluates the effectiveness of nonlinear viscoelastic damping in controlling base-excited vibrations. It investigates the robustness of nonlinear base isolation performance in controlling system response to a wide set of possible excitation spectra, showing that tuned nonlinear RLRB provides loads isolation in a wider range of excitation spectra.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Engineering, Mechanical
Marco Amabili, Prabakaran Balasubramanian, Giovanni Ferrari
Summary: This study explores the increase in damping with vibration amplitude and the increase in stiffness with vibration frequency in nonlinear vibrations of rectangular plates. A fractional linear solid model is applied to capture these phenomena and the frequency-dependent nonlinear damping. The results are compared with experimental data, showing good agreement in various aspects of the vibration response.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Xiaoming Peng, Yadong Shang
Summary: This paper investigates the long time behavior of a quasilinear viscoelastic equation with nonlinear damping, and establishes the existence of global attractors under suitable assumptions.
Article
Mathematics, Applied
Abdelkarim Kelleche, Nasser-eddine Tatar
Summary: This paper addresses the stabilization of a nonlinear axially moving viscoelastic string. Global existence of solutions is proven using the potential well method under suitable conditions on initial data, and the damping produced by the viscoelastic term ensures exponential decay of solutions with weaker conditions on the relaxation function and the use of a suitable boundary controller.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Civil
Pengcheng Wang, Xinkai Wu, Xiaozheng He
Summary: This research explores the vulnerability of nonlinear vehicle platoons characterized by oscillatory behavior caused by external perturbations. A vibration-theoretic approach is proposed to characterize the platoon vulnerability and obtain the resonance frequency. The closed-form formulas of damping intensity and resonance frequency are derived through rigorous analysis. Simulation results show that overdamped platoons are more robust against perturbations, while underdamped platoons can be destabilized easily by perturbations at the resonance frequency.
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
(2023)
Article
Mathematics, Applied
Muhammad Mustafa
Summary: In this paper, we investigate a nonlinear abstract equation subject to the competing effects of viscoelastic and frictional dampings. By making general assumptions on the behavior of g and h, we establish an explicit and optimal energy decay result, showing a combination of generality and optimality in one formula for the energy decay rates of this system.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Construction & Building Technology
Nasrin Jafari, Mojtaba Azhari
Summary: This paper studies the geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties based on the Von-Karman assumptions. A novel solution is proposed to predict the nonlinear frequencies of time-dependent plates according to the nonlinear frequencies of plates not dependent on time, greatly reducing the cost of calculations.
STEEL AND COMPOSITE STRUCTURES
(2023)
Article
Engineering, Civil
Salwa A. Mohamed, Amr E. Assie, Mohamed A. Eltaher
Summary: The manuscript introduces a nonlinear mathematical model for investigating the nonlinear bending response of Bi-directional functionally graded plates resting on elastic foundations. A unified higher order shear plate theory is employed to account for the shear influence with parabolic distribution. The gradation of materials is described by a power law function. The developed model is solved using a novel incremental-iterative method and the differential/integral quadrature method to numerically discretize the governing equations with variable-coefficients.
THIN-WALLED STRUCTURES
(2023)
Article
Engineering, Mechanical
Sheng Wang, Yongou Zhang, Wenyong Guo, Ting Pi, Xiaofeng Li
Summary: An improved incremental harmonic balance method (IHBM) is proposed to solve periodic responses of continuous nonlinear stiffness systems. This paper focuses on investigating nonlinear damping parts using the proposed IHBM method. The study demonstrates that the method can accurately obtain the dynamics of nonlinear systems.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yizhao Zhan, Shengxiang Zou, Xiongxiong He, Mingxuan Sun
Summary: This article focuses on incremental adaptive control for nonlinear systems in nonaffine form, developing incremental adaptive mechanisms and presenting corresponding control schemes to avoid numerical integration. The use of the implicit function theorem helps solve the intractability problem of the nonaffine structure, with robustness of tracking error characterized and effectiveness of the control design verified through numerical results.
Article
Mathematics, Applied
Mohammad M. Al-Gharabli, Salim A. Messaoudi
Summary: The paper investigates the interaction between a viscoelastic damping and a nonlinear frictional damping in a piezoelectric beam model with nonlinear source terms. By making general assumptions on the relaxation function and the nonlinear feedback, explicit formulae for the energy decay rates of this system are established, and it is proven that the energy decays at a rate dictated by the weaker damping. These results substantially improve some earlier related results in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
T. S. Jang
Summary: The presented iterative semi-analytical method converts differential equations to integral equations with the introduction of a pseudo-parameter, allowing for solutions without relying on small perturbation parameters. This method offers a wide application in handling strongly nonlinear physical problems effectively.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics
Mi Jin Lee, Jum-Ran Kang
Summary: This paper focuses on the energy decay rates of the viscoelastic wave equation with nonlinear time-varying delay, nonlinear damping at the boundary, and acoustic boundary conditions. General decay rate results are derived without imposing certain conditions and growth assumptions, using the multiplier method and properties of convex functions.
Article
Mathematics, Applied
Baowei Feng, Sun-Hye Park
Summary: This paper considers a viscoelastic equation with nonlinear distributed delay and nonlinear damping effects. A general decay criterion is established through the perturbed energy method and properties of convex functions, under general conditions that do not involve differential inequalities for the kernel function. The stability result of the wave equation with linear delay and linear damping is extended to the nonlinear case.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Mechanical
Rahul Mishra, Rajneesh Bhardwaj, Salil S. Kulkarni, Mark C. Thompson
Summary: This study investigates the effect of structural nonlinearity on the vortex-induced vibration of a rigid circular cylinder at a fixed mass ratio of m* = 2.546 and Re = 150. By changing the damping ratio and nonlinearity strength, the response of the cylinder to VIV is examined. Increasing system nonlinearity leads to richer spectral content in displacement and force signals, indicating a potential benefit for energy extraction applications.
JOURNAL OF FLUIDS AND STRUCTURES
(2021)
Article
Mechanics
Ismail Esen, Mohamed A. Eltaher, Alaa A. Abdelrahman
Summary: This article investigates the dynamic responses of symmetric and sigmoid FG Timoshenko beam subjected to moving mass. The study explores the influences of gradation type, gradation index, elastic foundation stiffnesses, inertia, and variable velocity of the moving mass on the dynamic response. The Hamilton principle and finite element method are used for modeling and solving the system.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Mechanics
Alaa A. Abdelrahman, Ismail Esen, Ahmed Amin Daikh, Mohamed A. Eltaher
Summary: In this study, a nonclassical size dependent model was developed to investigate the dynamic behavior of CNTs reinforced composite beams under moving load. The effects of various parameters such as elastic foundation parameters, volume fraction, CNTs configuration, nonclassical parameters, and moving load velocity were analyzed. The obtained results provide valuable insights for the design and manufacturing of composite CNTs beams.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Mechanics
M. A. Eltaher, R. A. Shanab, N. A. Mohamed
Summary: This article presents an enhanced mathematical model and closed-form solutions to explore the dynamic vibration response of perforated viscoelastic nanostructure thin/thick nanobeams with a size-dependent continuum model and different boundary conditions. The influences of viscoelastic parameter, nonlocal softening coefficient, supporting conditions, and filling/spacing ratio on the vibration response are analyzed.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Mechanics
Ahmed-Amine Daikh, Mohamed-Ouejdi Belarbi, Drai Ahmed, Mohamed Sid Ahmed Houari, Mehmet Avcar, Abdelouahed Tounsi, Mohamed A. Eltaher
Summary: In this study, a quasi-3D analytical plate theory is developed to explore the bending behavior of a new model of functionally graded plate structures (FGPSs). Different types of functionally graded nanoplates are examined, and the material gradation is described using cosine functions. The modified continuum nonlocal strain gradient theory is utilized, and the Galerkin method is used to solve the equilibrium equations under various boundary conditions. The results are compared to existing literature to confirm the accuracy and consistency of the analytical model. A comprehensive parametric study is also performed to determine the sensitivity of the bending response to various factors.
Article
Mathematics
Gamal S. S. Abdelhaffez, Ahmed Amine Daikh, Hussein A. A. Saleem, Mohamed A. A. Eltaher
Summary: A mathematical model of tricoated functionally graded materials (FGMs) is proposed in this paper to analyze analytically the buckling problem of coated FG spherical nanoshells resting on an orthotropic elastic foundation subjected to biaxial loads. The study considers the size-dependent and microstructure effects using the nonlocal strain gradient theory and applies the principle of virtual work to obtain equilibrium equations. The Galerkin technique is used to solve the obtained differential equations under various boundary conditions. A detailed parametric analysis is conducted to investigate the influence of different schemes of coated FGMs, gradient material distribution, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and orthotropic elastic foundation on the critical buckling loads.
Article
Mathematics
Ammar Melaibari, Salwa A. Mohamed, Amr E. Assie, Rabab A. Shanab, Mohamed A. Eltaher
Summary: This study analyzes the responses of beams and plates using middle surface (MS) and neutral surface (NS) formulations. It derives the relations between the displacement field variables on NS and MS, and defines modified boundary conditions for immovable simply supported plates. The study shows that the responses of BDFG plates based on MS and NS formulations are identical for clamped and movable simply supported boundary conditions. However, there are differences in the responses for immovable simply supported boundary conditions if fixation constraints at different planes are not properly treated.
Article
Mechanics
Ahmed Amine Daikh, Mohamed-Ouejdi Belarbi, Sattar Jedari Salami, Miloud Ladmek, Abdelkader Belkacem, Mohamed Sid Ahmed Houari, Hani Magdy Ahmed, Mohamed A. Eltaher
Summary: This paper presents a mathematical model to analyze the static bending response of laminated composite beams reinforced by functionally graded fibers and randomly oriented single-walled carbon nanotubes. Various schemes of material distributions and types of elastic foundations are considered, and the equilibrium equations are derived using the virtual work principle and solved numerically using Fourier series. A detailed parametric analysis is performed to investigate the impact of different distribution patterns, volume fractions, and elastic foundation parameters on the deflection of the composite beam.
Article
Engineering, Aerospace
Hao-Xuan Ding, M. A. Eltaher, Gui-Lin She
Summary: A nonlinear analysis is conducted to study the low-velocity impact behavior of a graphene platelets-reinforced metal foam cylindrical shell with spinning motion in a thermal environment. The effects of geometric imperfections, spinning velocity, boundary conditions, graphene platelets distribution patterns, foam distribution types, foam coefficient, graphene platelets weight fraction, temperature changes, impactor's radius and initial velocity, prestressing force, and damping coefficient on the impact problems are discussed in detail using the Runge-Kutta method.
AEROSPACE SCIENCE AND TECHNOLOGY
(2023)
Article
Engineering, Civil
Ahmed Amine Daikh, Mohamed-Ouejdi Belarbi, Abdelhak Khechai, Li Li, Samir Khatir, Alaa A. Abdelrahman, Mohamed A. Eltaher
Summary: The main objective of this research is to analytically analyze the static problem of a new model of functionally graded materials, known as the bi-coated FGM plate, and propose a Quasi-3D higher-order shear deformation plate theory. The model is validated and numerical results demonstrate the impact of hardcore and softcore distributions, gradation indices, and boundary conditions on static bending deflection and stresses of the bi-coated FGM plate.
ENGINEERING STRUCTURES
(2023)
Article
Engineering, Aerospace
Faisal Baakeel, Mohamed A. Eltaher, Muhammad Adnan Basha, Ammar Melibari, Alaa A. Abdelrhman
Summary: In this study, a numerical simulation model was developed to validate the results of the 3D-elastisity theory on laminated sandwich plates and examine the load response in terms of deflection and stresses. The model was also used to analyze the natural frequencies of different plate configurations. The developed model can be used for the design and study of novel bio-inspired composite structures.
ADVANCES IN AIRCRAFT AND SPACECRAFT SCIENCE
(2023)
Article
Engineering, Multidisciplinary
Norhan A. Mohamed, Rabab A. Shanab, Mohamed A. Eltaher, Alaa A. Abdelrahman
Summary: This manuscript presents a mathematical model and numerical solution to predict the vibration responses of nonlocal strain gradient perforated viscoelastic nanobeam under dynamic moving loads. The effects of micro-structure, size length scales, and viscoelastic damping are considered. The proposed method provides insights into the dynamic behavior of viscoelastic perforated nanobeams under moving load.
RESULTS IN ENGINEERING
(2023)
Article
Mechanics
Amr E. Assie, Salwa A. Mohamed, Rabab A. Shanab, Rasha M. Abo-bakr, Mohamed A. Eltaher
Summary: This article develops a mathematical model to study the static stability of bi-directional functionally graded porous unified plate and discusses the significant factors affecting the static stability and buckling loads through parametric studies.
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS
(2023)
Article
Mechanics
H. M. Abo-Bakr, R. M. Abo-Bakr, S. A. Mohamed, M. A. Eltaher
Summary: This study investigates multiobjective shape optimization of nonuniform microbeams made of functionally graded materials. The goal is to discover optimal shape functions and volume fraction distribution to maximize critical buckling load and fundamental frequency while minimizing mass and material cost. The study presents the static and dynamic behavior of axially functionally graded material nonuniform microbeam based on Timoshenko beam theory with modified couple stress theory. Multiobjective particle swarm optimization is applied to search for Pareto optimal solutions, considering shape functions parameters, types, and FGM power index as design variables. Several cases are studied to demonstrate the effectiveness of multiobjective optimal shape design of axially functionally graded beams.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
