Article
Mathematics, Applied
Yanqing Wang, Han Wu, Fengliu Yang, Quan Wang
Summary: An efficient method has been developed to investigate the vibration and stability of moving plates immersed in fluid using the Kirchhoff plate theory and finite element method. The study shows that the natural frequency of the submersed moving plates decreases with an increase in the axial speed, leading to a coupling phenomenon between the first- and second-order modes. Additionally, the natural frequency decreases with an increase in fluid density or immersion level, and significantly drops if the plate is located near a rigid wall.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2021)
Article
Environmental Sciences
Yangyang Luo, Dapeng Zhang
Summary: This paper comprehensively studies the linear and non-linear dynamics of a slender and uniform pipe conveying pulsating fluid while moving axially in an incompressible fluid. The vibration equations of the system are established and solved numerically, and the linear and non-linear responses of the system are analyzed. The influence of key system parameters on non-linear responses is also investigated.
FRONTIERS IN MARINE SCIENCE
(2022)
Article
Automation & Control Systems
Yi Cheng, Yuhu Wu, Bao-Zhu Guo
Summary: This article discusses boundary stabilization for a nonlinear axially moving beam under boundary velocity feedback controls within the framework of absolute stability. By utilizing the Faedo-Galerkin approximation and priori estimates, the exponential stability of the closed-loop system is successfully established.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Mathematics, Applied
Han Wu, Feng Liu Yang, Yan Qing Wang
Summary: The study presents a semi-analytical method to analyze the free vibration of an axially traveling plate partially submerged in a viscous and orthogonally flowing liquid. Results show that as the thickness of the plate increases, the effect of liquid viscosity on the natural frequencies of the plate weakens. The magnitude of the liquid viscosity effect is positively correlated with the distance between the plate and rigid wall, and the width of the liquid domain. Additionally, the plate is more likely to reach critical speed when the orthogonal liquid velocity is higher, and liquid viscosity plays a significant role in the vibrational behavior of the immersed traveling plate when the liquid velocity is relatively large.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2021)
Article
Automation & Control Systems
Bo Li, Zohreh Eskandari
Summary: This paper investigates a discrete-time seasonally forced SIR epidemic model for different types of bifurcations. The existence of different types of bifurcations in the model is proven analytically and numerically. The study includes one and two parameters bifurcations, as well as flip, Neimark-Sacker, and strong resonances bifurcations. The obtained results are verified through graphical representations.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Construction & Building Technology
Zhe Zhang, Hongxiang Yang, Zhongjin Guo, Lili Zhu, Weiyan Liu
Summary: This paper examines the nonlinear vibrations of an axially moving viscoelastic beam under transverse harmonic excitation. The motion equation of the viscoelastic beam is discretized into a Duffing system with nonlinear fractional derivative using Galerkin's method. The viscoelasticity of the moving beam is described by the fractional Kelvin-Voigt model based on the Caputo definition. The primary resonance is analytically investigated using the averaging method. A parametric study is conducted to display the influences of the fractional order and viscosity coefficient on steady-state responses by analyzing response curves. The validity of the study is confirmed through comparisons between analytical solutions and numerical ones, with stability determined by the Routh-Hurwitz criterion. It is found that changing the viscosity of the system can suppress undesirable responses.
ADVANCES IN CIVIL ENGINEERING
(2022)
Article
Mechanics
Zhihua Wu, Yimin Zhang, Guo Yao
Summary: This paper investigates the natural frequency and stability of axially moving functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular thin plates. The study derives the equations of motion for the plates and analyzes the variations of natural frequencies with axial moving velocity, as well as the stability of the plates. The effects of various parameters on the natural frequencies and stability are discussed.
Article
Automation & Control Systems
Yi Cheng, Yuhu Wu, Bao-Zhu Guo
Summary: This paper investigates absolute stability for an axially moving Kirchhoff beam under nonlinear boundary feedback controls, proposing an effective controller demonstrated through theoretical analysis and numerical simulations. The well-posedness of the resulting closed-loop system is established using an approximation method, and the exponential stability of the closed-loop is developed through the integral-type multiplier method.
Article
Mathematics, Applied
Meng Su, Lizhi Niu, Wenting Zhang, Zhicong Ren, Wei Xu
Summary: This paper introduces a transformation method for general bilateral rigid vibro-impact systems, inspired by the Ivanov transformation technique, which can convert the impact system to a system without impact terms. This method can be directly applied to common vibro-impact systems, ensuring good continuity of the system.
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
Mechanics
Alireza Asnafi
Summary: This paper studied the critical velocity of chaos for an axially moving viscoelastic string under noisy axial tension using an analytic approach. A Wiener process non-Gaussian bonded noise was used to model the noisy fluctuations of axial force, and the Melnikov-based criterion was chosen to obtain the boundaries of chaotic behavior and the critical velocity. It was found that the unstable area and critical velocity are dependent on the bandwidth of the noise, and some results were validated using Poincare maps to ensure the correctness of the method.
Article
Engineering, Aerospace
Feng Liu Yang, Yan Qing Wang, Yunfei Liu
Summary: This paper focuses on the low-velocity impact response of axially moving graphene platelet reinforced metal foam plates. It investigates the effect of foam distribution, graphene platelet patterns, weight fraction, foam coefficient, plate speed, impactor mass, and impact velocity on the impact response of axially moving graphene platelet reinforced metal foam plates.
AEROSPACE SCIENCE AND TECHNOLOGY
(2022)
Article
Engineering, Electrical & Electronic
Man Zhang, Ji-Xian Dong
Summary: The transverse vibration of axially moving trapezoidal plates was investigated by establishing a differential equation and calculating the complex frequency curve to analyze instability types. The results showed the presence of two main instability types: divergence and flutter, with different modal orders related to the parameters of the trapezoidal plate.
JOURNAL OF NANOELECTRONICS AND OPTOELECTRONICS
(2021)
Article
Engineering, Civil
Jin-Peng Song, Gui-Lin She
Summary: This paper investigates the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. The motion equations are derived based on nonlinear Kirchhoff plate theory, and the Galerkin method is used to obtain the nonlinear ordinary differential control equation. The resonance response of GPLRMF plates is obtained by perturbation method, and the effects of various factors on the resonance behavior are investigated.
STRUCTURAL ENGINEERING AND MECHANICS
(2023)
Article
Mathematics, Applied
Abdelkarim Kelleche, Nasser Eddine Tatar
Summary: This paper focuses on stabilizing a nonlinear axially moving string through adaptive boundary control. Using the Crandall-Liggett theorem in the framework of nonlinear semigroup theory, the existence and uniqueness of a solution of the closed loop system are addressed. The control is constructed through low-gain adaptive velocity feedback and it is shown to exponentially stabilize the closed loop system.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2021)
Article
Engineering, Multidisciplinary
Moaz Sibtain, Kelly Yee, Oscar Zi Shao Ong, Mergen H. Ghayesh, Marco Amabili
Summary: This study investigates the coupled dynamics of a multi-layered microbeam with size-dependent effects. It is found that increasing the power term constant of the material grading or the value of the localized mass imperfection leads to a decrease in the natural frequencies of the microbeam, while increasing the length-scale parameter results in an increase in the natural frequencies of transverse modes.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mechanics
Amit Yadav, Marco Amabili, Sarat Kumar Panda, Tanish Dey
Summary: This paper presents the dynamic instability and nonlinear vibration analysis of fluid-filled laminated composite circular cylindrical shells subjected to harmonic axial loading. The mathematical model is prepared using higher-order shear deformation theory, and the nonlinear responses are computed using the pseudo-arclength continuation method and the incremental harmonic balance method.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Review
Mechanics
Hossein B. Khaniki, Mergen H. Ghayesh, Rey Chin, Marco Amabili
Summary: Soft structures have the ability to undergo reversible large strains and deformations under different types of loadings. Nonlinear elastic models have been developed to accurately model these large deformations and strains, as linear elastic models have their limitations. Among these models, hyperelastic strain energy density models provide a good fit for the mechanical behavior of biological tissues. With advancements in biomechanical devices, it is important to review the latest works in this field, as in-vivo and in-vitro studies have significantly increased in the past few years. Additionally, accurate modeling of soft structures is crucial for various applications such as prosthetics, soft robots, and wearing devices.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2023)
Article
Engineering, Biomedical
Ivan D. Breslavsky, Marco Amabili
Summary: The authors found that a stress-strain curve for uniaxial tension of an aortic intact wall cannot be obtained by combining the strain energy functions of the three individual aortic layers. However, it is possible to fit the intact wall experimental curves with the combination of the strain energy functions of the three individual layers if residual strains are added. By varying these parameters, it is possible to find a solution with the combined responses of the individual layers matching the experimental stress-strain curves of the intact wall.
JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS
(2023)
Article
Materials Science, Multidisciplinary
Stanislas Le Guisquet, Marco Amabili
Summary: This study characterizes the viscoelastic properties of a hydrogel in sol-gel transition by measuring the vibration response of a rigid circular cylindrical container's bottom silicone membrane. A finite-element numerical model was built for identification of the hydrogel's storage shear modulus and loss tangent. It was found that membrane vibration can be used to characterize the viscoelastic mechanical properties of a hydrogel in sol-gel transition in a more versatile way.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Engineering, Mechanical
Marco Amabili
Summary: This study investigates whether it is necessary to satisfy the natural boundary conditions in nonlinear vibrations of rectangular plates. Accurate expansions of plate displacements and nonlinear damping are introduced to satisfy the natural boundary conditions by energy minimization and achieve results that agree with experiments.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Engineering, Mechanical
Prabakaran Balasubramanian, Giovanni Ferrari, Celia Hameury, Tarcisio M. P. Silva, Abdulaziz Buabdulla, Marco Amabili
Summary: Positive Position Feedback (PPF) is a leading algorithm for actively suppressing mechanical vibrations in thin-walled structures. This study proposes a method for estimating participation matrices based on experimental measurements, simplifying the design of PPF controls and eliminating the need for electromechanical modeling. This opens up possibilities for the widespread use of Active Vibration Control (AVC) techniques.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Engineering, Biomedical
Nathan Jen, Jake Hadfield, Guilherme M. Bessa, Marco Amabili, David S. Nobes, Hyun-Joong Chung
Summary: Regulating pulsatile flow is important for optimal separation and mixing, heat transfer, and maintaining homeostasis. Inspired by the human aorta, researchers developed a bio-inspired approach using elastomeric tubes with fabric jackets to regulate pulsatile flow. Evaluation in a mock-circulatory flow loop showed effective flow regulation, and the tunable design may be applicable for tubing systems requiring passive self-regulation of pulsatile flow.
JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS
(2023)
Review
Engineering, Biomedical
Xiaochen Wang, Harry J. Carpenter, Mergen H. Ghayesh, Andrei Kotousov, Anthony C. Zander, Marco Amabili, Peter J. Psaltis
Summary: Large aortic aneurysm and acute and chronic aortic dissection require surgery, but a clear understanding of the mechanisms leading to aortic failure and better risk assessment is still lacking. Biomechanical analysis of the aorta can provide valuable insights into aortic abnormalities and help clinicians stratify patient risks. This review categorizes existing studies into theoretical, in vivo, experimental, and combined investigations to provide a comprehensive overview of the current state-of-the-art in aortic biomechanics and stimulate further research. Combining experimental and computational approaches may lead to more accurate risk prediction for the aortic system.
JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS
(2023)
Article
Engineering, Mechanical
Celia Hameury, Giovanni Ferrari, Abdulaziz Buabdulla, Tarcisio M. P. Silva, Prabakaran Balasubramanian, Giulio Franchini, Marco Amabili
Summary: Positive Position Feedback (PPF) is an active vibration control algorithm commonly used for vibration reduction in thin-walled structures. Fractional order PPF (FOPPF) is a recent development that improves the spillover characteristics through the use of fractional calculus. However, current literature on FOPPF lacks consideration for multiple-input-multiple-output (MIMO) systems and lacks experimental work. To address this gap, a MIMO FOPPF control architecture was tested numerically and experimentally on a cantilever composite sandwich beam.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Engineering, Mechanical
Flavio Augusto Xavier Carneiro Pinho, Marco Amabili, Zenon Jose Guzman Nunez Del Prado, Frederico Martins Alves da Silva
Summary: This work applies Sanders-Koiter's nonlinear shell theory to study the nonlinear moderate-amplitude vibrations of doubly curved shells. The nonlinear equations of motion are determined using two different approximations of the strain-displacement relations for shallow and non-shallow shells. The backbone curves are obtained using a combination of the multiple shooting method and an Euler-Newtonian predictor-corrector continuation algorithm. The mode influence of selected points on the backbone curves is analyzed, revealing internal resonances and changes in the dynamic behavior of shells undergoing moderate-amplitude vibrations.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Brian Painter, Marco Amabili
Summary: In this study, the non-planar vibration response of a beam with initial geometric imperfections is investigated using a geometrically nonlinear beam model. The experimental data shows good agreement with the beam model response around the resonant frequency of the first bending mode.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Civil
B. Kh. Eshmatov, R. A. Abdikarimov, M. Amabili, N. I. Vatin
Summary: This work focuses on the study of an anisotropic viscoelastic fiber-reinforced simply supported rectangular plate. By considering the direction of the fibers, the dynamic behavior of the plate and the dynamic stability problem of anisotropic reinforced plates were investigated. The results highlight the importance of considering the viscoelastic properties of the material when solving dynamic problems of anisotropic reinforced plates made of composite materials.
MAGAZINE OF CIVIL ENGINEERING
(2023)
Article
Acoustics
M. Amabili, H. R. Moghaddasi
Summary: Studies on nonlinear vibrations of circular cylindrical shells containing fluid have focused mostly on thin simply supported shells, leaving a lack of research on the behavior of thick cantilevered shells with shear and thickness deformations. This article presents, for the first time, models of thin and thick circular cylindrical shells with clamped-free boundary conditions based on the third-order shear deformation theory with thickness stretch. The derived governing differential equations describe the shell-fluid interaction. Results show that increasing the fluid level and decreasing the shell thickness in linear free vibration analysis significantly raise the fluid free-surface wave elevation, limiting the application of linear sloshing theory. The presence of the fluid changes the nonlinear behavior from softening to hardening, and intensifies the shell thickness deformation. Additionally, the contained liquid reduces the circumferential dynamic contraction caused by large amplitude vibrations.
JOURNAL OF SOUND AND VIBRATION
(2024)
Article
Engineering, Biomedical
Marco Amabili, Giulio Franchini, Meisam Asgari, Francesco Giovanniello, Mergen H. Ghayesh, Ivan D. Breslavsky
Summary: This study investigated the mechanical characteristics of an aorta affected by Klippel-Trenaunay syndrome. The results showed reduced stiffness and decreased response to vasoactive agents in the circumferential direction.
JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS
(2023)
Article
Mechanics
E. Mubai, D. P. Mason
Summary: The two-dimensional turbulent thermal classical far wake is investigated in this study. The turbulence is described using the Boussinesq hypothesis for Reynolds stresses and Prandtl's mixing length model for eddy viscosity and eddy thermal conductivity. Two conservation laws are derived for the thermal boundary layer equations using the multiplier method, and two conserved quantities are obtained from the conserved vectors and boundary conditions. Lie point symmetry associated with the momentum and thermal conserved vectors is derived, showing that the momentum and thermal mixing lengths are proportional. An invariant solution is obtained numerically using a shooting method, and analytically when v = 0, kappa = 0.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Daniel J. Arrigo, Travis C. Chism
Summary: This paper investigates the governing equations for plane stress deformations of isotropic incompressible hyperelastic materials. The authors previously discovered a linearization method for the plane strain case of the Varga material, and in this paper, they further demonstrate that the governing equations for the plane stress case can also be linearized.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
A. P. Chugainova, R. R. Polekhina
Summary: This article numerically investigates the conditions for the decay of a nonlinear wave into a system of waves traveling at different velocities in a viscoelastic weakly anisotropic medium. Solutions of a hyperbolic system of equations are studied in the region of nonuniqueness of parameters, where a solution to the Riemann problem can be constructed with both a single wave and a system of waves corresponding to the same initial data.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Yu. N. Grigoriev, E. I. Kaptsov, S. V. Meleshko
Summary: This paper studies the mathematical properties of gasdynamics equations with thermochemical nonequilibrium and provides solutions for two different models. The results show that the solutions to the modified system of equations are physically consistent and can describe the effects of thermochemical nonequilibrium.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Y. Hao, X. Y. Guo, Y. B. Fu
Summary: This paper investigates the nonlinear stochastic dynamic response of a three-degree-of-freedom(3-DOF) airfoil with high substructural nonlinearity under vertical turbulent disturbances. The effects of parameters such as the incoming velocity, turbulence scale and intensity on the stochastic dynamics behavior of the system are clarified.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
T. Flament, J. -F. Deu, A. Placzek, M. Balmaseda, D. -M. Tran
Summary: This paper focuses on the numerical computation of vibrations in geometrically nonlinear structures induced by aeroelastic coupling with fluid flow using reduced order models (ROM). The proposed ROM formulation utilizes projection on a basis of reduced dimension enhanced with dual modes, allowing for the accurate capture of dynamic characteristics and adaptation to unsteady aerodynamic loads. The limitations of the classical Implicit Condensation method are highlighted, while the ROM proposed overcomes these limitations and accurately captures the dynamics.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Sidhartha Sankar Roy, Kishore Chandra Biswal
Summary: This study investigates the non-linear slosh dynamics of a sloped wall tank with a bottom-mounted object under seismic excitation. The potential flow theory is used to model the liquid domain using a mixed Eulerian-Lagrangian method. The study successfully quantifies the non-linear seismic response of the tank and the influence of the internal object on the hydrodynamic behavior. A parametric investigation is conducted by altering the object's height. Comparison with linear analysis justifies the necessity of non-linear analysis. The developed non-linear finite element model is found to be more effective and can be used in designing structure-coupled sloped wall TLDs.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Kapil Dev, Om P. Suthar
Summary: This study presents stability analyses of thermosolutal convection in a Newtonian fluid-saturated Darcy porous layer under non-uniform inclined heating, considering the presence of the Soret effect. The results reveal the destabilizing effect of the solutal Darcy-Rayleigh number and Lewis number on the system's stability, while the Soret parameter has a non-monotonic effect depending on the horizontal Rayleigh number.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Sandhya Maurya, Dia Zeidan, Manoj Pandey
Summary: This paper investigates a two-phase mass flow model governed by gravity, which involves solid particles and a viscous fluid. By utilizing the Lie symmetries admitted by the system, similarity solutions for the (2+1)-dimensional two-phase mass flow model are obtained. Through analytical solutions and numerical analysis, the physical behaviors of the resulting systems are successfully analyzed.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Longfei Tan, Wei Zhang, Zixun Wang, Bowen Hou, Wei Sun
Summary: This study investigates the factors influencing the stiffness variation characteristics of a bolted joint during service, including macro deviation, micro-topography, and hysteresis characteristics. Through experiments and finite element modeling analysis, it is found that macro deviations and micro-topography on the bearing surface can cause irregular dynamic changes in the stiffness of the bolted joint, significantly affecting the dynamic/static response of the entire structure.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
Article
Mechanics
Yu Xiao, Ze-Qi Lu, Nan Wu
Summary: This study investigates the characteristics of a magnet-engaged nonlinear piezoelectric energy generator stimulated by friction-induced vibration (FIV) in two distinct design configurations (in parallel and in-series). The results indicate that factors such as decay factor, dynamic friction coefficient, static friction coefficient, and normal force have an effect on the stability of the system and the generation of FIV. The in-parallel systems exhibit a higher charging power within the same operating range, while the in-series systems are more likely to excite FIV with a wider operating range.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2024)
