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Helicity in dispersive fluid mechanics Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-16 S.L. Gavrilyuk, H. Gouin
By dispersive models of fluid mechanics we are referring to the Euler–Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is considered as a constraint. The corresponding Euler–Lagrange equations include, in particular, the van der Waals–Korteweg model of capillary fluids, the model of fluids
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Stochastic dynamics of a nonlinear vibration energy harvester subjected to a combined parametric and external random excitation: The distinct cases of Itô and Stratonovich stochastic integration Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-16 Subramanian Ramakrishnan, Aman Kumar Singh
The Stratronovich and Itô interpretations of a stochastic integral are mathematically consistent, distinct representations that yield contrasting response characteristics for stochastic dynamical systems subjected to multiplicative noise, such as parametric random excitation. The contrasting dynamics from the two interpretations currently remain unexplored in vibration energy harvester dynamics. We
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Nonlinear bending of a soft slab subjected to vertical compression: A continuum mechanics model Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-16 Lingling Chen, Tianyu Huang, Xinyu Xing, Shengyou Yang
The small bending behavior of linear elastic materials has been widespread in engineering in the history of mechanics. With the occurrence of soft materials, finite deformation bending is of great interest due to the high nonlinearity in large bending deformation. Previous theories primarily focus on the pure bending assumption, which is hard to achieve in practical bending experiments of soft materials
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Modeling and dynamic analysis of fractional order nonlinear viscoelastic rod Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-16 Meihua Zhang, Yajuan Hao, Yiming Chen, Gang Cheng, Thierry Barrière, Jingguo Qu
A fractional order constitutive behavior law is proposed in this paper to describe the viscoelasticity of the nonlinear rod. The fractional governing equation of the nonlinear viscoelastic rod is established. An effective algorithm based on the shifted Legendre polynomials is used to solve the governing equation directly in the time domain. The effectiveness of the proposed numerical algorithm is confirmed
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On fluid-saturated poro-hyperelastic rotating cylinder: A centrifugal filtration Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-15 M. Taghipour Darzinaghibi, A. Hassani, Sh. Rahmani, A.M. Goudarzi
One of the applications of porous materials is centrifugal filtration. This study develops the Lagrangian equations that govern a steady-state, fluid-saturated, poro-hyperelastic, axisymmetric rotating cylinder. The formulation assumes incompressible solid and Newtonian fluid constituents to address the filtration process. The differential scheme takes into account the impact of porosity on the reduction
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Development of the variation-of-elastic-energy-based virtual fields method for parameter identification of incompressible and compressible hyperelastic materials Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-14 Mingliang Jiang, Xinwei Du, Zhujiang Wang
The virtual fields method (VFM) has played a pivotal role in parameter identification of hyperelastic materials, spanning from rubbers to soft tissues. A key challenge in VFM lies in calculating the internal virtual work, which necessitates the computation of the stress and its conjugate virtual strain. In this study, we introduce a novel theoretical framework for VFM, which directly computes the internal
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Riemann problem for a general variable coefficient Burgers equation with time-dependent damping Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-13 Richard De la cruz, Yun-guang Lu, Xian-ting Wang
In this paper, we study the Riemann problem for a general variable coefficient Burgers equation with time-dependent damping. We use a nonlinear time-dependent viscosity equation with a similarity variable. Thus, when the viscosity goes to zero, we obtain Riemann solutions to the general variable coefficient Burgers equation with time-dependent damping. Moreover, we use the Lax–Friedrichs scheme to
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A novel nonlinear oscillator consisting torsional springs and rigid rods Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-09 Xinyi Huang, Qingjie Cao
In this paper, we propose an archetypal double-winged novel nonlinear oscillator composed of torsional springs and rigid rods which behaves smooth and discontinuous dynamics and a kind of special collision pendulum depending on the varying of a geometrical parameter. The system behaves complicated equilibrium bifurcations with different geometrical states, leading to a series of buckling phenomenon
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Mechanical and vibration characteristics investigation of the elastic ring squeeze film damper-rotor considering oil film sealing and leakage Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-08 Kai Sun, Zhong Luo, Lei Li, Fayong Wu, Haotian Hao
Elastic ring squeeze film damper (ERSFD) is extensively used in industrial rotating systems due to its excellent noise control and vibration suppression characteristics. However, the oil film sealing and leakage has a profound effect on the mechanical and vibration characteristics of the ERSFD and the ERSFD-rotor during operation. The sealing and leakage reduce the axial flow of the oil film, leading
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Moment Lyapunov exponent and stochastic stability of a vibro-impact system driven by non-Gaussian colored noise Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-08 Dongliang Hu, Ningping Guo, Kun Zhao, Juan L.G. Guirao, Huatao Chen
Vibro-impact phenomena are prevalent in practical engineering, making research on their stochastic dynamic characteristic of great practical significance. However, the research on stochastic stability and bifurcation of vibro-impact systems is still limited, especially the moment stability. In this paper, based on the th moment Lyapunov exponent, the stochastic stability of a vibro-impact system driven
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The subloading surface model in hyperelastic-based plasticity with time integration algorithms in intermediate and current configurations Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-07 Reza Toluei, Mahsa Kharazi
This paper introduces a novel application of subloading surface concept to effectively model the elastoplastic behavior of materials in the finite strain regime. The subloading surface approach allows for a smoother and more seamless transition from the elastic to the plastic region. Two time integration schemes are presented in this study, one in the intermediate configuration and the other in the
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Influences of external moment on the contact characteristics of angular contact ball bearings under combined loads Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-06 Wenbing Tu, Chenlu Liu, Hao Wang, Dengliang Hu, Wennian Yu
Angular contact ball bearings are widely used in rotating machinery. The external moment about the bearing lateral direction (i.e. the lateral moment) applied to a bearing affects the service life and performance of the bearings by influencing its internal contact characteristics. This work established a quasi-dynamic model of the ball bearing by comprehensively considering the inclination angle of
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Walking control of semi-passive robot via a modified Q-learning algorithm Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-06 Zhongkui Sun, Yining Zhou, Wei Xu, Yuexin Wang
The analysis and control of stability of passive biped robot has been the subject of an in-depth study because of its unique characteristics. This work gives a new perspective aiming at a force applied on foot of collision phase of walking process of passive robot, which is a completely new way of applying impulse force that is different from the previous. Therefore, the new equation has been derived
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Supercritical and subcritical aeroelastic behaviors of a three-dimensional wing coupled with a nonlinear energy sink Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-04 Chengde Huang, Guannan Zheng, Xueyuan Nie, Guowei Yang
This paper studies the flutter control of a three-dimensional wing using a nonlinear energy sink (NES), which has a purely cubic stiffness and a linear damper. The structural model is derived by Lagrange's equations and the aerodynamics is modeled using the auto regressive with exogenous input method. Both models are solved in a tightly coupling manner to obtain time domain results. Then, the structural
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Delayed resonator for complete vibration suppression of primary structures with nonlinear stiffness Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-03-02 Yifan Liu, Li Cheng
Delayed resonator (DR) is an active vibration absorber and is known for its complete vibration suppression capability by manipulating the feedback loop delay. This work aims to extend the DR concept from the widely considered linear applications to suppress vibrations on primary structures with nonlinear stiffness, based on the motivation that absolute linearity does not exist and nonlinearity is inherent
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Modelling of bifurcation of electro-elastic materials: Advantages and limits of the Stroh's compound matrix formulation for spherical shells Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-29 Ricardo Díaz-Calleja, Damian Ginestar, Pedro Llovera-Segovia, Alfredo Quijano-López
The instability and bifurcation phenomena in electro-elastic membranes and shells are receiving more attention because of their practical applications in actuators, sensors, robotics or in biological tissues used as surgical prosthetic replacements. The case where mechanical and electrical stress are applied is of particular importance since the material behaviour becomes more complex and difficult
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Nonlinear modeling of nanoscale interaction forces between atomic force microscope and carbon nanotubes Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-27 Moharam Habibnejad Korayem, Rouzbeh Nouhi Hefzabad
This paper introduces a non-linear non-classical model of nanoscale interaction forces between atomic force microscope and carbon nanotubes in a manipulation process. To accurately model the 3D manipulation process, Prandtl-Tomlinson friction model and the Hertz, JKR, and Lundberg contact mechanics theories were employed, taking into account the CNT geometry and manipulation conditions. The applied
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Nonlinear model updating of the rotor-bearing system by multi-harmonic balance method and analytical sensitivity derivation Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-26 Tianxu Zhu, Chaoping Zang, Xunkai Wei, Hu Chen, Hao Wang
Responses of the bearing system are usually predicted or tested, to analyze its nonlinear dynamic characteristics. However, responses predicted from the bearing model constructed by Hertz contact theory usually show differences with their tested counterparts, denoting the improper setting of the nonlinear contact parameters. It is compulsory to reduce such differences and obtain a precise bearing model
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Biomechanical stresses in a residually stressed idealized intervertebral disc Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-23 Gerhard A. Holzapfel, Ray W. Ogden
Intervertebral discs are soft biological tissues that have an important function in accommodating the movement of the spine during which the discs deform and act as shock absorbers to protect the spine from damage. Therefore, it is important to understand and model their mechanical properties to predict their response under various loading conditions. Towards this end, a simplified geometry of a single
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Energy of a non-linear viscoelastic model compatible with fractional relaxation Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-19 Andrea Giusti, Andrea Mentrelli, Tommaso Ruggeri
Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in Ruggeri (2024). This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the non-linear realm, provided that the viscous energy function is given. This work aims at establishing a possible constitutive law for the viscous energy such that the relaxation
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Cytokine-induced instabilities in a reaction–diffusion-chemotaxis model of Multiple Sclerosis: Bifurcation analysis and well-posedness Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-17 F. Gargano, M.C. Lombardo, R. Rizzo, M. Sammartino, V. Sciacca
In this paper, we develop a model for the evolution of the Multiple Sclerosis pathology that considers the modulatory influence of cytokines on the activation rate of macrophages. Our starting point is the reaction–diffusion-chemotaxis model proposed in 4, and we modify the macrophage activation mechanism. What triggers the immune cells into an active state is still debated in the medical literature
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Dynamics of accelerating and decelerating flows: A boundary layer examination with non-similar approach and convective boundary condition Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-16 Mojeed T. Akolade, Gabriel Samaila, Michael O. Oni, Abdulhakeem Yusuf, Peter Bukar Malgwi, Taiwo S. Yusuf, Yusuf O. Tijani
Moisture/air-flow over the aircraft wing and bonnet of a moving car in aerodynamical systems exhibit dynamic behavior characterized by accelerating and decelerating flows. These analysis is essential and applicable in various fields, including physics, engineering, and fluid mechanics. The present investigation aim to explore the dynamics of accelerating and decelerating flows within the framework
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Energy transfer for enhanced acoustic black hole effect through a cable-induced mechanical nonlinearity Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-15 Xiang Sun, Gaetan Kerschen, Li Cheng
Acoustic black hole (ABH) structures hold great promise for numerous engineering applications. Stemming from a power-lawed thickness decrease, bending waves are slowed down to produce wave compression and energy concentration, conducive to vibration/sound radiation control and energy harvesting. However, in existing linear studies, the ABH effect shows a deficiency at low frequencies, typically below
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Accuracy and temporal analysis of non-Newtonian models of blood in the computational FFR – Numerical implementation Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-15 M. Fernandes, L.C. Sousa, C.C. António, S.I.S. Pinto
Non-invasive assessment of stenosed coronary is a goal for clinical applications. Thus, engineering aligned with medicine has been the solution to solve this problem. This work, serving as a proof of concept, has the main goal to predict the non-invasive fractional flow reserve (FFR) in an atherosclerotic coronary artery. A 3-element Windkessel and Womersley models were used to model boundary conditions
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A novel concept of components system stiffness and stiffness model application for VSV adjustment mechanism Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-13 Jing Chang, Zhong Luo, Hongwei Zhang, Jiang Zhao, Qingkai Han, Fangjun Han
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Numerical continuation and stability of nonlinear systems with distributed delays: Application to fluid-induced impacts of tubes in cross-flow Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-13 Roberto Alcorta, Benoit Prabel, Sebastien Baguet, Philipe Piteau
Fluid–elastic instability is the main source of concern during the design of heat-exchanger tube bundles. The associated research has focused on the understanding of the physical mechanisms behind this phenomenon and the establishing of models capable of predicting its onset; also some concomitant work has been done to establish post-instability behaviour and to prevent from excessive wear in possible
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A new constitutive relation to describe the response of bones Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-12 J. Arumugam, P. Alagappan, J. Bird, M. Moreno, K.R. Rajagopal
Trabecular bone, a solid that has a heterogeneous porous structure, demonstrates nonlinear stress–strain relationship, even within the small strain region, when subject to stresses. It also exhibits different responses when subject to tension and compression. This study presents the development of an implicit constitutive relation between the stress and the linearized strain specifically tailored for
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Large twisting of non-circular cylinders in unconstrained elasticity Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-11 Federico Oyedeji Falope, Luca Lanzoni, Angelo Marcello Tarantino
This paper deals with the equilibrium problem of non-circular cylinders subjected to finite torsion. A three-dimensional kinematic model is formulated, where, in addition to the rigid rotation of the cross sections, the large twist of the cylinder also generates in- and out-of-plane pure deformation of the cross sections and the variation of the cylinder length. Following the semi-inverse approach
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Vehicle shimmy performance analysis using inerter-based suppression mechanism and considering steering linkage clearance Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-11 Yong Wang, Bingbing Xu, Wenlong Chen, Haodong Meng
Vehicle shimmy could occur in the running process when the wheel encounters external disturbance, which affects the vehicle safety and stability. Four types of passive inerter-based suppression mechanisms are proposed to enhance the vehicle shimmy performance, the steering linkage clearance is considered as the nonlinear factor existing in the vehicle system. The vehicle shimmy model using inerter-based
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Harmonic balance formulation for nonlinear wave-scattering clusters Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-10 Joshua R. Tempelman, Kathryn H. Matlack, Alexander F. Vakakis
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Catastrophic bifurcations in an aggregated carbon nanotube reinforced microbeam in the framework of the MCST Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-09 Ling Luo, Jing Xu, Hadi Arvin
Recently in engineering science, studies have been conducted in the field of using large-amplitude vibrations, especially when a system undergoes a superharmonic excitation. This is accomplished in order to determine the location and depth of a crack in a structure, promote the energy absorption process, and for system identification purposes. Some studies demonstrated that energy absorption can be
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A complete deterministic model of point contact mixed lubrication coupling dual-mode effects of surface fractal characteristics Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-09 Xin Yu, Yunyun Sun, Shijing Wu
For mixed lubrication under point contact, a complete model is proposed including two modes of direct effects of surface roughness on the oil film thickness and rough solid contact characteristic. A new method to describe initial oil film thickness is established based on the effects of the holistic interface roughness. The real contact area of the interface is directly obtained by the sum of all solid
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Wave propagation and multi-stopband behavior of metamaterial lattices with nonlinear locally resonant membranes Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-08 Yichang Shen, Walter Lacarbonara
Wave propagation and stopband behavior in square lattices hosting nonlinear resonators made of suspended piezoelectric membranes with a central mass are investigated by treating asymptotically the wave propagation equations obtained via a projection method combined with the Floquet-Bloch theorem. The metamaterial membrane resonators made of a piezoelectric polymer are designed to exploit the piezoelectric
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An approach to the micro-strain distribution inside nanoparticle structure Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-07 A.S. Abdel-Rahman, Youssef A. Sabry
Williamson-Hall, Stocks-Wilson, Scherrer, Halder-Wagner, and Size-Strain Plot (SSP) methods are used essentially to ensure the material particle size falls at the nano-level. They treat the broadening in the XRD peak as a sum of Gauss and Lorentz diffraction probability functions. In this work, an approach to the microstrain distribution is presented as a strain distribution (SD) model, assuming a
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An enhanced magnetically coupled bistable energy harvester with a spring oscillator: A numerical and experimental study Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-05 Qiubo Jiang, Chuanyun Yu, Qiang Gao, Ning Zhang, Beibei Sun
Introducing the dynamic effect of magnetic coupling to a conventional bistable energy harvester is likely to further enhance its working bandwidth and output power. In this paper, a novel two-degree-of-freedom magnetically coupled bistable energy harvester employing an auxiliary spring oscillator is proposed. The governing equations of the system are first established based on the magnetic dipole model
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Indentation of sandwich beams: Comparison of Vlasov, Winkler, and shear theories with composite surfaces reinforced by CNTs and ANN model Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-30 Aseel j. Mohammed, Hatam k. Kadhom, Mohammed Al-Bahrani, HassabAlla M.A. Mahmoud
The use of sandwich structures has spread to a wide range of fields today. As a result of their thin top and low stiffness, sandwich beams are very susceptible to local loads. One practical solution to increase the sandwich structure's indentation resistance is to add bending strength to the top. The structural properties of carbon nanotubes make them well-suited for use in polymer matrixes; their
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Elastic bending and transverse compression of a thin plate with density-dependent Young’s modulus Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-04 Barış Erbaş, Julius Kaplunov, Kumbakonam R. Rajagopal
The equilibrium equation governing the plane strain static problem for a thin elastic layer is studied using asymptotic analysis for a material with generalized Young’s modulus weakly dependent on the mass density. Within the context of the adopted scaling, the effect of a physical nonlinearity arises at the second order along with shear deformation and other linear phenomena. Refined equations for
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Motion of liquid particles in the field of 1:1 resonance nonlinear wave structures in a fluid beneath an ice cover Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-03 A.T. Il’ichev, A.S. Savin, A. Yu Shashkov
A fluid layer of finite depth described by Euler’s equations is considered. The ice cover is modeled by a geometrically non-linear elastic Kirchhoff–Love plate. The trajectories of liquid particles under the ice cover are found in the field of a nonlinear surface traveling waves of small, but finite amplitude, indicating the focusing and defocusing of nonlinear carrier wave, namely, a solitary wave
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Micro-mechanical interpretation of the non-linear tensile response of structured rods. Experiments on prototyped Gedankenmodelle with wavy sub-rods and application to Carbon NanoTube fibers Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-03 Claudio Boni, Gianni Royer-Carfagni
In order to demonstrate the wide range of inelastic non-linear tensile responses observed in structured fibers of various types, an ideal phenomenological model (Gedankenmodell) is theoretically analyzed, prototyped and tested. This consists in a rod made of a regular ensemble of sticks in a brickwork-like three-dimensional grid, hooped by elastic bands. The stick lateral faces are wavy surfaces in
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A constitutive model of nanoporous NiTi shape memory alloys considering tensile-compressive asymmetry, grain size and porosity Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-30 Bingfei Liu, Jiahe Dong
A constitutive model of the macroscopic behaviors of nanoporous Shape Memory Alloys (SMAs) is developed, and the effects of tensile-compressive asymmetry, grain size, and porosity are all considered because the influences of these factors cannot be ignored. A finite-volume, three-phase micromechanical model that contains the grain boundary phase, grain-core phase, and uniformly distributed pores is
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Analytical study on transverse behaviour of love-type waves in a corrugated cylindrical composite structure: A perturbation theory Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-30 Moumita Mahanty, Pulkit Kumar, Abhishek Kumar Singh, Amares Chattopadhyay
The current study focuses on the analysis of propagation characteristics of Love-type waves in a corrugated composite cylindrical structure, with corrugation at the lateral surface. The corrugated cylindrical structure is composed of two regions of functional gradient fiber-reinforced material media with distinct radii. The amplitude of corrugation at the outermost lateral surface is assumed to be
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Analytical and computational study of compressible neo-Hookean model using VAM for two types of global warping constraints Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-02 Shravan Kumar Bhadoria, Ramesh Gupta Burela
The current work focuses on the nonlinear analysis of the compressible neo-Hookean plates using the Variational Asymptotic Method (VAM), with particular emphasis on the two types of global warping constraints. The two sets of warping constraints used are: Leverage Global Rotation Constraint (LGRC) and Derivative Global Rotation Constraint (DGRC). The aim is to investigate the effect of these constraints
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Stability of nonlinear normal modes in the system of coupled pendulums in a magnetic field Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-02 Yulia E. Surganova, Yuri V. Mikhlin
The dynamics of the system of two elastically connected pendulums located in a magnetic field is considered when the masses of the pendulums differ significantly. In this case, both coupled and localized nonlinear normal modes (NNMs) can be observed. Such modes are constructed by the multiple scales method. The stability of NNMs is studied using a numerical-analytical procedure, which is related to
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Vibration characterization of a planar multi-degree-of-freedom industrial machine Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-01 Jingxuan Wang, Senkai Mo, Guo Yao
This paper analyzes the dynamic character of a planar multi-degree-of-freedom industrial machine using an industrial robot as a reference model. A nonlinear dynamics model of a multi-body structure including the end effector, base and the manipulator is established using the Lagrange's principle. The validity was verified by ADAMS simulation with the established dynamic model. Focusing on the low-frequency
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A nonlinear approach to viscoelasticity via Rational Extended Thermodynamics Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-01 Tommaso Ruggeri
In the one-dimensional isothermal case, we introduce a simple model of nonlinear viscoelasticity within the Rational Extended Thermodynamics (RET) framework. The differential system is entirely determined by the universal principles of RET, exhibiting symmetric hyperbolic form and ensuring the existence of smooth solutions for appropriately small initial data. In the linear case, the equation for viscous
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A consistent transversely-isotropic hyper-viscoelastic model: Finite element implementation and mechanical characterization of biological tissues Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-01 Manu Hegde, K. Karthik, Vishwanath Managuli, Subraya Krishna Bhat
Soft tissues like skeletal muscles, ligaments and tendons exhibit transversely-isotropic hyper-viscoelastic (VE) behavior. Simulating the mechanical response of such soft tissues under various types of loading scenario requires accurate constitutive models. Several models have been proposed towards this goal. Although these models successfully capture the deformations under different kinds of loadings
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Modeling the mechanical behavior of cement stabilized macadam with defects based on particle flow theory Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-01 Guofang Zhao, Xueke Hou, Xinqiang Wang, Yongkang Yan, Bo Qiao, Zhanyou Yan
The material of cement stabilized macadam is a discontinuous, inhomogeneous and quasi-brittle material. When it is locally damaged, it will be very limited to analyze the crack propagation and stress transfer with the theory of homogeneity and continuum. In order to study the meso-mechanical properties of cement stabilized macadam, a discrete element model of cement stabilized macadam was constructed
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Intermodal targeted energy transfer (IMTET) in a model with multi-stability Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-02-01 O.V. Gendelman
The paper addresses the phenomenon of intermodal targeted energy transfer (IMTET), i.e., an intensive redistribution of the oscillatory energy among the system modes beyond any resonance conditions. The IMTET allows substantial mitigation of the external excitations through more efficient use of the internal damping capabilities of the system. Contrary to previously explored designs based on impacts
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New nonlinear models of dynamic longitudinal deformation of a viscoelastic rod Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-29 Yu A. Chirkunov, M. Yu Chirkunov
In this paper we study a general model of dynamic longitudinal deformation of a viscoelastic rod with a nonlinear dependence of the stress on the strain and on the strain rate. This model is given by a nonlinear differential equation with partial derivatives of the third order. A group classification of this model which depends on two arbitrary functions is carried out. Six basic models are obtained
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Branching of axial compression histories of solid cylinders undergoing thermo-chemo-mechanical changes Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-18 A. Wineman
This work considers the uniaxial compressive creep of a solid elastomeric circular cylinder under a fixed dead load as it undergoes time dependent and temperature dependent changes in its macromolecular structure. The changes occur at temperatures exceeding 100 °C and consist of chemical scission of macromolecular network junctions and their re-crosslinking to form new networks in new reference configurations
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Vibration stability and bifurcation analysis of spur gear systems based on time-varying backlash and random load Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-18 Hongtai Shi, Weitao Chen, Jingbin Li, Zhipeng Wang, Long Jiang
Gear backlash and random load affect the stability of gear transmission, which are the main factors causing meshing impact. This study presents the establishment of a six-degree-of-freedom model for the spur gear system, employing the lumped parameter theory and D'Alembert's principle. The model comprehensively incorporates the effects of time-varying meshing stiffness (TVMS), static transmission error
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An extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-11 Ilias G. Mavromatis, Ioannis A. Kougioumtzoglou, Pol D. Spanos
An extrapolation approach within the Wiener path integral (WPI) technique is developed for determining the stochastic response of diverse nonlinear dynamical systems. Specifically, the WPI technique treats the system response joint transition probability density function (PDF) as a functional integral over the space of all possible paths connecting the initial and the final states of the response vector
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Single input-single output coupled resonators with nonlinear self-excitation for multiple mass sensing Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-11 Hiroshi Yabuno, Mai Zhang, Takumi Furihata, Walter Lacarbonara
A theoretical formulation and an experimental investigation into multiple mass sensing using self-excited coupled resonators is discussed. To construct a single input-single output (SISO) system, multiple resonators with different natural frequencies (frequency-mistuned resonators) are connected to a common shuttle mass, with resonators individually functionalized to absorb a specific analyte/mass
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Weakly nonlinear stability analysis of non-isothermal parallel flow in a vertical porous annulus Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-07 Arshan Khan, P. Bera
The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial
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Nonlinear characteristics of floating involute spline coupling in a hydraulic disc brake with inner hub rim crack propagation Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-06 Kun Yue, Liming Wang, Hai Lan, Wennian Yu, Yimin Shao, Zaigang Chen
Spline coupling is the key component in a hydraulic disc brake (HDB) system, which has been widely used in many high power density industrial machinery. Crack failure, as one of the most widespread and dangerous spline defects, directly threatens the operating safety of HDB system. To this end, a dynamic modelling method for floating involute spline coupling system is presented to study the nonlinear
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Nonlinear periodic response of viscoelastic laminated composite plates using shooting technique Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-06 Deepak Kumar, Badri Prasad Patel
The nonlinear periodic response of viscoelastic laminated composite plates subjected to harmonic excitation is carried out in time domain using the generalized Maxwell model in the form of a Boltzmann integral. The integral form of the viscoelastic constitutive relation is converted to the incremental form for the finite element formulation based on the Reissner–Mindlin plate theory incorporating von
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On the number of mechanical configurations for nonlinear stiffness systems designed based on a linear spring with a nonlinear boundary Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2024-01-05 Qiangqiang Li, Qingjie Cao
In this paper, we present an integrated method for designing nonlinear stiffness systems based on a general spring-boundary model (GSBM) to study the number of mechanical configurations for nonlinear stiffness systems designed by the combination of a linear spring with a nonlinear boundary. GSBM consists of a lumped mass, a special-shaped track, a roller rolling in the track and a general linear spring
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Nonparametric identification of a MEMS resonator actuated by levitation forces Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2023-12-30 Mohammed Abdel Razzaq, Rodrigo T. Rocha, Yu Tian, Shahrzad Towfighian, Sami F. Masri, Mohammad I. Younis
This work presents nonparametric identification of a Micro-Electro-Mechanical Systems (MEMS) beam subjected to a non-classical nonlinear electrostatic (levitation) force. The approach is based on the Restoring Force Surface method and the Chebyshev polynomials. The study examines the main challenges associated with the used approach as applied to small-scale systems, such as the inability to measure
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Vibration of solid and thin-walled slender structures made of soft materials by high-order beam finite elements Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2023-12-31 A. Pagani, P. Chiaia, E. Carrera
In this work, high-order beam (1D) finite element models for the modal analysis of structures made of compressible and nearly-incompressible hyperelastic soft materials are presented in the well-established framework of Carrera Unified Formulation (CUF). In this investigation, the modal behavior of soft structures subjected to progressively increasing loads can be correctly predicted by higher-order
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A nonlinear dynamic approach for analyzing dynamic stiffness of ball bearings at different raceway diameters and guiding clearances Int. J. Non-Linear Mech. (IF 3.2) Pub Date : 2023-12-30 Song Deng, Jinshuai Shen, Can Yang
In this work, the stiffness matrix model is integrated into the dynamic model of ball bearings, in which the dynamic forces real-timely affect the stiffness calculation to form the dynamic stiffness, which is a novel solution for the dynamic performance analysis of ball bearings under different loads, assemblies and bearing structures. Then, the main influencing factors for the magnitude of bearing