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Amplitude region for triggering frequency locking in internal resonance response of two nonlinearly coupled micro-resonators Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-16 Xuefeng Wang; Ronghua Huan; Weiqiu Zhu; Zhan Shi; Xueyong Wei; Guoqiang Cai
In this paper, the internal resonance response of two nonlinearly coupled micro beams with frequency ratio approximately 1:3 is investigated and an interesting phenomenon called frequency locking is observed experimentally. A nonlinear dynamic model of the coupled system is established and solved using multi scale method to explain this phenomenon, and the amplitude region for triggering frequency
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A nonlinear model of thick shells for large-amplitude vibrations Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-19 Hamid Reza Moghaddasi; Mojtaba Azhari; Mohammad Mehdi Saadatpour; Saeid Sarrami-Foroushani
Nonlinear shell modeling is always accompanied by simplifying assumptions on some computational parameters. In the latest nonlinear model based on eight parameters, that considers the displacement field as third-order polynomials in all three directions of curvilinear system, rotational inertia and shear deformations are also included; however, nonlinear terms are eliminated from some dependent variables
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Sedov type solution of the equations of hydraulic longitudinal waves Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-19 S.V. Meleshko; S. Moyo; S.V. Sukhinin
The motion of a polytropic compressible fluid or gas in a non-uniform channel with elastic walls and a specified cross-section A(x,p) depending on a given point x and the pressure p is examined. The form of a cross-section A=kxαpβ is considered in this paper. Particular cases arising from the analysis that lead to an exact solution of the equations of the hydraulic longitudinal waves are given. For
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Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-16 L. Angela Mihai; Manal Alamoudi
We examine theoretically the dynamic inflation and finite amplitude oscillatory motion of inhomogeneous spherical shells and cylindrical tubes of stochastic hyperelastic material. These bodies are deformed by radially symmetric uniform inflation, and are subjected to either a surface dead load or an impulse traction, uniformly applied in the radial direction. We consider composite shells and tubes
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Nonlinear dynamics of heterogeneous shells Part 1. Statics and dynamics of heterogeneous variable stiffness shells Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-08 J. Awrejcewicz; A.V. Krysko; S.A. Mitskevich; M.V. Zhigalov; V.A. Krysko
The increasing complexity of the constructive forms and shell elements structure leads to the need to develop both the theory and methods for solving static and dynamic problems for non-homogeneous (heterogeneous) shells. By the shell heterogeneity, we mean heterogeneity in a broad sense: these are inclusions in the shell body of the different rigidity elements and, as a special case, these are holes;
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Investigation of dynamic behavior of a cable-stayed cantilever beam under two-frequency excitations Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-07 Yunyue Cong; Houjun Kang; Guirong Yan
Many civil structures and facilities can be modeled using cable-stayed cantilever beams. This study is to investigate the nonlinear dynamic response and dynamic behavior of a cable-stayed cantilever beam subjected to two different external excitations through theoretical analyses. First, the equations of motion of the cable and the beam are established. Then, based on the Galerkin method, dynamic structural
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Conservation laws for a spherical top on a plane with friction Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-04 Alexander A. Kilin; Elena N. Pivovarova
This paper is concerned with the analysis of the influence of the friction model on the existence of additional integrals of motion in a system describing the sliding of a spherical top on a plane. We consider a model in which the friction is described not only by the force applied at the point of contact, but also by an additional friction torque. It is shown that, depending on the chosen friction
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Buckling and postbuckling of extensible, shear-deformable beams: Some exact solutions and new insights Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2021-01-06 Samir Emam; Walter Lacarbonara
This paper presents exact solutions for the buckling loads and postbuckling states of extensible, shear deformable beams. The governing equation for the large-amplitude lateral deformation of beams in compression is expanded in Taylor series up to the cubic nonlinearity. Closed-form solutions in terms of the axial and shear stiffnesses are developed for statically determinate and statically indeterminate
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A note on a class of generalized neo-Hookean models for isotropic incompressible hyperelastic materials Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-26 Cornelius O. Horgan
In a recent paper in this journal by Anssari-Benam and Bucchi (2021), the authors have proposed a new two-parameter constitutive model for isotropic incompressible hyperelastic generalized neo-Hookean materials. The model reflects the limiting chain extensibility characteristic of non-Gaussian molecular models for rubber. A major contribution of Anssari-Benam and Bucchi (2021) is in showing that the
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Usability of finite elements based on the absolute nodal coordinate formulation for deformation analysis of the Achilles tendon Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-16 Leonid Obrezkov; Pernilla Eliasson; Ajay B. Harish; Marko K. Matikainen
This work explores the modelling of soft tissues, particularly the Achilles tendon, using the absolute nodal coordinate formulation (ANCF).The anisotropic Gasser–Ogden–Holzapfel (GOH) potential energy function provided the necessary anisotropic elastic feature descriptions. A generalized one-dimensional Maxwell model described the viscoelastic effects. Finally, a parameter-based damage model characterized
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A review on the statics and dynamics of electrically actuated nano and micro structures Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-03 Hossein B. Khaniki; Mergen H. Ghayesh; Marco Amabili
Nano and micro electro-mechanical systems (NEMS and MEMS) have been attracting a large amount of attention recently as they have extensive current/potential applications. However, due to their scale, molecular interaction and size effects are considerably high which needs to be considered in the theoretical modelling of their electro-mechanical behaviour. Both nano- and micro-scale electrically actuated
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Nonlinear stress analysis of shell structures in buckling and snapping problems by exact geometry solid-shell elements through sampling surfaces formulation Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-11 G.M. Kulikov; M. Bohlooly; S.V. Plotnikova; M.A. Kouchakzadeh; B. Mirzavand
In this paper, the nonlinear three-dimensional (3D) stress analysis of shell structures in buckling and snapping problems is presented. The exact geometry or geometrically exact (GeX) hybrid-mixed four-node solid-shell element is developed using a sampling surfaces (SaS) method. The SaS formulation is based on the choice of N SaS parallel to the middle surface to introduce the displacements of these
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Investigating amplitude death in a coupled nonlinear aeroelastic system Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-15 Ashwad Raaj; Sirshendu Mondal; Venkatramani Jagdish
Coupling nonlinear dynamical systems can lead to a host of phenomena, one of which leads to the complete cessation of their oscillations. This phenomenon is referred to as amplitude death (AD) in the dynamical systems literature. Recently, there is a growing interest to mitigate oscillatory or dynamic instabilities in a variety of engineering systems using AD. Deriving impetus from the same, we investigate
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The saddle case of a nonsmooth Rayleigh–Duffing oscillator Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-08 Zhaoxia Wang; Hebai Chen
We consider a single degree freedom oscillator in order to accurately represent some modeling with ship roll damping. The proposed oscillator is a nonsmooth Rayleigh–Duffing equation ẍ+aẋ+bẋ|ẋ|+cx+dx3=0. The main goal of this paper is to study the global dynamics of the nonsmooth Rayleigh–Duffing oscillator in the case d<0, i.e., the saddle case. The nonsmooth Rayleigh–Duffing oscillator is only
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Nonlinear dynamics of heterogeneous shells. Part 2. Chaotic dynamics of variable thickness shells Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-08 A.V. Krysko; J. Awrejcewicz; S.A. Mitskevich; M.V. Zhigalov; V.A. Krysko
In the second part of the article, the nonlinear dynamics and stability of nonhomogeneous variable thickness axisymmetric shells are analyzed. The mathematical model is based on the Kirchhoff–Love kinematic hypothesis. The resulting system of partial differential equations is reduced to an algebraic equations system by the Ritz method. The convergence of the applied numerical methods is investigated
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Nonlinear dynamics of vortex-induced vibration of a nonlinear beam under high-frequency excitation Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-03 Pradyumna Kumar Sahoo; S. Chatterjee
The present article studies the nonlinear dynamics and effects of high-frequency excitations (HFE) on a forced 2-D coupled beam and wake oscillator model ascribing vortex-induced vibrations. Oscillatory strobodynamics (OS) theory is employed for studying the characteristics of the system in slow time-scale. Linear stability analysis is performed near the equilibrium point of the system for both with
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Non-linear panel instabilities at high-subsonic and low supersonic speeds solved with strongly coupled CIRA FSI framework Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-27 Davide Cinquegrana; Pier Luigi Vitagliano
Nonlinear aspects of aeroelastic stability are here investigated for two and three dimensional panels in high subsonic and low supersonic flows. The effects of edge constraints and initial conditions on post-flutter behaviour are also studied. Such phenomena are crucial for spatial launchers development, that has renewed interest due to a larger number of commercial companies in the frame of space
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Uncertainty analysis of heart dynamics using Random Matrix Theory Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-28 Augusto Cheffer; Thiago G. Ritto; Marcelo A. Savi
This paper deals with the uncertainty analysis of the cardiac system described by a mathematical model. The model is composed of three-coupled nonlinear oscillators with time-delayed connections. The main idea is to investigate heart dynamics using the Random Matrix Theory, modeling uncertainties and establishing the impact of the probabilistic model on the dynamic response of the system Two advantages
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Surface waves in the magnetopause: Regularity and time evolution Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-12-01 Manuel Núñez
The equation describing surface waves in a one-dimensional magnetohydrodynamic discontinuity involves the Hilbert transform and is therefore nonlocal. It is found that by taking the analytic function whose real part is the first order perturbation one obtains a local equation. This equation yields several integral equalities which may be studied with the help of certain classical results of the theory
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A multiphase virtual mass model for debris flow Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-16 Parameshwari Kattel; Khim B. Khattri; Shiva P. Pudasaini
In a rapidly moving multiphase mass flow, drag and virtual mass forces are important interfacial forces. However, in many existing literatures, virtual mass force has often been ignored or employed empirically. In this contribution, we construct analytical, full and explicit expressions for the virtual mass coefficients in the true three-phase typical debris flow consisting of coarse-solid, fine-solid
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The Riemann problem for a drift-flux model of compressible two-phase flow in a variable cross-section duct Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-27 Qinglong Zhang
The Riemann problem for isentropic drift-flux model of compressible two-phase flow in a variable cross-section duct is considered. First, the two-phase duct flow model is established based on the balance laws. Then, by averaging the equations of single phase flow, the drift-flux model in a variable cross-section duct is deduced. The model includes two parts: mass conservation and momentum conservation
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Delay dynamics of a levitating motor with two-limit control strategy Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-26 B. Shayak
In a recent work (Shayak, 2019), I have proposed a new comparator-based control algorithm for a magnetically levitated motor. The rotor dynamics are governed by a sixth order nonlinear differential equation, whose stability analysis is treated as given. Here we consider this device from a dynamical systems viewpoint. We first present a simplified model which is a second order nonlinear delay differential
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Stiffness distribution of a spherical gel structure and bifurcation analysis with application to stem-cell differentiation Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-30 Xiaoyi Chen; Hui-Hui Dai
In biophysics, gel substrates have been used to do stem-cell differentiation by utilizing the stiffness distribution in the gel. However, in the currently available designs, the stiffness range may not be large enough and there also lacks a quantitative control. In this paper, we introduce a mechanical–chemical model for a spherical gel structure which generates an inhomogeneous deformation in the
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Static deflection modeling of combined flexible beams using elliptic integral solution Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-24 Ke Xu; Haitao Liu; Juliang Xiao
A beam composed of serially connected flexible segments can definitely diversify the option of components for the design of compliant mechanisms. Although the static deflection of such a beam can be considered as the superposition of the deflections of all segments, there is still a lack of available modeling methods due to the comprehensive interactions. This paper presents a method for modeling the
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Large deflections of folded cantilever: Experiments and elastica analysis Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-19 L.N. Virgin; R.H. Plaut
Folded cantilevers have been utilized in MEMS devices, particularly for suspension. The structures consist of a horizontal beam segment fixed at its left end, a short downward connector (joint) at the right end, and a lower horizontal segment under the upper one. Here, the left end of the lower segment is free and a downward concentrated load is applied there. Experiments are conducted on five folded
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Dynamic analysis of straight stepped microbeams Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-13 Nouha Alcheikh; Hassen M. Ouakad; Mohammad I. Younis
This works aims to investigate the dynamics of Micro-electro-mechanical systems (MEMS) straight multi-stepped micro-beams. An analytical model is presented based on the Euler–Bernoulli beam theory and the Galerkin discretization. The effect of various parameters on the natural frequencies of micro-beams is examined, including the effects of varying the geometry (number of steps and their ratios), the
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Synchronization characteristics of an array of coupled MEMS limit cycle oscillators Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-02 Aditya Bhaskar; B. Shayak; Richard H. Rand; Alan T. Zehnder
The dynamics of a proposed microelectromechanical system (MEMS) consisting of an array of limit cycle oscillators (LCOs) are analyzed. The LCOs have dissimilar limit cycle frequencies and are coupled in a nearest-neighbor configuration via electrostatic fringing fields. The emergence of synchrony in the array is outlined for two cases: self-synchronization of the array to a single frequency, and entrainment
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A generalised neo-Hookean strain energy function for application to the finite deformation of elastomers Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-16 Afshin Anssari-Benam; Andrea Bucchi
We present a new model within the class of generalised neo-Hookean strain energy functions for application to the finite deformation of incompressible elastomers. The model has a simple form with only two parameters, namely μ and N with structural roots, and is derived within the classical framework of statistical mechanics for freely jointed molecular chains in rubber elasticity Using existing experimental
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Influence of debonding on nonlinear deflection responses of curved composite panel structure under hygro-thermo-mechanical loading–macro-mechanical FE approach Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-04 Chetan Kumar Hirwani; Subrata Kumar Panda; Pradeep Kumar Mishra
The excess geometrical deformation due to the in-plane hygrothermal and transverse mechanical loading are computationally (through a customized MATLAB code) obtained for the weakly bonded structure using the different kinematic theories in combination with the finite element steps. To evaluate the nonlinear deflection data a macro mechanical model is prepared mathematically considering the stretching
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Geometrically nonlinear dynamic analysis of laminated composite plate using a nonpolynomial shear deformation theory Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-04 Babu Ranjan Thakur; Surendra Verma; B.N. Singh; D.K. Maiti
A computationally efficient C0 finite element model in conjunction with the nonpolynomial shear deformation theory (NPSDT) is extended to examine the free and forced vibration behavior of laminated composite plates. The employed NPSDT assumes the nonlinear distribution of in-plane displacements which qualify the requirement of traction free boundary conditions at the top and bottom surfaces. The present
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Minimal number of discrete velocities for a flow description and internal structural evolution of a shock wave Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-11-02 Jae Wan Shim
A fluid flow is described by fictitious particles hopping on homogeneously distributed nodes with a given finite set of discrete velocities. We emphasize that the existence of a fictitious particle having a discrete velocity among the set in a node is given by a probability. We describe a compressible thermal flow of the level of accuracy of the Navier–Stokes equation by 25 or 33 discrete velocities
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Dynamics and nonlinear effects of a compact near-zero frequency vibration isolator with HSLD stiffness and fluid damping enhancement Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-27 X. Gao; H.D. Teng
Aiming to isolate disturbance vibration for heavy payloads with low frequency, a novel hydro-pneumatic near-zero frequency vibration isolator is proposed, which possesses high-static and low-dynamic (HSLD) stiffness. And different from most isolators existing previously, a nonlinear damping strategy realized by fluid damping mechanism is implemented into the device in order to enhance vibration isolation
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Equilibria determination of elastic articulated duoskelion beams in 2D via a Riks-type algorithm Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-17 Emilio Barchiesi; Francesco dell’Isola; Alberto M. Bersani; Emilio Turco
The overall behavior of an articulated beam structure constituted by elements arranged according to a specific chirality is studied. The structure as a whole, due to its slenderness and geometry, is called duoskelion beam. The name duoskelion is a neologism which is inspired by the Greek word δύοσκέλιον (two-legged). A discrete model for shearable beams, formulated recently, is exploited to investigate
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Analysis of discontinuous dynamics of a 2-DOF system with constrained spring cushions Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-17 Min Gao; Jinjun Fan; Chunliang Li
We investigate the dynamical characteristics of a two degrees of freedom friction oscillator with constrained spring cushions. Based on the discontinuity resulted from the rough contact surface and the nonsmoothness resulted from fixed spring, different boundaries and domains are given in phase space. The G-functions are introduced to determine whether the passable, grazing, sliding and stick motions
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On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-16 Vasyl Martsenyuk; Krzysztof Augustynek; Andrzej Urbas
The model of interaction of two strains of the virus is considered in the paper. The model is based on a nonstationary system of differential equations with delays and takes into account populations of susceptible, first-time and re-infected individuals across two strains. For small values of the delays, the conditions of global asymptotic stability are obtained with the help of Lyapunov functionals
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On occurrence of bursting oscillations in a dynamical system with a double Hopf bifurcation and slow-varying parametric excitations Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-20 Miaorong Zhang; Qinsheng Bi
Slow-fast analysis has been extensively used in the past to study the occurrence of bursting oscillations. Most bursting oscillations studies are performed on the low dimensional autonomous systems where only codimension-1 bifurcations take place at the transitions of quiescent and spiking states. However, in high dimensional slow-fast dynamical systems, there exist higher co-dimensional bifurcations
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A generalized strain energy function using fractional powers: Application to isotropy, transverse isotropy, orthotropy, and residual stress symmetry Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-28 S. Mukherjee; A.K. Mandal
In this paper, we propose a generalized strain energy density function based on invariants of stretch tensor with arbitrary exponents. We employ polynomial, logarithmic and exponential functions of these invariants to develop the strain energy functions. We also study characteristics and applications of the proposed model for isotropy, transverse isotropy, orthotropy with a special focus on initial/residual
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Nonlinear response analysis for a dual-rotor system supported by ball bearing Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-12 Zhenyong Lu; Shun Zhong; Huizheng Chen; Xiaodong Wang; Jiajie Han; Chao Wang
Rolling element bearings are used as main supports and are key sources of vibrations for aero-engine rotor systems. Mainly including the inner and outer rings, cages, and balls or rollers, the complicated mechanical structures of rolling element bearings exhibit nonlinear behaviors due to the bearing clearance, nonlinear Hertzian contact forces, and defects. Due to imbalanced rotations, which are unavoidable
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Nonlinear Model Order Reduction via Nonlinear Moment Matching with Dynamic Mode Decomposition Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-10 Danish Rafiq; Mohammad Abid Bazaz
In this manuscript, we propose a novel reduction framework for obtaining Reduced Order Models (ROMs) of large-scale, nonlinear dynamical systems. We advocate the use of Nonlinear Moment Matching (NLMM) with the Dynamic Mode Decomposition (DMD) to get a much efficient dimensionality reduction scheme. While NLMM does not require the expensive computation of the time-displaced snapshot ensemble of the
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Control of Neimark–Sacker bifurcation in a type of weak impulse excited centrifugal governor system Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-08 Zengyao Lv; Huidong Xu; Zihao Bu
Centrifugal governors play an important role in rotating machinery such as diesel engines and steam engines. This paper considers two impulse excitations of the freewheel. The feedback control issue of the Neimark–Sacker bifurcation design of the centrifugal governor system is studied. A feedback control method is addressed to realize the control objectives of the existence, stability and the mean
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Strong point explosion in vibrationally exciting gas Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-28 P. Siriwat; Yu.N. Grigoriev; S.V. Meleshko
For problems with strong shock waves a modification of the Landau–Teller equation in the system of two-temperature gas dynamics is proposed. This allows for extending the admitted Lie algebra of the system by the generator of simultaneous scaling of the independent variables. On this basis a class of self-similar solutions of the one-dimensional unsteady flows of a vibrationally excited gas is obtained
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Nonlinear effects in the vibrations of flexural tensegrity beams Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-10-02 Claudio Boni; Gianni Royer-Carfagni
Flexural tensegrity is a structural principle for which the integrity under flexure of a beam formed by a chain of segments in unilateral contact is provided by an unbonded prestressing tendon anchored to the end segments, with the possible interposition of linear springs and linear dashpots. These are activated by the inflexion of the beam as a consequence of the particular shape of the contact surfaces
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Nonlinear analysis of thin-walled beams with highly deformable sections Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-28 E. Carrera; A. Pagani; D. Giusa; R. Augello
This work proposes an alternative approach for the nonlinear analysis of 2D, thin-walled lattice structures. The method makes use of the well-established Carrera Unified Formulation (CUF) for the implementation of high order 1D finite elements, which lay along the thickness direction. In this manner, the accuracy of the mathematical model does not depend on the finite element discretization and can
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Stable handspring maneuvers with passive flight phases: Results from an inverted pendulum-like template Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-18 Ali Tehrani Safa; Ali Nouriani; Aria Alasty
Inverted pendulum (IP) has been broadly used to model locomotor systems. In this paper, we demonstrate that an IP-like model could simulate stable periodic handspring maneuvers with passive flight phases. The model is a 2-D symmetric rigid body which is merely controlled during the contact phase. To benefit from an open-loop sensorless strategy, the control policy is implemented only by an unvaried
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Bifurcation of magnetorheological film–substrate elastomers subjected to biaxial pre-compression and transverse magnetic fields Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-22 M. Rambausek; K. Danas
This work investigates the primary sinusoidal bifurcation wrinkling response of single- and multi-layered magnetorheological elastomer (MRE) film–substrate systems subjected to combined transverse applied magnetic fields and in-plane biaxial pre-compression. A recently proposed continuum model that includes the volume fraction of soft-magnetic particles is employed to analyze the effect of the magnetic
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A comparison of computational models for wrinkling of pressurized shell-core systems Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-20 Tomo Veldin; Marko Lavrenčič; Boštjan Brank; Miha Brojan
Four nonlinear computational models for the surface wrinkling of curved shell-core systems under external pressure are presented. Three of the considered finite element models neglect the displacements tangential to the shell surface. Two of the models are static formulations and the other two are derived in the dynamic framework. For the latter, the energy-decaying time-stepping algorithm is applied
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Surface instabilities in graded tubular tissues induced by volumetric growth Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-22 Yang Liu; Zhouyu Zhang; Giuseppe Devillanova; Zongxi Cai
Growth-induced pattern formation in tubular tissues is intimately correlated to normal physiological functions. Moreover, either the microstructure or certain diseases can give rise to material inhomogeneity, which can lead to a change of shape in the tissue. Therefore, it is of fundamental importance to understand surface instabilities and pattern transitions of graded tubular tissues. In this paper
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Vibration mitigation and dynamics of a rotor-blade system with an attached nonlinear energy sink Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-22 Yanbo Cao; Hongliang Yao; Qiufeng Li; Peiran Yang; Bangchun Wen
Excessive vibration of rotor-blade systems has been a main reason for the failure of rotating machinery. Therefore, methods capable of simultaneously suppressing vibrations rotor and blade are urgently needed. Considering this, a nonlinear energy sink (NES) with piecewise linear stiffness is used to satisfy the requirements. Firstly, the structure and working mechanism of the NES are introduced. And
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Simulation of wrinkling in incompressible anisotropic thin sheets with wavy fibers Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-21 M. Taylor; M. Shirani
A two-dimensional plate theory is derived for incompressible transversely isotropic fiber-reinforced materials with wavy fibers. Single-layer plates and two-layer laminates are considered. Numerical simulations of axially loaded rectangular sheets in the post-buckling regime illustrate the marked effect fiber waviness has on both the wrinkling patterns and the effective axial stiffness. For fibers
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Mode transitions in buckling and post-buckling of stretched-twisted strips Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-19 Saeideh Faghfouri; Franz G. Rammerstorfer
The complex buckling behavior of one of the simplest structures, an elastic thin strip under combined stretch and twist loading represents a fascinating example for structural stability analysis. For stretched-twisted strips, in contrast to solely stretched strips, not just the computation of the post-buckling process but also the simulation of the pre-buckling behavior and the determination of the
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On the forward and backward motion of milli-bristlebots Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-09-08 D. Kim; Z. Hao; A.R. Mohazab; A. Ansari
This works presents the theoretical analysis and experimental observations of the bidirectional motion of a millimeter-scale bristle robot (milli-bristlebot) with an on-board piezoelectric actuator. First, the theory of the motion, based on the dry-friction model, is developed and the frequency regions of the forward and backward motion, along with the resonant frequencies of the system are predicted
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Influence of dissipation on extreme oscillations of a forced anharmonic oscillator Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-29 B. Kaviya, R. Suresh, V.K. Chandrasekar, B. Balachandran
Dynamics of a periodically forced anharmonic oscillator with cubic nonlinearity, linear damping, and nonlinear damping, is studied. To begin with, the authors examine the dynamics of an anharmonic oscillator with the preservation of parity symmetry. Due to this symmetric nature, the system has two neutrally stable elliptic equilibrium points in positive and negative potential-wells. Hence, the unforced
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Bifurcation of a finitely deformed functionally graded dielectric elastomeric tube Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-28 Weijian Zhou, Yingjie Chen, Yipin Su
Soft functionally graded materials have attracted intensive attention owing to their special material inhomogeneity and are realized as various applications. In this paper, we theoretically investigate the finite deformation and superimposed bifurcation behaviors of an incompressible functionally graded dielectric tube subject to a combination of axial stretch and radial voltage. The theoretical framework
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Growth and patterns of residually stressed core–shell soft sphere Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-27 Congshan Liu, Yangkun Du, Chaofeng Lü, Weiqiu Chen
Many biological tissues and organisms are in a state of residual stress, which should be considered rather than ignored as in many previous studies. In this work, we establish a theoretical model to study the growth and patterns of a residually stressed core–shell soft sphere. The effect of the initial residual stress is considered by employing a modified multiplicative decomposition growth model.
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Measurement of the Poisson’s ratio and Young’s modulus of an isotropic material with T-shape contact resonance atomic force microscopy Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-27 Feifei Gao, Yin Zhang
The Poisson’s ratio and the Young’s modulus play an important role in the characterization of nanomaterial mechanical properties. They are the vital parameters of understanding nanoscale material behavior. Here we report a method of quantitatively determining the values of the Poisson’s ratio and the Young’s modulus with a T-shape contact resonance atomic force microscopy. Unlike the cantilever of
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Nonlinear analysis of functionally graded beams using the dual mesh finite domain method and the finite element method Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-24 J.N. Reddy, Praneeth Nampally, Arun R. Srinivasa
In this paper, geometrically nonlinear analysis of functionally graded beams using the dual mesh finite domain method (DMFDM) and the finite element method is presented. The DMFDM makes use of a primal mesh of finite elements and associated approximation for the variables of the formulation and a dual mesh of control domains, which does not overlap the primal mesh, for the satisfaction of the governing
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Progressive damage analysis of composite laminates subjected to low-velocity impact using 2D layer-wise structural models Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-24 M.H. Nagaraj, E. Carrera, M. Petrolo
The present work deals with the progressive damage analysis of composite laminates subjected to low-velocity impact. We develop a numerical model using higher-order structural theories based on the Carrera Unified Formulation (CUF) with Lagrange polynomials and resulting in a 2D refined layer-wise model. To model damage, we use a combination of the continuum damage-based CODAM2 intralaminar damage
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Internal resonances among the first three modes of a hinged–hinged beam with cubic and quintic nonlinearities Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-24 Ali Kandil
This paper presents a derivation of a hinged–hinged Euler–Bernoulli beam including cubic and quintic nonlinearities. Then, a three-mode Galerkin discretization technique has been utilized to generate a system of ordinary differential equations governing the temporal deflections of the first three modes of the studied beam. The pioneering work of Nayfeh and Mook (1995) has shown the absence of internal
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Surface pressure reduces stability in bilayered systems under compression Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-22 Mohsen Darayi, Maria A. Holland
Buckling instabilities of layered materials are an important phenomenon that has been analyzed both analytically and numerically, but generally only in the absence of surface pressure. In this study, we present a linear stability analysis of the wrinkling of an inhomogeneous bilayer made up of dissimilar neo-Hookean elastic materials, under uniaxial compression with pressure applied to the top surface
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Approximations to limit cycles for a nonlinear multi-degree-of-freedom system with a cubic nonlinearity through combining the harmonic balance method with perturbation techniques Int. J. Non-Linear Mech. (IF 2.313) Pub Date : 2020-08-19 A.P. Lewis
This paper presents an approach to obtaining higher order approximations to limit cycles of an autonomous multi-degree-of-freedom system with a single cubic nonlinearity based on a first approximation involving first and third harmonics obtained with the harmonic balance method. This first approximation, which is similar to one which has previously been reported in the literature, is an analytical