Статті в журналах: "Nonlinears"

1

Mikhlin, Yuri V., and Konstantin V. Avramov. "Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments." Applied Mechanics Reviews 63, no. 6 (2010): 060802. http://dx.doi.org/10.1115/1.4003825.

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2

Šram, Miroslav, Zvonimir Vrselja, Igor Lekšan, Goran Ćurić, Kristina Selthofer-Relatić, and Radivoje Radić. "Epicardial Adipose Tissue Is Nonlinearly Related to Anthropometric Measures and Subcutaneous Adipose Tissue." International Journal of Endocrinology 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/456293.

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Introduction. Adipose tissue is the largest endocrine organ, composed of subcutaneous (SAT) and visceral adipose tissue (VAT), the latter being highly associated with coronary artery disease (CAD). Expansion of epicardial adipose tissue (EAT) is linked to CAD. One way of assessing the CAD risk is with low-cost anthropometric measures, although they are inaccurate and cannot discriminate between VAT and SAT. The aim of this study is to evaluate (1) the relationship between EAT thickness, SAT thickness and anthropometric measures in a cohort of patients assessed at the cardiology unit and (2) determine predictive power of anthropometric measures and EAT and SAT thickness in establishment of CAD.Methods. Anthropometric measures were obtained from 53 CAD and 42 non-CAD patients. Vascular and structural statuses were obtained with coronarography and echocardiography, as well as measurements of the EAT and SAT thickness.Results. Anthropometric measures showed moderate positive correlation with EAT and SAT thickness. Anthropometric measures and SAT follow nonlinearS curverelationship with EAT. Strong nonlinearpower curverelationship was observed between EAT and SAT thinner than 10 mm. Anthropometric measures and EAT and SAT were poor predictors of CAD.Conclusion. Anthropometric measures and SAT have nonlinear relationship with EAT. EAT thickness and anthropometric measures have similar CAD predictive value.

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3

Harbi, Abida. "Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES." Journal of Applied Mathematics 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/893182.

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4

Safouhi, Hassan, and Philip Hoggan. "Three-center nuclear attraction, three-center two-electron Coulomb and hybrid integrals over B functions evaluated using the nonlinearS transformation." International Journal of Quantum Chemistry 90, no. 1 (2002): 119–35. http://dx.doi.org/10.1002/qua.962.

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5

TRUEBA, JOSÉ L., JOAQUÍN RAMS, and MIGUEL A. F. SANJUÁN. "ANALYTICAL ESTIMATES OF THE EFFECT OF NONLINEAR DAMPING IN SOME NONLINEAR OSCILLATORS." International Journal of Bifurcation and Chaos 10, no. 09 (September 2000): 2257–67. http://dx.doi.org/10.1142/s0218127400001419.

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This paper reports on the effect of nonlinear damping on certain nonlinear oscillators, where analytical estimates provided by the Melnikov theory are obtained. We assume general nonlinear damping terms proportional to the power of velocity. General and useful expressions for the nonlinearly damped Duffing oscillator and for the nonlinearly damped simple pendulum are computed. They provide the critical parameters in terms of the damping coefficient and damping exponent, that is, the power of the velocity, for which complicated behavior is expected. We also consider generalized nonlinear damped systems, which may contain several nonlinear damping terms. Using the idea of Melnikov equivalence, we show that the effect of nonlinear dissipation can be equivalent to a linearly damped nonlinear oscillator with a modified damping coefficient.

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6

Tejedor Sastre, María Teresa, and Christian Vanhille. "Nonlinear Maximization of the Sum-Frequency Component from Two Ultrasonic Signals in a Bubbly Liquid." Sensors 20, no. 1 (December 23, 2019): 113. http://dx.doi.org/10.3390/s20010113.

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Techniques based on ultrasound in nondestructive testing and medical imaging analyze the response of the source frequencies (linear theory) or the second-order frequencies such as higher harmonics, difference and sum frequencies (nonlinear theory). The low attenuation and high directivity of the difference-frequency component generated nonlinearly by parametric arrays are useful. Higher harmonics created directly from a single-frequency source and the sum-frequency component generated nonlinearly by parametric arrays are attractive because of their high spatial resolution and accuracy. The nonlinear response of bubbly liquids can be strong even at relatively low acoustic pressure amplitudes. Thus, these nonlinear frequencies can be generated easily in these media. Since the experimental study of such nonlinear waves in stable bubbly liquids is a very difficult task, in this work we use a numerical model developed previously to describe the nonlinear propagation of ultrasound interacting with nonlinearly oscillating bubbles in a liquid. This numerical model solves a differential system coupling a Rayleigh–Plesset equation and the wave equation. This paper performs an analysis of the generation of the sum-frequency component by nonlinear mixing of two signals of lower frequencies. It shows that the amplitude of this component can be maximized by taking into account the nonlinear resonance of the system. This effect is due to the softening of the medium when pressure amplitudes rise.

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7

Kotzev, Miroslav, Xiaotang Bi, Matthias Kreitlow, and Frank Gronwald. "Equivalent circuit simulation of HPEM-induced transient responses at nonlinear loads." Advances in Radio Science 15 (September 21, 2017): 175–80. http://dx.doi.org/10.5194/ars-15-175-2017.

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Abstract. In this paper the equivalent circuit modeling of a nonlinearly loaded loop antenna and its transient responses to HPEM field excitations are investigated. For the circuit modeling the general strategy to characterize the nonlinearly loaded antenna by a linear and a nonlinear circuit part is pursued. The linear circuit part can be determined by standard methods of antenna theory and numerical field computation. The modeling of the nonlinear circuit part requires realistic circuit models of the nonlinear loads that are given by Schottky diodes. Combining both parts, appropriate circuit models are obtained and analyzed by means of a standard SPICE circuit simulator. It is the main result that in this way full-wave simulation results can be reproduced. Furthermore it is clearly seen that the equivalent circuit modeling offers considerable advantages with respect to computation speed and also leads to improved physical insights regarding the coupling between HPEM field excitation and nonlinearly loaded loop antenna.

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8

Liu, Lijun. "A simple nonlinearH∞control design method: Polynomial nonlinear control." International Journal of Robust and Nonlinear Control 28, no. 17 (September 12, 2018): 5406–23. http://dx.doi.org/10.1002/rnc.4322.

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9

Gu, Xiyao, Junlian Yin, Jintao Liu та Yulin Wu. "A Nonlineark-εTurbulence Model Applicable to High Pressure Gradient and Large Curvature Flow". Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/405202.

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Most of the RANS turbulence models solve the Reynolds stress by linear hypothesis with isotropic model. They can not capture all kinds of vortexes in the turbomachineries. In this paper, an improved nonlineark-εturbulence model is proposed, which is modified from the RNGk-εturbulence model and Wilcox'sk-ωturbulence model. The Reynolds stresses are solved by nonlinear methods. The nonlineark-εturbulence model can calculate the near wall region without the use of wall functions. The improved nonlineark-εturbulence model is used to simulate the flow field in a curved rectangular duct. The results based on the improved nonlineark-εturbulence model agree well with the experimental results. The calculation results prove that the nonlineark-εturbulence model is available for high pressure gradient flows and large curvature flows, and it can be used to capture complex vortexes in a turbomachinery.

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10

Zahariev, Andrey, and Hristo Kiskinov. "Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation." Mathematics 8, no. 3 (March 10, 2020): 390. http://dx.doi.org/10.3390/math8030390.

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In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system.

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11

Abdel-Rohman, Mohamed, and Hasan Al-Sanad. "Control of Nonlinear Vibrations of Foundations Built in Sandy Soil." Journal of Vibration and Control 2, no. 1 (January 1996): 53–68. http://dx.doi.org/10.1177/107754639600200104.

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Sandy soils behave nonlinearly at stress levels below the peak stress. This influences the dynamic response of the foundations built on sandy soil. This paper shows first the nonlinear vibration response of a block-type foundation due to the vertical, horizontal, and rocking excitations. The nonlinear vibration responses are compared with the linear response assuming linear soil behavior. The second part of the paper shows how to control the harmful effects due to the nonlinear vibrations using passive and active control mechanisms attached to the foundation.

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12

Wineman, Alan. "Dimensional changes during shear without normal tractions (the Poynting effect) in nonlinear viscoelastic fiber-reinforced solids." Mathematics and Mechanics of Solids 25, no. 3 (November 17, 2019): 582–96. http://dx.doi.org/10.1177/1081286519885162.

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When a rectangular block of a nonlinear material is subjected to a simple shearing deformation, specific normal tractions are required to ensure that the distances between the faces of the block, i.e. its dimensions, do not change. This work investigates the time-dependent dimensional changes during shear in the absence of these normal tractions (the Poynting effect) that occur in a block composed of an incompressible nonlinearly viscoelastic fiber-reinforced solid. The material is modeled using the Pipkin–Rogers nonlinear single integral constitutive equation for viscoelasticity. This constitutive equation is used because (1) it exhibits the essential features of nonlinear viscoelasticity; (2) it is straightforward to include the material symmetry restrictions due to the reinforcing fibers. A system of nonlinear Volterra integral equations is formulated for the dimensional changes in the block. Numerical solutions are presented for the case when the standard reinforcing model for nonlinearly elastic fiber-reinforced materials is incorporated in the Pipkin–Rogers constitutive framework. The results illustrate how the time-dependent dimensional changes depend on the fiber orientation and the viscoelastic properties of the fibers relative to those of the matrix.

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13

Kosek, Zdeněk. "Nonlinear boundary value problem for a system of nonlinear ordinary differential equations." Časopis pro pěstování matematiky 110, no. 2 (1985): 130–44. http://dx.doi.org/10.21136/cpm.1985.108595.

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14

Umran, Fadhil A. "Experimental observation of the far field diffraction patterns of functionalization single and multi-walled carbon nanotubes using nonlinear diffraction technique." Iraqi Journal of Physics (IJP) 17, no. 40 (March 3, 2019): 33–41. http://dx.doi.org/10.30723/ijp.v17i40.402.

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Nonlinear diffraction pattern can be induced by focusing CWlaser into a thin quartzes cuvette containing nanofluid. The numberof revealed pattern rings indicates to the nonlinear behavior of fluid.Here, the nonlinear refractive index of each of functionalized singlewall carbon nanotube (F-SWCNTs) suspention and multi wall carbonnanotube (F-MWCNTs) suspention have been investigatedexperimentally .Each of CNTs suspention was at volume fraction of13×10−5 and 6×10−5. Moreover the laser source at wavelength of473 nm was used. The results show that SWCNTs suspentionpossesses higher nonlinearty than other at the same volume fraction

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15

SUN, WEIGANG, YUEYING YANG, CHANGPIN LI, and ZENGRONG LIU. "SYNCHRONIZATION INSIDE COMPLEX DYNAMICAL NETWORKS WITH DOUBLE TIME-DELAYS AND NONLINEAR INNER-COUPLING FUNCTIONS." International Journal of Modern Physics B 25, no. 11 (April 30, 2011): 1531–41. http://dx.doi.org/10.1142/s0217979211100473.

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In this article, synchronization inside complex networks with double time-delays and nonlinear inner-coupling functions are studied. Here double time-delays mean that each node vector field and every coupling node have retard time, while nonlinear inner-coupling functions refer to all the components of every node that are nonlinearly coupled. The theoretical criterion respecting synchronization is derived. And illustrative numerical examples are also given.

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16

Peng, Jiehua, Jiashi Tang, and Zili Chen. "Parameter Identification of Weakly Nonlinear Vibration System in Frequency Domain." Shock and Vibration 11, no. 5-6 (2004): 685–92. http://dx.doi.org/10.1155/2004/634785.

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A new method of identifying parameters of nonlinearly vibrating system in frequency domain is presented in this paper. The problems of parameter identification of the nonlinear dynamic system with nonlinear elastic force or nonlinear damping force are discussed. In the method, the mathematic model of parameter identification is frequency response function. Firstly, by means of perturbation method the frequency response function of weakly nonlinear vibration system is derived. Next, a parameter transformation is made and the frequency response function becomes a linear function of the new parameters. Then, based on this function and with the least square method, physical parameters of the system are identified. Finally, the applicability of the proposed technique is confirmed by numerical simulation.

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17

Vatanshenas, Ali. "Nonlinear Analysis of Reinforced Concrete Shear Walls Using Nonlinear Layered Shell Approach." Nordic Concrete Research 65, no. 2 (December 1, 2021): 63–79. http://dx.doi.org/10.2478/ncr-2021-0014.

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Abstract This study discusses nonlinear modelling of a reinforced concrete wall utilizing the nonlinear layered shell approach. Rebar, unconfined and confined concrete behaviours are defined nonlinearly using proposed analytical models in the literature. Then, finite element model is validated using experimental results. It is shown that the nonlinear layered shell approach is capable of estimating wall response (i.e., stiffness, ultimate strength, and cracking pattern) with adequate accuracy and low computational effort. Modal analysis is conducted to evaluate the inherent characteristics of the wall to choose a logical loading pattern for the nonlinear static analysis. Moreover, pushover analysis’ outputs are interpreted comprehensibly from cracking of the concrete until reaching the rupture step by step.

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18

Lehrer, Devon, Martin Guay, and Veronica Adetola. "Adaptive Estimation in Nonlinearly Parameterized Discrete-Time Nonlinear Systems." IFAC Proceedings Volumes 44, no. 1 (January 2011): 1534–39. http://dx.doi.org/10.3182/20110828-6-it-1002.03736.

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19

Ciarlet, Philippe G., and Sorin Mardare. "Nonlinear Saint-Venant compatibility conditions for nonlinearly elastic plates." Comptes Rendus Mathematique 349, no. 23-24 (December 2011): 1297–302. http://dx.doi.org/10.1016/j.crma.2011.10.019.

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20

Farza, M., M. M’Saad, T. Maatoug, and M. Kamoun. "Adaptive observers for nonlinearly parameterized class of nonlinear systems." Automatica 45, no. 10 (October 2009): 2292–99. http://dx.doi.org/10.1016/j.automatica.2009.06.008.

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21

JOVANOVIC, D., P. K. SHUKLA, and B. ELIASSON. "Evolution of nonlinearly coupled drift wave-zonal flow system in a nonuniform magnetoplasma." Journal of Plasma Physics 76, no. 5 (February 18, 2010): 665–71. http://dx.doi.org/10.1017/s0022377810000061.

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AbstractThe amplitude modulation of a finite amplitude drift wave by zonal flows in a non-uniform magnetoplasma is considered. The evolution of a nonlinearly coupled drift wave-zonal flow (DW-ZF) system is governed by a nonlinear equation for the slowly varying envelope of the drift waves, which drives (via the Reynolds stress of the drift wave envelope) the second equation for zonal flows. The nonlinear dispersion relation for the modulational instability of a drift wave pump is derived and analyzed. In a special case, the DW-ZF system of equations reduces to the cubic nonlinear Schrödinger equation, which admits localized solutions in the form of DW envelope solitons, accompanied by a shock-like ZF structure. Numerical solutions of the nonlinearly coupled DW-ZF systems reveal that an arbitrary spatial distribution of the DW rapidly decays into an array of localized drift wave structures, propagating with different speeds, that are robust and, in many respect, behave as solitons. The corresponding ZF evolves into the sequence of shocks that produces a strong shearing, i.e. multiple plasma flows in alternating directions.

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22

Dindienė, Lina, and Arvydas Jokimaitis. "Estimation of the convergence rate of two-dimensional random index vectors maxima." Lietuvos matematikos rinkinys 52 (December 15, 2011): 365–68. http://dx.doi.org/10.15388/lmr.2011.tt04.

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Nonlinearly normalized maxima of independent and identically distributed random vectors are pre-sented in this work. We’ve obtained nonuniform estimate of convergence in transfer theorem in case when normalization is nonlinear.

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23

Sampaio, Júlio Cesar Santos, and Igor Leite Freire. "Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/804703.

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The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out.

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24

Gerasimchuk, V. S., I. V. Gerasimchuk, and N. I. Dranik. "Solutions of Nonlinear Schrodinger Equation with Two Potential Wells in Linear / Nonlinear Media." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 2 (June 25, 2016): 168–76. http://dx.doi.org/10.15407/mag12.02.168.

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25

DATE, G., M. KRISHNA, and M. V. N. MURTHY. "ASYMPTOTIC ANALYSIS AND SPECTRUM OF THREE ANYONS." International Journal of Modern Physics A 09, no. 15 (June 20, 1994): 2545–61. http://dx.doi.org/10.1142/s0217751x94001011.

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The spectrum of anyons confined in a harmonic oscillator potential shows both linear and nonlinear dependence on the statistical parameter. While the existence of exact linear solutions has been shown analytically, the nonlinear dependence has been arrived at by numerical and/or perturbative methods. We develop a method which shows the possibility of a nonlinearly interpolating spectrum. To be specific we analyze the eigenvalue equation in various asymptotic regions for the three-anyon problem.

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26

Liu, Xiaofang, and Guodong Sun. "Nonlinear character analysis for bistability in virus–immune dynamics." Future Virology 14, no. 10 (October 2019): 655–62. http://dx.doi.org/10.2217/fvl-2019-0059.

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Structured abstract Aim: The nonlinear characters of two linearly stable equilibrium states (virus and immune) for a theoretical virus-immune model are analyzed. Methods: Conditional nonlinear optimal perturbation (CNOP), Lyapunov method and linear singular vector method. Results & conclusion: Two linearly stable equilibrium states (immune-free and immune) with linear methods are nonlinearly unstable using the CNOP method. When the CNOP-type of initial perturbation is used in the model, the immune-free (immune) equilibrium state will be made into the immune (immune-free) equilibrium state. Through computing the variations of nonlinear terms of the model, the nonlinear effect of immune proliferation plays an important role in abrupt changes of the immune-free equilibrium state compared with the linear term. For the immune equilibrium state, the nonlinear effect of viral replication is also an important factor.

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27

Knobloch, H. W. "Observability of nonlinear systems." Mathematica Bohemica 131, no. 4 (2006): 411–18. http://dx.doi.org/10.21136/mb.2006.133974.

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28

Kubáček, Lubomír. "Nonlinear error propagation law." Applications of Mathematics 41, no. 5 (1996): 329–45. http://dx.doi.org/10.21136/am.1996.134330.

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29

Michels, Robert, Martin Schaarschmidt, and Frank Gronwald. "Experimental Investigation of a Nonlinear Energy Storage Effect due to High Power Electromagnetic Excitation." Advances in Radio Science 18 (December 10, 2020): 75–82. http://dx.doi.org/10.5194/ars-18-75-2020.

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Abstract. The susceptibility of interference victims can significantly be influenced by the presence of nonlinear circuit elements. In addition to the well known occurrence of intermodulation-frequencies, other effects can be observed as well. Recently, a nonlinear energy storage effect has been discovered which is due to the presence of nonlinearly loaded loop antennas if excited by an HPEM-excitation. In this contribution, this effect is further studied by experiment. It is seen that the nonlinear energy storage effect can be reproduced by means of a rather simple experimental setup. This allows to straighforwardly study parameter variations in order to attain an improved understanding of the considered effect.

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30

He, Ji-Huan, Qian Yang, Chun-Hui He, and Yasir Khan. "A Simple Frequency Formulation for the Tangent Oscillator." Axioms 10, no. 4 (November 26, 2021): 320. http://dx.doi.org/10.3390/axioms10040320.

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The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this relationship is critical in the design of a packaging system and a microelectromechanical system (MEMS). This paper proposes a straightforward frequency prediction method for nonlinear oscillators with arbitrary initial conditions. The tangent oscillator, the hyperbolic tangent oscillator, a singular oscillator, and a MEMS oscillator are chosen to elucidate the simple solving process. The results, when compared with those obtained by the homotopy perturbation method, exhibit a good agreement. This paper introduces a very convenient procedure for attaining quick and accurate insight into the vibration property of a nonlinear vibration system.

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31

Ibrahim, E. A., and S. P. Lin. "Weakly Nonlinear Instability of a Liquid Jet in a Viscous Gas." Journal of Applied Mechanics 59, no. 2S (June 1, 1992): S291—S296. http://dx.doi.org/10.1115/1.2899503.

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The weakly nonlinear instability of a viscous liquid jet emanated into a viscous gas contained in a coaxial vertical circular pipe is investigated as an initial-value problem. The linear stability theory predicted that the jet may become unstable either due to capillary pinching or due to interfacial stress fluctuation. The results of nonlinear stability analysis shows no tendency of supercritical stability for both of the linearly unstable modes. In fact, the nonlinear growth rate of the disturbance is faster than the exponential growth rate of the linear normal mode disturbance for the same flow parameters. Moreover, the most amplified linear normal mode disturbance evolves nonlinearly into a nonsinusoidal wave of shorter wavelength. No nonlinear instability is found for the linearly stable disturbances. Thus, while the linear theory is adequate for the prediction of the onset of jet breakup, nonlinear theory is required to describe the outcome of the jet breakup.

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32

GUTSCHMIDT, STEFANIE, and ODED GOTTLIEB. "INTERNAL RESONANCES AND BIFURCATIONS OF AN ARRAY BELOW THE FIRST PULL-IN INSTABILITY." International Journal of Bifurcation and Chaos 20, no. 03 (March 2010): 605–18. http://dx.doi.org/10.1142/s0218127410025910.

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A nonlinear continuum model is used to investigate the dynamic behavior of an array of N nonlinearly coupled microbeams. Investigations concentrate on the region below the array's first pull-in instability, which is shown to be governed by several internal three-to-one and combination resonances. The nonlinear equations of motion for a two-element system are solved using the asymptotic multiple-scales method for the weak nonlinear system. The analytically obtained periodic response of two coupled microbeams is numerically evaluated by a continuation technique and complemented by a numerical analysis of a three-element array which exhibits quasi-periodic responses and lengthy chaotic transients. This study of small-size microbeam arrays serves for design purposes and the understanding of nonlinear nearest-neighbor interactions of medium- and large-size arrays.

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33

Berik, Pelin, and Peter L. Bishay. "Parameter Identification of the Nonlinear Piezoelectric Shear d15 Coefficient of a Smart Composite Actuator." Actuators 10, no. 7 (July 19, 2021): 168. http://dx.doi.org/10.3390/act10070168.

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The objective of this work is to characterize the nonlinear dependence of the piezoelectric d15 shear coefficient of a composite actuator on the static electric field and include this effect in finite element (FE) simulations. The Levenberg-Marquardt nonlinear least squares optimization algorithm implemented in MATLAB was applied to acquire the piezoelectric shear coefficient parameters. The nonlinear piezoelectric d15 shear constant of the composite actuator integrated with piezoceramic d15 patches was obtained to be 732 pC/N at 198 V. The experimental benchmark was simulated using a three-dimensional piezoelectric FE model by taking piezoelectric nonlinearity into consideration. The results revealed that the piezoelectric shear d15 coefficient increased nonlinearly under static applied electric fields over 0.5 kV/cm. A comparison between the generated transverse deflections of the linear and nonlinear FE models was also performed.

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34

CHANDRAN, VINOD, STEVE ELGAR, and CHARLES PEZESHKI. "BISPECTRAL AND TRISPECTRAL CHARACTERIZATION OF TRANSITION TO CHAOS IN THE DUFFING OSCILLATOR." International Journal of Bifurcation and Chaos 03, no. 03 (June 1993): 551–57. http://dx.doi.org/10.1142/s021812749300043x.

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Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

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35

Zhou, Qin, Yu Zhong, Houria Triki, Yunzhou Sun, Siliu Xu, Wenjun Liu, and Anjan Biswas. "Chirped Bright and Kink Solitons in Nonlinear Optical Fibers with Weak Nonlocality and Cubic-Quantic-Septic Nonlinearity." Chinese Physics Letters 39, no. 4 (April 1, 2022): 044202. http://dx.doi.org/10.1088/0256-307x/39/4/044202.

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This work focuses on chirped solitons in a higher-order nonlinear Schrödinger equation, including cubic-quintic-septic nonlinearity, weak nonlocal nonlinearity, self-frequency shift, and self-steepening effect. For the first time, analytical bright and kink solitons, as well as their corresponding chirping, are obtained. The influence of septic nonlinearity and weak nonlocality on the dynamical behaviors of those nonlinearly chirped solitons is thoroughly addressed. The findings of the study give an experimental basis for nonlinear-managed solitons in optical fibers.

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36

Zhu, Yun-Peng, Z. Q. Lang, and Yu-Zhu Guo. "Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria." Nonlinear Dynamics 104, no. 3 (April 22, 2021): 2553–71. http://dx.doi.org/10.1007/s11071-021-06429-9.

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AbstractIn engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices.

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37

Wang, Jinbo, Michael A. Spall, Glenn R. Flierl, and Paola Malanotte-Rizzoli. "Nonlinear Radiating Instability of a Barotropic Eastern Boundary Current." Journal of Physical Oceanography 43, no. 7 (July 1, 2013): 1439–52. http://dx.doi.org/10.1175/jpo-d-12-0174.1.

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Abstract Linear and nonlinear radiating instabilities of an eastern boundary current are studied using a barotropic quasigeostrophic model in an idealized meridional channel. The eastern boundary current is meridionally uniform and produces unstable modes in which long waves are most able to radiate. These long radiating modes are easily suppressed by friction because of their small growth rates. However, the long radiating modes can overcome friction by nonlinear energy input transferred from the more unstable trapped mode and play an important role in the energy budget of the boundary current system. The nonlinearly powered long radiating modes take away part of the perturbation energy from the instability origin to the ocean interior. The radiated instabilities can generate zonal striations in the ocean interior that are comparable to features observed in the ocean. Subharmonic instability is identified to be responsible for the nonlinear resonance between the radiating and trapped modes, but more general nonlinear triad interactions are expected to apply in a highly nonlinear environment.

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38

Gally, Tristan, Christopher M. Gehb, Philip Kolvenbach, Anja Kuttich, Marc E. Pfetsch, and Stefan Ulbrich. "Robust Truss Topology Design with Beam Elements via Mixed Integer Nonlinear Semidefinite Programming." Applied Mechanics and Materials 807 (November 2015): 229–38. http://dx.doi.org/10.4028/www.scientific.net/amm.807.229.

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In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness matrix depends nonlinearly on the cross-sectional areas of the beams, this leads toa nonlinear SDP. We present numerical results using a sequential SDP approach and compare them toresults obtained via a general method for robust PDE-constrained optimization applied to the equationsof linear elasticity. Furthermore, we present two mixed integer semidefinite programs (MISDP), onefor the optimal choice of connecting elements, which is nonlinear, and one for the correspondingproblem with discrete cross-sectional areas.

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39

Jerome, Trevor W. "Application of methods to determine time-dependent damping of flanged, bolted plates." Journal of the Acoustical Society of America 150, no. 4 (October 2021): A342. http://dx.doi.org/10.1121/10.0008522.

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The dynamic and steady-state response of flanged, bolted plates when excited with a hammer and acoustic methods exhibit nonlinear effects. Established Hilbert methods are used to estimate time-dependent and amplitude-dependent damping due to the joint, and the findings are presented here. Nonlinear damping of this system is sensitive to boundary conditions, and each of the first few modes behave nonlinearly in unique ways. Insight gained from knowledge about relationships between amplitude and damping may help to better understand friction joint dynamics.

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40

WU, Jian, Qingwei CAO, and Hui LI. "AN APPROACH FOR MADM PROBLEMS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS BASED ON NONLINEAR FUNCTIONS." Technological and Economic Development of Economy 22, no. 3 (September 14, 2015): 336–56. http://dx.doi.org/10.3846/20294913.2014.989931.

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This paper investigates an approach for multiple attribute decision making (MADM) problems with interval-valued intuitionistic fuzzy numbers (IVIFNs). To do that, the nonlinear score, accuracy and hesitation functions of IVIFNs are developed based on the normal distribution. The novelty of these nonlinear functions is that they have an additional variance value, which can have more information to rank IVIFNs than Xu and Chen’s score function and Ye’s accuracy function. Based on these nonlinear functions, a ranking method for IVIFNs is proposed. Furthermore, a nonlinearly optimized model is proposed to obtain attribute weights by integrating these nonlinear functions. Then, we develop an approach for interval-valued intuitionistic fuzzy MADM programs in which two cases are considered: the attribute weight information is known and particularly known. In the end, we apply the proposed approach to select green supplier.

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41

Chithiika Ruby, V., P. Muruganandam, and M. Senthilvelan. "Nonlinear time evolution of coherent states with observation of super revivals in a generalized isotonic oscillator." International Journal of Geometric Methods in Modern Physics 11, no. 04 (April 2014): 1450027. http://dx.doi.org/10.1142/s0219887814500273.

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In this paper, we investigate revival and super revivals of nonlinear coherent states while generating these states through the interaction of coherent states of a generalized isotonic oscillator with the nonlinear media during time evolution. We construct the f-deformed generalized isotonic oscillator which is a non-isochronous partner of the generalized isotonic oscillator. We connect these two nonlinear oscillators through deformed ladder operators. The generalized isotonic oscillator possesses linear energy spectrum whereas f-deformed generalized isotonic oscillator exhibits nonlinear energy spectrum. The presence of the cubic nonlinearity in the f-deformed oscillator motivates us to study revivals, super and fractional revivals of coherent states which are nonlinearly evolved. We also investigate time-dependent expectation values of uncertainties in certain canonically conjugate variables and demonstrate that at revival and super revival times the uncertainty relation attains its minimum value.

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42

Yim, S. C. S., and S. Narayanan. "Modeling and Identification of a Nonlinear SDOF Moored Structure, Part 2—Comparisons and Sensitivity Study." Journal of Offshore Mechanics and Arctic Engineering 126, no. 2 (May 1, 2004): 183–90. http://dx.doi.org/10.1115/1.1710874.

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A system-identification technique based on the Reverse Multiple-Input/Single-Output (R-MI/SO) procedure is applied to identify the parameters of an experimental mooring system exhibiting nonlinear behavior. In Part 1, two nonlinear small-body hydrodynamic Morison type formulations: (A) with a relative-velocity (RV) model, and (B) with an independent-flow-field (IFF) model, are formulated. Their associated nonlinear system-identification algorithms based on the R-MI/SO system-identification technique: (A.1) nonlinear-structure linearly damped, and (A.2) nonlinear-structure coupled hydrodynamically damped for the RV model, and (B.1) nonlinear-structure nonlinearly damped for the IFF model, are developed for an experimental submerged-sphere nonlinear mooring system under ocean waves. The analytic models and the associated algorithms for parametric identification are described. In this companion paper (Part 2), we use the experimentally measured input wave and output system response data and apply the algorithms derived based on the multiple-input/single-output linear analysis of the reverse dynamic systems to identify the system parameters. The two nonlinear models are examined in detail and the most suitable physical representative model is selected for the mooring system considered. A sensitive analysis is conducted to investigate the coupled hydrodynamic forces modeled by the Morison equation, the nonlinear stiffness from mooring lines and the nonlinear response. The appropriateness of each model is discussed in detail.

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43

Panah, Manouchehr, AR Khorshidvand, SM Khorsandijou, and Mohsen Jabbari. "Axisymmetric nonlinear behavior of functionally graded saturated poroelastic circular plates under thermo-mechanical loading." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 8 (November 20, 2021): 4313–35. http://dx.doi.org/10.1177/09544062211051684.

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In functionally graded saturated poroelastic circular plates with immovable simply supported and clamped rims, the axisymmetric nonlinear bending under transverse thermo-mechanical loading has been parametrically studied and compared with the axisymmetric postbuckling and nonlinear bending under thermal loading. Based on the classical plate theory, Love–Kirchhoff hypotheses and Sander’s assumptions, the general coupled nonlinear radial and transverse equilibrium equations, central continuity, symmetry and boundary conditions has been derived in ordinary and state-spatial forms. The corresponding difference equations have been achieved by using the generalized differential quadrature method. The equations have been assembled and numerically solved by using the Newton–Raphson iterative algorithm. The effects of the mechanical and thermal loads, pore distribution type, porosity parameter, Skempton’s coefficient, and thickness and boundary condition type on the behavior of the deflection, whether caused by thermo-mechanical bending, thermal postbuckling, or thermal bending, have been investigated in detail. From the parametric study, a novel quantity determining bending behavior has been found. The axisymmetric themo-mechanical nonlinear bending deflection is inversely and nonlinearly proportional to thermal load when the quantity is greater than a critical value and is nonlinearly proportional to thermal load when the quantity is less than a critical value. It was verified that the plate behavior complies with the general rules known for FG saturated poroelastic circular plates and with those known for metal–ceramic functionally graded circular plates whose governing equations are mathematically analogous to those of the current research.

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44

Miranda-Colorado, Roger, Carlos Chavez, and Luis T. Aguilar. "Integral Sliding Modes with NonlinearH∞-Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances." Mathematical Problems in Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/4876019.

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This paper presents a methodology for controlling nonlinear time-varying minimum-phase underactuated systems affected by matched and unmatched perturbations. The proposed control structure consists of an integral sliding mode control coupled together with a global nonlinearH∞-control for rejecting vanishing and nonvanishing matched perturbations and for attenuating the unmatched ones, respectively. It is theoretically proven that, using the proposed controller, the origin of the free-disturbance nonlinear system is asymptotically stabilized, while the matched disturbances are rejected whereas theL2-gain of the corresponding nonlinear system with unmatched perturbation is less than a given disturbance attenuation levelγwith respect to a given performance output. The capability of the designed controller is verified through a flexible joint robot manipulator typically affected by both classes of external perturbations. In order to assess the performance of the proposed controller, an existing sliding modes controller based on a nonlinear integral-type sliding surface is also implemented. Both controllers are then compared for trajectory tracking tasks. Numerical simulations show that the proposed approach exhibits better performance.

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45

Ortega, Romeo, Xiangbin Liu, Hongye Su, and Jian chu. "Immersion and Invariance Adaptive Control of Nonlinearly Parameterized Nonlinear Systems *." IFAC Proceedings Volumes 43, no. 14 (September 2010): 641–46. http://dx.doi.org/10.3182/20100901-3-it-2016.00294.

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46

Xiangbin Liu, R. Ortega, Hongye Su, and Jian Chu. "Immersion and Invariance Adaptive Control of Nonlinearly Parameterized Nonlinear Systems $ $." IEEE Transactions on Automatic Control 55, no. 9 (September 2010): 2209–14. http://dx.doi.org/10.1109/tac.2010.2052389.

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47

Zhu, Wenxing, and M. M. Ali. "Discrete dynamic convexized method for nonlinearly constrained nonlinear integer programming." Computers & Operations Research 36, no. 10 (October 2009): 2723–28. http://dx.doi.org/10.1016/j.cor.2008.12.002.

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48

Negrello, Camille, Pierre Gosselet, and Christian Rey. "Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems." Mathematics 9, no. 24 (December 8, 2021): 3165. http://dx.doi.org/10.3390/math9243165.

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We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, dedicated to nonlinear substructured and condensed formulations with dual approach, i.e., nonlinear analogues to the Finite Element Tearing and Interconnecting (FETI) solver. By increasing the importance of local nonlinear operations, this new technique reduces communications between processors throughout the parallel solving process. Moreover, the tangent systems produced at each step still have the exact shape of classically preconditioned linear FETI problems, which makes the tractability of the implementation barely modified. The efficiency of this new preconditioner is illustrated on two academic test cases, namely a water diffusion problem and a nonlinear thermal behavior.

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49

Carter, Glenn S., and Michael C. Gregg. "Persistent Near-Diurnal Internal Waves Observed above a Site of M2 Barotropic-to-Baroclinic Conversion." Journal of Physical Oceanography 36, no. 6 (June 1, 2006): 1136–47. http://dx.doi.org/10.1175/jpo2884.1.

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Abstract Near-diurnal internal waves were observed in velocity and shear measurements from a shipboard survey along a 35-km section of the Kaena Ridge, northwest of Oahu. Individual waves with upward phase propagation could be traced for almost 4 days even though the ship transited approximately 20 km. Depth–time maps of shear were dominated by near-diurnal waves, despite the fact that Kaena Ridge is a site of considerable M2 barotropic-to-baroclinic conversion. Guided by recent numerical and observational studies, it was found that a frequency of ½M2 (i.e., 24.84-h period) was consistent with these waves. Nonlinear processes are able to transfer energy within the internal wave spectrum. Bicoherence analysis, which can distinguish between nonlinearly coupled waves and waves that have been independently excited, suggested that the ½M2 waves were nonlinearly coupled with the dominant M2 internal tide only between 525- and 595-m depth. This narrow depth range corresponded to an observed M2 characteristic emanating from the northern edge of the ridge. The observations occurred in close proximity to the internal tide generation region, implying a rapid transfer of energy between frequencies. Strong nonlinear interactions seem a likely mechanism. Nonlinear transfers such as these could complicate attempts to close local single-constituent tidal energy budgets.

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50

Ahmad, Kartini, Anuar Ishak, and Roslinda Nazar. "Micropolar Fluid Flow and Heat Transfer over a Nonlinearly Stretching Plate with Viscous Dissipation." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/257161.

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The flow and heat transfer of a micropolar fluid past a nonlinearly stretching plate is studied numerically, by taking into account the viscous dissipation effect. It is assumed that the plate is stretched nonlinearly from the slot where it is issued. The governing system of partial differential equations is transformed into ordinary differential equations, which are then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters, namely, the material parameterK, the Eckert number Ec, the Prandtl number Pr, and the nonlinear stretching parametern, on the flow field and the heat transfer characteristics are obtained and discussed. The velocity and the temperature profiles are also illustrated to aid the validity of the numerical results obtained. It is found that both the local Nusselt number and the magnitude of the skin friction coefficient increase with the nonlinear stretching parametern, and the opposite trend occurs asKincreases for fixedn.

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