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Relevant bibliographies by topics / Nonlinear Dynamic Equations

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Academic literature on the topic 'Nonlinear Dynamic Equations'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Nonlinear Dynamic Equations"

1

Feireisl, Eduard. "Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions." Applications of Mathematics 34, no. 1 (1989): 46–56. http://dx.doi.org/10.21136/am.1989.104333.

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MA, TIAN, and SHOUHONG WANG. "DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS." Chinese Annals of Mathematics 26, no. 02 (2005): 185–206. http://dx.doi.org/10.1142/s0252959905000166.

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Yang, Min, Weiming Xiao, Erjing Han, Junjuan Zhao, Wenjiang Wang, and Yunan Liu. "Dynamic analysis of negative stiffness noise absorber with magnet." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 7 (2023): 183–88. http://dx.doi.org/10.3397/in_2022_0031.

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In the paper, the negative stiffness membrane absorber with magnet has been taken as a nonlinear noise absorber. The dynamic characteristics of the nonlinear noise absorber have been studied by nonlinear dynamics theory and numerical simulation. The dynamic equations of the system were established under harmonic excitation. The slow flow equations of the system are derived by using complexification averaging method, and the nonlinear equations which describe the steady-state response are obtained. Bifurcation diagram, amplitude frequency diagram and phase diagram are used to study the nonlinea

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Tie, Yu Jia, Wei Yang, and Hao Yu Tan. "Spacecraft Attitude and Orbit Coupled Nonlinear Adaptive Synchronization Control." Advanced Materials Research 327 (September 2011): 6–11. http://dx.doi.org/10.4028/www.scientific.net/amr.327.6.

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Precise dynamic model of spacecraft is essential for the space missions, to be completed successfully. Nevertheless, the independent orbit or attitude dynamic models can not meet high precision tasks. This paper developed a 6-DOF relative coupling dynamic model based upon the nonlinear relative motion dynamics equations and attitude kinematics equations described by MRP. Nonlinear synchronization control law was designed for the coupled nonlinear dynamic model, whose close-loop system was proved to be global asymptotic stable by Lyapunov direct method. Finallly, the simulation results illustra

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Gebrel, Ibrahim F., and Samuel F. Asokanthan. "Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes." Vibration 4, no. 4 (2021): 805–21. http://dx.doi.org/10.3390/vibration4040045.

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This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure

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Shan, Li Jun, Xue Fang, and Wei Dong He. "Nonlinear Dynamic Model and Equations of RV Transmission System." Advanced Materials Research 510 (April 2012): 536–40. http://dx.doi.org/10.4028/www.scientific.net/amr.510.536.

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The nonlinear dynamics model of gearing system is developed based on RV transmission system. The influence of the nonlinear factors as time-varying meshing stiffness, backlash of the gear pairs and errors is considered. By means of the Lagrange equation the multi-degree-of-freedom differential equations of motion are derived. The differential equations are very hard to solve for which are characterized by positive semi-definition, time-variation and backlash-type nonlinearity. And linear and nonlinear restoring force are coexist in the equations. In order to solve easily, the differential equa

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Piprek, Patrick, Michael M. Marb, Pranav Bhardwaj, and Florian Holzapfel. "Trajectory/Path-Following Controller Based on Nonlinear Jerk-Level Error Dynamics." Applied Sciences 10, no. 23 (2020): 8760. http://dx.doi.org/10.3390/app10238760.

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This study proposes a novel, nonlinear trajectory/path-following controller based on jerk-level error dynamics. Therefore, at first the nonlinear acceleration-based kinematic equations of motion of a dynamic system are differentiated with respect to time to obtain a representation connecting the translation jerk with the (specific) force derivative. Furthermore, the path deviation, i.e., the difference between the planned and the actual path, is formulated as nonlinear error dynamics based on the jerk error. Combining the derived equations of motion with the nonlinear error dynamics as well as

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Xia, Xie, Huang Hong-Bin, Qian Feng, Zhang Ya-Jun, Yang Peng, and Qi Guan-Xiao. "Dynamic Equations and Nonlinear Dynamics of Cascade Two-Photon Laser." Communications in Theoretical Physics 45, no. 6 (2006): 1042–48. http://dx.doi.org/10.1088/0253-6102/45/6/018.

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Bohner, M., and S. H. Saker. "Oscillation criteria for perturbed nonlinear dynamic equations." Mathematical and Computer Modelling 40, no. 3-4 (2004): 249–60. http://dx.doi.org/10.1016/j.mcm.2004.03.002.

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Ma, Tian, and Shouhong Wang. "Bifurcation of Nonlinear Equations: II. Dynamic Bifurcation." Methods and Applications of Analysis 11, no. 2 (2004): 179–210. http://dx.doi.org/10.4310/maa.2004.v11.n2.a2.

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Dissertations / Theses on the topic "Nonlinear Dynamic Equations"

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Peters, James Edward II. "Group analysis of the nonlinear dynamic equations of elastic strings." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/29348.

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Sotoudeh, Zahra. "Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41179.

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Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations

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See, Chong Wee Simon. "Numerical methods for the simulation of dynamic discontinuous systems." Thesis, University of Salford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358276.

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Zigic, Jovan. "Optimization Methods for Dynamic Mode Decomposition of Nonlinear Partial Differential Equations." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103862.

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Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations. Naturally, reduced-order modeling techniques come at the price of either computational accuracy or computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This thesis focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides one study of an existing optimization framework for the DMD method known as the Optimized DMD and

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Brown, Andrew M. "Design, construction and analysis of a chaotic vibratory system." Thesis, Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/18172.

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SOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.

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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variationa

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Qu, Zheng. "Nonlinear Perron-Frobenius theory and max-plus numerical methods for Hamilton-Jacobi equations." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/92/71/22/PDF/thesis.pdf.

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Une approche fondamentale pour la résolution de problémes de contrôle optimal est basée sur le principe de programmation dynamique. Ce principe conduit aux équations d'Hamilton-Jacobi, qui peuvent être résolues numériquement par des méthodes classiques comme la méthode des différences finies, les méthodes semi-lagrangiennes, ou les schémas antidiffusifs. À cause de la discrétisation de l'espace d'état, la dimension des problèmes de contrôle pouvant être abordés par ces méthodes classiques est souvent limitée à 3 ou 4. Ce phénomène est appellé malédiction de la dimension. Cette thèse porte sur

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Ferrara, Joseph. "A Study of Nonlinear Dynamics in Mathematical Biology." UNF Digital Commons, 2013. http://digitalcommons.unf.edu/etd/448.

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We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.

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Larson, David F. H. "Modeling nonlinear stochastic ocean loads as diffusive stochastic differential equations to derive the dynamic responses of offshore wind turbines." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/105690.

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Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (page 54).<br>A procedure is developed for modeling stochastic ocean wave and wind loads as diffusive stochastic differential equations (SDE) in a state space form to derive the response statistics of offshore structures, specifically wind turbines. Often, severe wind and wave systems are highly nonlinear and thus treatment as linear systems is not applicable, leading to computationally expensive Monte Carlo simulations

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Challa, Subhash. "Nonlinear state estimation and filtering with applications to target tracking problems." Thesis, Queensland University of Technology, 1998.

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Books on the topic "Nonlinear Dynamic Equations"

1

Grusa, K. U. Mathematical analysis of nonlinear dynamic processes. Longman Scientific & Technical, 1988.

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Oscillations in planar dynamic systems. World Scientific, 1996.

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Papageorgiou, Evangelos C. Development of a dynamic model for a UAV. Naval Postgraduate School, 1997.

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Murthy, V. R. Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems. National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1994.

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Grusa, Karl-Ulrich. Mathematical analysis of nonlinear dynamic processes: An introduction to processes governed by partial differential equations. Longman Scientific & Technical, 1988.

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6

UNESCO. Working Group on Systems Analysis. Meeting. Lotka-Volterra-approach to cooperation and competition in dynamic systems: Proceedings of the 5th Meeting of UNESCO's Working Group on System Theory held on the Wartburg, Eisenach (GDR), March 5-9, 1984. Akademie-Verlag, 1985.

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Maurice, Holt, Packard Andrew, and Institute for Computer Applications in Science and Engineering., eds. Simulation of a controlled airfoil with jets. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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1941-, Brunner H., Zhao Xiao-Qiang, and Zou Xingfu 1958-, eds. Nonlinear dynamics and evolution equations. American Mathematical Society, 2006.

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9

Verhulst, F. Nonlinear differential equations and dynamical systems. Springer-Verlag, 1990.

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Verhulst, Ferdinand. Nonlinear Differential Equations and Dynamical Systems. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-97149-5.

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Book chapters on the topic "Nonlinear Dynamic Equations"

1

Simonovits, András. "Nonlinear Difference Equations." In Mathematical Methods in Dynamic Economics. Palgrave Macmillan UK, 2000. http://dx.doi.org/10.1057/9780230513532_4.

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Georgiev, Svetlin G. "Nonlinear Dynamic Equations and Optimal Control Problems." In Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76132-5_15.

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Wang, Chao, Ravi P. Agarwal, Donal O’Regan, and Rathinasamy Sakthivel. "Nonlinear Dynamic Equations on Translation Time Scales." In Theory of Translation Closedness for Time Scales. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38644-3_6.

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Georgiev, Svetlin G. "Oscillations of Second-Order Nonlinear Functional Dynamic Equations." In Functional Dynamic Equations on Time Scales. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15420-2_9.

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Georgiev, Svetlin G. "Nonlinear Integro-Dynamic Equations and Optimal Control Problems." In Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76132-5_16.

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Socha, Leslaw. "Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS)." In Linearization Methods for Stochastic Dynamic Systems. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-72997-6_4.

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Święch, Andrzej. "HJB Equation, Dynamic Programming Principle, and Stochastic Optimal Control." In Nonlinear Partial Differential Equations for Future Applications. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4822-6_5.

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Mas-Gallic, S. "A Particle in Cell Method for the Isentropic Gas Dynamic System." In Navier—Stokes Equations and Related Nonlinear Problems. Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1415-6_29.

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Georgiev, Svetlin G., and Khaled Zennir. "Boundary Value Problems for Nonlinear First Order Dynamic Equations." In Boundary Value Problems on Time Scales, Volume I. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003173557-1.

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Georgiev, Svetlin G., and Khaled Zennir. "Boundary Value Problems for Nonlinear Second Order Dynamic Equations." In Boundary Value Problems on Time Scales, Volume I. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003173557-5.

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Conference papers on the topic "Nonlinear Dynamic Equations"

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Siranosian, Antranik A., Miroslav Krstic, Andrey Smyshlyaev, and Matt Bement. "Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2532.

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We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and

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Caruntu, Dumitru I. "On Internal Resonance of Nonlinear Nonuniform Beams." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2647.

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This paper reports the case of internal resonance three-to-one with frequency of excitation near natural frequency in the case of bending vibrations of nonuniform cantilever with small damping. The case of nonlinear curvature, moderately large amplitudes, is considered. The method of multiple scales is applied directly to the nonlinear partial-differential equation of motion and boundary conditions. The phase-amplitude equations are analytically determined. Steady-state response is reported.

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Bava, G. P., P. Debernadri, L. A. Lugiato, and F. Castelli. "Dynamic Model for Optical Bistability in Multiple Quantum-Well Structures." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.tdsls66.

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We formulate a set of dynamical equations, which govern the dynamical evolution of optically bistable systems based on Multiple Quantum Well Structures, in conditions of quasi-resonance with an excitonic line. The steady state diagrams indicate the possibility of bistability in this system.

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Xianmin, Zhang, and Guo Xuemei. "Nonlinear Dynamic Performance Analysis of Elastic Linkage Mechanisms." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4206.

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Abstract In this paper, the generalized nonlinear equations of motion for elastic linkage mechanism systems are presented, in which the gross motion and elastic deformation coupling terms and the geometric nonlinearity effects are taken into account. The equations of motion are period and time-varying nonlinear equations. According to the characteristics, solution method for this kind nonlinear equations is investigated, and an efficient closed-form iterative procedure is presented. The effects of geometric nonlinearity on linkage mechanisms are studied. The results of this study are important

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Bélanger, Nicolas, and Pierre-André Bélanger. "Cascadable rms characteristics and average dynamic of pulses in dispersive nonlinear lossy fibers." In Nonlinear Guided Waves and Their Applications. Optica Publishing Group, 1998. http://dx.doi.org/10.1364/nlgw.1998.nsnps.p8.

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More accurate equations describing the propagation law of the three rms parameters in average- soliton regime are presented. These equations are cascadable from a piece of fiber to another making them useful for designing dispersion maps. Finally, the average soliton dynamic is generalized to any pulse shape even if the hyperbolic secant seems to be the optimal case.

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Ru, P., P. K. Jakobsen, and J. V. Moloney. "Nonlocal Adiabatic Elimination in the Maxwell-Bloch Equation." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.mc6.

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Adiabatic elimination is a standard procedure applied to the Maxwell-Bloch laser equations when one variable or more is slaved to the remaining variables. An important case in point is a laser with an extremely large gain bandwidth satisfying the condition γ⊥ ≫ γ||, k where γ⊥ is the polarization dephasing rate, γ|| the de-energization rate and k the cavity damping constant. For example, color center gain media satisfy this criterion and support hundreds of thousands of longitudinal modes in synchronous pumped mode-locking operation. For simple single mode plane wave models the crude adiabatic

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Song, X., and Q. X. Zhang. "Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales." In 2015 International Conference on Electrical, Automation and Mechanical Engineering. Atlantis Press, 2015. http://dx.doi.org/10.2991/eame-15.2015.221.

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Müller, R. "Dynamic Behavior of Directly Modulated Single-Quantum-Well Semiconductor Lasers." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.tdsls86.

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This paper deals theoretically with light emission from GRIN-SCH single-quantum-well diode lasers where the optical transitions between the first subbands (n=1) as well as between the second ones (n=2) are taken into account, see Fig.1. The mathematical model consists of three rate equations describing the time evolution of the carrier concentration N and the photon densities P1, P2 at the frequencies γ1 = E1/h and γ2 = E2/h, Moreover, nonlinear gain suppression depending on P1 and P2 and noise terms are considered too. In addition, algebraic equations are used giving the gain at the two frequ

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Crouch, David D., Diana M. Lininger, and Dana Z. Anderson. "Theory of Bistability and Self-Pulsing in an Optical Ring Circuit Having Saturable Photorefractive Gain, Loss, and Photorefractive Feedback." In Nonlinear Dynamics in Optical Systems. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.dmmpcps483.

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We present a theory for an optical ring circuit in which gain, loss, and feedback are provided by means of refractive-index gratings in photorefractive crystals. Maxwell’s equations and the Kukhtarev charge transport model describe the evolution of the optical fields and the gratings, respectively. Steady-state solutions of the equations exhibit bistability. Dynamic solutions, obtained numerically, exhibit either history-dependent bistability due to the dependence of the feedback coupling element on its past, or self pulsing, depending on the relative speeds of the photorefractive gain and los

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Gudetti, Jacinth Philemon, Seyed Jamaleddin Mostafavi Yazdi, Javad Baqersad, Diane Peters, and Mohammad Ghamari. "Data-Driven Modeling of Linear and Nonlinear Dynamic Systems for Noise and Vibration Applications." In Noise and Vibration Conference & Exhibition. SAE International, 2023. http://dx.doi.org/10.4271/2023-01-1078.

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<div class="section abstract"><div class="htmlview paragraph">Data-driven modeling can help improve understanding of the governing equations for systems that are challenging to model. In the current work, the Sparse Identification of Nonlinear Dynamical systems (SINDy) is used to predict the dynamic behavior of dynamic problems for NVH applications. To show the merit of the approach, the paper demonstrates how the equations of motions for linear and nonlinear multi-degree of freedom systems can be obtained. First, the SINDy method is utilized to capture the dynamic behavior of line

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Reports on the topic "Nonlinear Dynamic Equations"

1

Michalopoulos, C. D. PR-175-420-R01 Submarine Pipeline Analysis - Theoretical Manual. Pipeline Research Council International, Inc. (PRCI), 1985. http://dx.doi.org/10.55274/r0012171.

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Describes the computer program SPAN which computes the nonlinear transient response of a submarine pipeline, in contact with the ocean floor, to wave and current excitation. The dynamic response of a pipeline to impact loads, such as loads from trawl gear of fishing vessels, may also be computed. In addition, thermal expansion problems for submarine pipelines may be solved using SPAN. Beam finite element theory is used for spatial discretization of the partial differential equations governing the motion of a submarine pipeline. Large-deflection, small-strain theory is employed. The formulation

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Hale, Jack, Constantine M. Dafermos, John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada255356.

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Dafermos, Constantine M., John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada271514.

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Archambault, M. R., and C. F. Edwards. Computation of Spray Dynamics by Direct Solution of Moment Transport Equations Inclusion of Nonlinear Momentum Exchange. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada381371.

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Wu, Yingjie, Selim Gunay, and Khalid Mosalam. Hybrid Simulations for the Seismic Evaluation of Resilient Highway Bridge Systems. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, 2020. http://dx.doi.org/10.55461/ytgv8834.

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Bridges often serve as key links in local and national transportation networks. Bridge closures can result in severe costs, not only in the form of repair or replacement, but also in the form of economic losses related to medium- and long-term interruption of businesses and disruption to surrounding communities. In addition, continuous functionality of bridges is very important after any seismic event for emergency response and recovery purposes. Considering the importance of these structures, the associated structural design philosophy is shifting from collapse prevention to maintaining funct

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