Статті в журналах: "Under-damped Systems"

1

Gawthrop, P. J., M. I. Wallace, S. A. Neild, and D. J. Wagg. "Robust real-time substructuring techniques for under-damped systems." Structural Control and Health Monitoring 14, no. 4 (2007): 591–608. http://dx.doi.org/10.1002/stc.174.

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2

Shahruz, S. M., and A. K. Packard. "Approximate Decoupling of Weakly Nonclassically Damped Linear Second-Order Systems Under Harmonic Excitations." Journal of Dynamic Systems, Measurement, and Control 115, no. 1 (March 1, 1993): 214–18. http://dx.doi.org/10.1115/1.2897403.

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A simple and commonly used approximate technique of solving the normalized equations of motion of a nonclassically damped linear second-order system is to decouple the system equations by neglecting the off-diagonal elements of the normalized damping matrix, and then solve the decoupled equations. This approximate technique can result in a solution with large errors, even when the off-diagonal elements of the normalized damping matrix are small. Large approximation errors can arise in lightly damped systems under harmonic excitations when some of the undamped natural frequencies of the system are close to the excitation frequency. In this paper, a rigorous analysis of the approximation error in lightly damped systems is given. Easy-to-check conditions under which neglecting the off-diagonal elements of the normalized damping matrix can result in large approximation errors are presented.

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3

Monsia, M. D., and Y. J. F. Kpomahou. "Simulating Nonlinear Oscillations of Viscoelastically Damped Mechanical Systems." Engineering, Technology & Applied Science Research 4, no. 6 (December 22, 2014): 714–23. http://dx.doi.org/10.48084/etasr.518.

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The aim of this work is to propose a mathematical model in terms of an exact analytical solution that may be used in numerical simulation and prediction of oscillatory dynamics of a one-dimensional viscoelastic system experiencing large deformations response. The model is represented with the use of a mechanical oscillator consisting of an inertial body attached to a nonlinear viscoelastic spring. As a result, a second-order first-degree Painlevé equation has been obtained as a law, governing the nonlinear oscillatory dynamics of the viscoelastic system. Analytical resolution of the evolution equation predicts the existence of three solutions and hence three damping modes of free vibration well known in dynamics of viscoelastically damped oscillating systems. Following the specific values of damping strength, over-damped, critically-damped and under-damped solutions have been obtained. It is observed that the rate of decay is not only governed by the damping degree but, also by the magnitude of the stiffness nonlinearity controlling parameter. Computational simulations demonstrated that numerical solutions match analytical results very well. It is found that the developed mathematical model includes a nonlinear extension of the classical damped linear harmonic oscillator and incorporates the Lambert nonlinear oscillatory equation with well-known solutions as special case. Finally, the three damped responses of the current mathematical model devoted for representing mechanical systems undergoing large deformations and viscoelastic behavior are found to be asymptotically stable.

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4

Nicholson, D. W. "Response Bounds for Nonclassically Damped Mechanical Systems Under Transient Loads." Journal of Applied Mechanics 54, no. 2 (June 1, 1987): 430–33. http://dx.doi.org/10.1115/1.3173032.

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Time-decaying upper bounds are derived for the response of damped linear mechanical systems under impulsive loads and under step loads. The bounds are expressed in terms of the extreme eigenvalues of the symmetric, positive definite constituent system matrices. The system is assumed to exhibit nonclassical damping by which we mean that classical normal modes do not occur: i.e., the modes are coupled (complex). The governing system equation is first reduced to a particular version of “state form” suited for application of the one-sided Lipschitz constant. A formal bound for general transient loads is then presented. This is specialized to the case of impulsive loads. For step loading, an overshoot measure is introduced which generalizes the corresponding notion for single degree-of-freedom systems. A bound is derived for the overshoot and for the settling time of the system. A simple example is given.

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5

Nicholson, David W. "Response Bounds for Damped Linear Mechanical Systems Under Prescribed Motion." Journal of Vibration and Acoustics 109, no. 4 (October 1, 1987): 422–24. http://dx.doi.org/10.1115/1.3269463.

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In earlier investigations, the author used extensions of two theorems of G. Strang to derive bounds on the displacements of a symmetric damped linear mechanical system subject to prescribed periodic forces. This work is extended in the current investigation to obtain bounds under prescribed periodic motions. For prescribed periodic forces, the bounds were expressed in terms of the extreme eigenvalues of several symmetric, positive definite matrices. In contrast, in the current case the bounds also depend on several nonsymmetric matrices. The bounds under prescribed motion are evaluated in an example and comparison is made with an exact result. The results reported here are new.

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6

Novella-Rodríguez, David F., Basilio del Muro-Cuéllar, German Hernandez-Hernández, and Juan F. Marquez-Rubio. "Delayed Model Approximation and Control Design for Under-Damped Systems." IFAC-PapersOnLine 50, no. 1 (July 2017): 1316–21. http://dx.doi.org/10.1016/j.ifacol.2017.08.127.

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7

Cai, G. O., and Y. K. Lin. "Nonlinearly damped systems under simultaneous broad-band and harmonic excitations." Nonlinear Dynamics 6, no. 2 (September 1994): 163–77. http://dx.doi.org/10.1007/bf00044983.

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8

Cox, S. J., and J. Moro. "A Lyapunov Function for Systems Whose Linear Part is Almost Classically Damped." Journal of Applied Mechanics 64, no. 4 (December 1, 1997): 965–68. http://dx.doi.org/10.1115/1.2789007.

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We show that one may construct a Lyapunov function for any classically damped linear system. The explicit nature of the construction permits us to show that it remains a Lyapunov function under both perturbation of the linear part and introduction of a nonlinear term. We apply our findings to a stability analysis of the discrete, as well as continuous, damped mechanical transmission line.

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9

Hu, B., and P. Eberhard. "Response Bounds for Linear Damped Systems." Journal of Applied Mechanics 66, no. 4 (December 1, 1999): 997–1003. http://dx.doi.org/10.1115/1.2791810.

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In this paper response bounds of linear damped systems are reviewed and new response bounds are presented for free vibrations and forced vibrations under impulsive, step, and harmonic excitation. In comparison to the response bounds available in the literature, the ones presented here are not only closer to the exact responses, but are also simpler to compute. Previous bounds are given only on the Euclidean norm of the state vector or the displacement vector. Here, the response bounds are also given on individual coordinates, information which is more meaningful in engineering.

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10

Park, I. W., J. S. Kim, and F. Ma. "Characteristics of Modal Coupling in Nonclassically Damped Systems Under Harmonic Excitation." Journal of Applied Mechanics 61, no. 1 (March 1, 1994): 77–83. http://dx.doi.org/10.1115/1.2901425.

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The normal coordinates of a nonclassically damped system are coupled by nonzero off-diagonal elements of the modal damping matrix. The purpose of this paper is to study the characteristics of modal coupling, which is amenable to a complex representation. An analytical formulation is developed to facilitate the evaluation of modal coupling. Contrary to widely accepted beliefs, it is shown that enhancing the diagonal dominance of the modal damping matrix or increasing the frequency separation of the natural modes need not diminish the effect of modal coupling. The effect of modal coupling may even increase. It is demonstrated that, within the practical range of engineering applications, neither diagonal dominance of the modal damping matrix nor frequency separation of the natural modes would be sufficient for neglecting modal coupling.

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11

Avraam, Tassos P., and Ioannis G. Raftoyiannis. "Stability of weakly-damped systems under follower loads exhibiting Hopf bifurcations." Mechanics Research Communications 36, no. 8 (December 2009): 867–74. http://dx.doi.org/10.1016/j.mechrescom.2009.07.001.

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12

Felszeghy, S. F. "The Development of Natural Modes of Free Vibration for Linear Discrete Systems from the Synchronous Motion Assumption." Journal of Vibration and Acoustics 111, no. 1 (January 1, 1989): 77–81. http://dx.doi.org/10.1115/1.3269827.

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By using the method of separation of variables, or more precisely, the method of searching for synchronous motions, conditions are derived under which a linear discrete viscously damped system exhibits free motions of the form of a product of an amplitude vector and a scalar function of time. These motions are the natural modes of the system. In particular, those conditions are investigated under which some but not all of the modal vectors, or mode shapes, of the damped system coincide with the undamped “classical” normal modes.

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13

Udwadia, Firdaus E., and Ramin S. Esfandiari. "Nonclassically Damped Dynamic Systems: An Iterative Approach." Journal of Applied Mechanics 57, no. 2 (June 1, 1990): 423–33. http://dx.doi.org/10.1115/1.2892007.

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This paper presents a new, computationally efficient, iterative technique for determining the dynamic response of nonclassically damped, linear systems. Such systems often arise in structural and mechanical engineering applications. The technique proposed in this paper is heuristically motivated and iteratively obtains the solution of a coupled set of second-order differential equations in terms of the solution to an uncoupled set. Rigorous results regarding sufficient conditions for the convergence of the iterative technique have been provided. These conditions encompass a broad variety of situations which are commonly met in structural dynamics, thereby making the proposed iterative scheme widely applicable. The method also provides new physical insights concerning the decoupling procedure and shows why previous approximate approaches for uncoupling nonclassically damped systems have led to large inaccuracies. Numerical examples are presented to indicate that, even under perhaps the least ideal conditions, the technique converges rapidly to provide the exact time histories of response.

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14

Wang, Zhihao, Yuxiang Zhou, Chuangjie Fang, and Jingwen Zhang. "Stochastic Optimization and Sensitivity Analysis of the Combined Negative Stiffness Damped Outrigger and Conventional Damped Outrigger Systems Subjected to Nonstationary Seismic Excitation." Structural Control and Health Monitoring 2023 (February 8, 2023): 1–22. http://dx.doi.org/10.1155/2023/4024741.

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In recent years, various kinds of damped outrigger systems, particularly with the negative stiffness devices, have been shown to effectively suppress excessive vibration induced by earthquake and wind. To gain insight into such systems, this paper proposes a stochastic optimization method to investigate optimal configurations of combined negative stiffness damped outriggers (NSDOs) and conventional damped outriggers (CDOs) subjected to nonstationary stochastic seismic excitation. The simplified analysis model of various combinations of damped outriggers is developed, and the state-space representation of outrigger systems is then formulated. The nonstationary seismic excitation is modeled as a uniformly modulated stationary Gaussian process with a time-modulating function following Clough–Penzien spectrum, and combining equations of motions of outrigger systems and seismic excitation gives rise to the augmented state-space representation of structure-damper-excitation and subsequently the differential Lyapunov equation. The optimal designs of damped outriggers are defined via the solution of the differential Lyapunov equation. The multiobjective optimization with Pareto optimal fronts is adopted to deal with conflicting objectives between harmful interstory drift and floor absolute acceleration. The sensitivity of negative stiffness devices on optimal objectives is also investigated. The optimal designs are further examined under real typical and near-fault earthquake records. The results demonstrate the efficacy of the proposed method and provide insight into the systems subjected to nonstationary seismic excitation. While the purely NSDO systems could have better performance with adequate negative stiffness devices, the proposed combined NSDO and CDO systems prove to be more effective with limited negative stiffness devices and thus provide more design flexibilities tailored to different application situations.

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15

Kounadis, A. N., and J. Raftoyiannis. "Dynamic stability criteria of nonlinear elastic damped/undamped systems under step loading." AIAA Journal 28, no. 7 (July 1990): 1217–23. http://dx.doi.org/10.2514/3.25197.

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16

Ghorai, Prasenjit, Somanath Majhi, Venkata Ramana Kasi, and Saurabh Pandey. "Parameter Identification of Delayed Under-Damped Systems Using On-Line Relay Autotuning." IEEE Transactions on Circuits and Systems II: Express Briefs 66, no. 7 (July 2019): 1197–201. http://dx.doi.org/10.1109/tcsii.2018.2876476.

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17

Aravind, M. A., N. S. Dinesh, and K. Rajanna. "Adaptive experience mapping based predictive controller for under-damped type 1 systems." International Journal of Dynamics and Control 6, no. 4 (January 27, 2018): 1719–36. http://dx.doi.org/10.1007/s40435-018-0396-0.

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18

Fu, Yaomin, and Sheldon Cherry. "Simplified seismic code design procedure for friction-damped steel frames." Canadian Journal of Civil Engineering 26, no. 1 (February 1, 1999): 55–71. http://dx.doi.org/10.1139/l98-043.

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This paper describes the development of a proposed seismic design procedure for friction-damped steel structures, which employs the lateral force provisions used in many modern building codes. Closed-form expressions are first derived that relate the normalized response of a single degree of freedom friction-damped system with the system parameters, such as bracing stiffness ratio, damper slip ratio, and frame member ductility. A parametric analysis is then used to reveal that the seismic displacement of a friction-damped frame can be controlled by combining the frame stiffness with the bracing stiffness of the friction damper component, while the seismic force can be controlled by the damper slip force. A force modification factor (equivalent to the code R-factor) and displacement estimate for a friction-damped system are next determined. The single degree of freedom results are subsequently used to develop expressions for dealing with the multi degree of freedom situation, which permits the seismic lateral force design procedure adopted by many current building codes to be applied to friction-damped systems. The proposed procedure allows the frame response to be controlled so that the displacement can be limited to small magnitudes and the overall structural shape to an essentially straight-line deformation. Design examples illustrate that friction-damped frame systems are economical and offer a better overall response performance than that provided by conventional systems under the design earthquake.Key words: passive energy dissipation system, friction damper, steel frame, design procedure, static analysis.

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19

Khound, Parthib, Peter Will, Antoine Tordeux, and Frank Gronwald. "The Over-Damped String Stability Condition for a Platooning System." SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL 3, no. 1 (June 30, 2023): 12–19. http://dx.doi.org/10.52846/stccj.2023.3.1.45.

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The over-damped string stability criterion is a very strong stability condition that not only addresses the stability in a stricter sense but also adequately captures the safety performance of a platoon. However, the mathematical representation of this criterion is incomplete in the literature. Here, this representation is completely described. Moreover, this article presents the mathematical test method to evaluate this stability condition for linear or linearized systems from the transfer function. The classical sting stability condition does not address the transient undesired convergent dynamics of a platoon, such as over-shooting, under-shooting or damped oscillating dynamics. This paper demonstrates that the over-damped string stability characteristic significantly attenuates these undesired convergent dynamics in the upstream direction. Thus, the advantage of this condition over the classical criterion for linear system is clarified theoretically and by simulation. Later, the numerical method to analyze the over-damped string stability criterion for nonlinear systems is discussed. Additionally, numerical simulations of an over-damped string stable adaptive cruise control (ACC) vehicle model are compared with that of some experimental test results on platoons of commercially implemented ACC equipped vehicles.

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20

Santhosh, B., S. Narayanan, and C. Padmanabhan. "Nonlinear Dynamics of Shrouded Turbine Blade System with Impact and Friction." Applied Mechanics and Materials 706 (December 2014): 81–92. http://dx.doi.org/10.4028/www.scientific.net/amm.706.81.

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Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state in the tangential direction, the interface also undergoes intermittent separation in the normal direction. The problem can thus be treated as a combination of impact and friction. In this work, the dynamics of dry friction damped oscillators which are representative models of dry friction damped bladed system is investigated. A one dimensional contact model which is capable of modeling the interface under constant and variable normal load is used. The steady state periodic solutions are obtained by multi - harmonic balance method (MHBM). Frequency response plots are generated for different values of normal load using the arc length continuation procedure. The MHBM solutions are validated using numerical integration. A single degree of freedom (dof) model under constant normal load with constant and variable friction coefficients, a dry friction damped two dof system under constant normal load and a two dof system under variable normal load are investigated. In the presence of variable normal load, the system shows multivalued frequency response and jump phenomenon. The optimal value of the normal load which gives minimum resonant response is also obtained.

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21

SUN, MIN, and JOSÉ-LUIS MENALDI. "Monotone Control of a Damped Oscillator Under Random Perturbations." IMA Journal of Mathematical Control and Information 5, no. 3 (1988): 169–86. http://dx.doi.org/10.1093/imamci/5.3.169.

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22

Abbas, Hussain, and Huang Hai. "Weight Size Determined Variable Step Size LMS Method for Identifying under Damped Systems." Applied Mechanics and Materials 511-512 (February 2014): 238–41. http://dx.doi.org/10.4028/www.scientific.net/amm.511-512.238.

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This paper presents a novel improvement to the LMS method which seeks to set different step sizes to different weights depending on their relative sizes. Sample numerical simulations carried out to identify different plant configurations shows that the proposed method provides an early convergence and thus identifies the plant earlier.

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23

Zabet, K., J. A. Rossiter, R. Haber, and M. Abdullah. "Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra." ISA Transactions 71 (November 2017): 403–14. http://dx.doi.org/10.1016/j.isatra.2017.08.002.

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24

Chikrii, Greta, and Ksenia Rastvorova. "One Game Problem for Oscillatory Systems." Cybernetics and Computer Technologies, no. 1 (March 30, 2021): 5–15. http://dx.doi.org/10.34229/2707-451x.21.1.1.

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The paper concerns the linear differential game of approaching a cylindrical terminal set. We study the case when classic Pontryagin’s condition does not hold. Instead, the modified considerably weaker condition, dealing with the function of time stretching, is used. The latter allows expanding the range of problems susceptible to analytical solution by the way of passing to the game with delayed information. Investigation is carried out in the frames of Pontryagin’s First Direct method that provides hitting the terminal set by a trajectory of the conflict-controlled process at finite instant of time. In so doing, the pursuer’s control, realizing the game goal, is constructed on the basis of the Filippov-Castaing theorem on measurable choice. The outlined scheme is applied to solving the problem of pursuit for two different second-order systems, describing damped oscillations. For this game, we constructed the function of time stretching and deduced conditions on the game parameters, ensuring termination of the game at a finite instant of time, starting from arbitrary initial states and under all admissible controls of the evader. Keywords: differential game, time-variable information delay, Pontryagin’s condition, Aumann’s integral, principle of time stretching, Minkowski’ difference, damped oscillations.

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25

Huang, Kejie, Xiaoqing Zhang, and Xiang Xiao. "Modelling of the corona characteristics under damped oscillation impulses." IET Generation, Transmission & Distribution 10, no. 7 (May 5, 2016): 1648–53. http://dx.doi.org/10.1049/iet-gtd.2015.0903.

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26

Phuc, Vu Duc, Van-The Tran, and Nguyen Van Quyen. "A novel design of the dynamic vibration absorbers for damped main systems under torsional excitation using least squares estimation of the equivalent linearization method." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 1 (June 4, 2018): 60–70. http://dx.doi.org/10.1177/1464419318779339.

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Torsional vibration usually occurs in the working process of machines and equipment such as in transmission drive and working shaft of machine tool. To reduce this vibration, the dynamic balancing method and dual mass flywheel systems are applied. There are fewer researches that used the dynamic vibration absorber for reducing the torsional vibration. However, an analytical solution for designing the optimal parameters of dynamic vibration absorbers attached to the damped main system is found to be difficult and complicated. This paper proposes a novel idea to approximately replace an original damped main system by an equivalent undamped system using the least squares estimation of equivalent linearization method. An explicit closed-form expression of the optimal damping ratio and tuning parameters of dynamic vibration absorber are determined for the undamped main system under torsional excitation. The expressions are quite simple and have effective practical applications. Numerical results for time and frequency responses of the system are presented to reveal stronger effect and accuracy of the proposed solution on the damped main system. It is observed that the torsional vibration of the damped main system has been reduced significantly also in the resonant region. The proposed expressions of the optimal parameters are powerful tools for design dynamic vibration absorber to reduce the torsional vibration of rotary system such as the transmission and working shafts, etc.

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27

Zhang, Weiguo, Lanyun Bian, and Yan Zhao. "Qualitative analysis and solutions of bounded travelling waves for the fluidized-bed modelling equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 2 (March 30, 2010): 241–57. http://dx.doi.org/10.1017/s030821050900064x.

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We apply the theory of planar dynamical systems to carry out a qualitative analysis for the planar dynamical system corresponding to the fluidized-bed modelling equation. We obtain the global phase portraits of this system under various parameter conditions and the existence conditions of bounded travelling-wave solutions of this equation. According to the discussion on relationships between the behaviours of bounded travelling-wave solutions and the dissipation coefficients ε and δ, we find a critical value λ0 for arbitrary travelling-wave velocity υ. This equation has a unique damped oscillatory solution as ∥ε + δυ∥ < λ0 and ∥ε + δυ∥ ≠ 0, while it has a unique monotone kink profile solitary-wave solution as ∥ε + δυ∥ > λ0. By means of the undetermined coefficients method, we obtain the exact bell profile solitary-wave solution and monotone kink profile solitary-wave solution. Meanwhile, we obtain the approximate damped oscillatory solution. We point out the positions of these solutions in the global phase portraits. Finally, based on integral equations that reflect the relationships between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate damped oscillatory solutions are presented.

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28

Masri, S. F., A. G. Chassiakos, and T. K. Caughey. "Identification of Nonlinear Dynamic Systems Using Neural Networks." Journal of Applied Mechanics 60, no. 1 (March 1, 1993): 123–33. http://dx.doi.org/10.1115/1.2900734.

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A procedure based on the use of artificial neural networks for the identification of nonlinear dynamic systems is developed and applied to the damped Duffing oscillator under deterministic excitation. The “generalization” ability of neural networks is invoked to predict the response of the same nonlinear oscillator under stochastic excitations of differing magnitude. The analogy between the neural network approach and a qualitatively similar nonparametric identification technique previously developed by the authors is illustrated. Some of the computational aspects of identification by neural networks, as well as their fault-tolerant nature, are discussed. It is shown that neural networks provide high-fidelity mathematical models of structure-unknown nonlinear systems encountered in the applied mechanics field.

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29

Shen, Jing-Chung. "NEW TUNING METHOD FOR PID CONTROL OF A PLANT WITH UNDER-DAMPED RESPONSE." Asian Journal of Control 2, no. 1 (October 22, 2008): 31–41. http://dx.doi.org/10.1111/j.1934-6093.2000.tb00143.x.

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30

Filiatrault, A., and S. Cherry. "Performance Evaluation of Friction Damped Braced Steel Frames under Simulated Earthquake Loads." Earthquake Spectra 3, no. 1 (February 1987): 57–78. http://dx.doi.org/10.1193/1.1585419.

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Анотація:

This paper presents the results obtained from tests of a new friction damping system, which has been proposed in order to improve the response of steel Moment Resisting Frames (MRF) and Braced Moment Resisting Frames (BMRF) during severe earthquakes. The system consists of a mechanism containing brake lining pads introduced at the intersection of frame cross-braces. Seismic tests of a three storey Friction Damped Braced Frame (FDBF) model were performed on an earthquake simulator table. The experimental results are compared with the findings of an inelastic time-history dynamic analysis. The results clearly indicate the superior performance of the FDBF compared to conventional building systems.

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31

Meng, Fan Wei, Zhen He, Zu Yu Yu, and Li Hua Wang. "Based on the PS/T Method Control Design of Flexible Systems." Applied Mechanics and Materials 236-237 (November 2012): 370–77. http://dx.doi.org/10.4028/www.scientific.net/amm.236-237.370.

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The lightly damped resonant poles of flexible system increased norm of coprime factor perturbation, which reduced robust of system after loop shaping design. This paper proposes approaches considering the performance of constraints, to select performance weight function through disturbance attenuation and to adjust the complementary sensitivity weight function through design index. The flexible satellite's attitude control demonstrates that the two approaches are able to rapidly select weight function under ensuring the system's robust and have the ability to depress disturbance.

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32

Shahruz, S. M., and G. Langari. "Closeness of the Solutions of Approximately Decoupled Damped Linear Systems to Their Exact Solutions." Journal of Dynamic Systems, Measurement, and Control 114, no. 3 (September 1, 1992): 369–74. http://dx.doi.org/10.1115/1.2897357.

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The simplest technique of decoupling the normalized equations of motion of a linear nonclassically damped second-order system is to neglect the off-diagonal elements of the normalized damping matrix. In this paper, the error introduced in the system response due to this decoupling technique is studied. Conditions are derived under which the solution of an approximately decoupled system is “close” to the exact solution of the system.

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33

Cenedese, Mattia, and George Haller. "How do conservative backbone curves perturb into forced responses? A Melnikov function analysis." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2234 (February 2020): 20190494. http://dx.doi.org/10.1098/rspa.2019.0494.

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Анотація:

Weakly damped mechanical systems under small periodic forcing tend to exhibit periodic response in a close vicinity of certain periodic orbits of their conservative limit. Specifically, amplitude-frequency plots for the conservative limit have often been noted, both numerically and experimentally, to serve as backbone curves for the near resonance peaks of the forced response. In other cases, such a relationship between the unforced and forced response was not observed. Here, we provide a systematic mathematical analysis that predicts which members of conservative periodic orbit families will serve as backbone curves for the forced–damped response. We also obtain mathematical conditions under which approximate numerical and experimental approaches, such as energy balance and force appropriation, are justifiable. Finally, we derive analytic criteria for the birth of isolated response branches (isolas) whose identification is otherwise challenging from numerical continuation.

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34

HUANG, DEBIN. "BREATHER COMPETITION AND PULSE ORBITS IN THE DAMPED DRIVEN SINE–GORDON EQUATION." International Journal of Bifurcation and Chaos 14, no. 07 (July 2004): 2363–73. http://dx.doi.org/10.1142/s0218127404010825.

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The generalized asymptotic inertial manifold (GAIM) of the damped driven Sine–Gordon equation is put forward to govern the long-term behavior of the full partial differential equation (PDE). We then study qualitatively the ordinary differential equation (ODE) by the singular perturbation-theory, which results from restricting the damped driven Sine–Gordon equation to its GAIM. Firstly an analytical criterion for the existence of the homoclinic orbit resulting in chaos is given. Further, the existence of the pulse orbits is showed under the same parametric values as those used in the previous numerical experiments. In our viewpoint these results reflect just the breather competition behavior observed numerically in the Sine–Gordon equation. By comparing with the earlier results obtained in the two-mode Fourier truncation system of the damped driven Sine–Gordon equation, we think that a reasonable discretization reduction from PDE to ODE is very important in the study of dynamics in the infinite dimensional dynamical systems.

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35

Güneyisi, Esra Mete, Mario D'Aniello, and Raffaele Landolfo. "Seismic Upgrading of Steel Moment-Resisting Frames by Means of Friction Devices." Open Construction and Building Technology Journal 8, no. 1 (December 31, 2014): 289–99. http://dx.doi.org/10.2174/1874836801408010289.

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In recent decades, several passive energy dissipation systems have been conceived in order to minimize the damage in structural and non-structural components of either new or existing buildings. In this study, the use of friction damped tension-compression diagonal braces for seismic upgrading of a steel moment resisting frames is investigated. To this aim, nonlinear time history analyses have been carried out on a set of representative frames with and without friction damped braces. In the nonlinear time history analyses, two sets of natural accelerograms compatible with seismic hazard levels of 10% and 2% probability of exceedance in 50 years have been considered. Under these records, the structural response has been comparatively investigated in terms of the maximum inter-storey drift ratio, maximum storey acceleration, residual drift ratio and displacement demand for the friction device. The results clearly highlighted that the application of friction damped braces allows reducing the damages to the main structural elements, thus significantly improving the seismic behaviour of the frame.

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36

Shahruz, S. M., and A. K. Packard. "Large errors in approximate decoupling of nonclassically damped linear second-order systems under harmonic excitations." Dynamics and Control 4, no. 2 (April 1994): 169–83. http://dx.doi.org/10.1007/bf01985940.

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37

Allawi, Abbas Abd Elmajeed, and Amneh Hamid Al Mukhtar. "The Use of the Artificial Damped Outrigger Systems in Tall R.C Buildings Under Seismic Loading." Journal of Engineering 22, no. 4 (April 1, 2016): 30–49. http://dx.doi.org/10.31026/j.eng.2016.04.03.

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This paper studies the combination of fluid viscous dampers in the outrigger system to add supplementary damping into the structure, which purpose to remove the dependability of the structure to lower variable intrinsic damping. This optimizes the accuracy of the dynamic response and by providing higher level of damping, basically minimizes the wanted stiffness of the structure while at the same time optimizing the achievement. The modal considered is a 36 storey square high rise reinforced concrete building. By constructing a discrete lumped mass model and using frequency-based response function, two systems of dampers, parallel and series systems are studied. The maximum lateral load at the top of the building is calculated, and this load will be applied at every floor of the building, giving a conservative solution. For dynamic study Response Spectrum Analysis was conducted and the behavior of the building was determined considering response parameters. MATLAB software, has been used in the dynamic analysis for three modes. For all modes, it is observed that the parallel system of dampers result in lower amplitude of vibration and achieved more efficiently compared to the damper is in series, until the parallel system arrives 100% damping for mode three.

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38

Greco, Rita, and Francesco Trentadue. "Structural Reliability Sensitivities under Nonstationary Random Vibrations." Mathematical Problems in Engineering 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/426361.

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Response sensitivity evaluation is an important element in reliability evaluation and design optimization of structural systems. It has been widely studied under static and dynamic forcing conditions with deterministic input data. In this paper, structural response and reliability sensitivities are determined by means of the time domain covariance analysis in both classically and nonclassically damped linear structural systems. A time integration scheme is proposed for covariance sensitivity. A modulated, filtered, white noise input process is adopted to model the stochastic nonstationary loads. The method allows for the evaluation of sensitivity statistics of different quantities of dynamic response with respect to structural parameters. Finally, numerical examples are presented regarding a multistorey shear frame building.

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39

Ng, C. S., and A. Bhattacharjee. "Landau Modes are Eigenmodes of Stellar Systems in the Limit of Zero Collisions." Astrophysical Journal 923, no. 2 (December 1, 2021): 271. http://dx.doi.org/10.3847/1538-4357/ac31ae.

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Abstract We consider the spectrum of eigenmodes in a stellar system dominated by gravitational forces in the limit of zero collisions. We show analytically and numerically using the Lenard–Bernstein collision operator that the Landau modes, which are not true eigenmodes in a strictly collisionless system (except for the Jeans unstable mode), become part of the true eigenmode spectrum in the limit of zero collisions. Under these conditions, the continuous spectrum of true eigenmodes in a collisionless system, also known as the Case–van Kampen modes, is eliminated. Furthermore, because the background distribution function in a weakly collisional system can exhibit significant deviations from a Maxwellian distribution function over long times, we show that the spectrum of Landau modes can change drastically even in the presence of slight deviations from a Maxwellian, primarily through the appearance of weakly damped modes that may be otherwise heavily damped for a Maxwellian distribution. Our results provide important insights for developing statistical theories to describe thermal fluctuations in a stellar system, which are currently a subject of great interest for N-body simulations as well as observations of gravitational systems.

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40

Terushkin, Maria, and Emilia Fridman. "Sampled-data observers for semilinear damped wave equations under spatially sampled state measurements." Automatica 106 (August 2019): 150–60. http://dx.doi.org/10.1016/j.automatica.2019.04.044.

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41

Dutta, Chitra, Anjan K. Dasgupta, and Jyotirmoy Das. "Near-equilibrium instabilities in closed chemical systems under nonideal conditions. 3. Damped oscillation in ionic environment." Journal of Physical Chemistry 93, no. 20 (October 1989): 7233–36. http://dx.doi.org/10.1021/j100357a040.

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42

Vitaliani, Renato V., Alessandro M. Gasparini, and Anna V. Saetta. "Finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading." International Journal of Solids and Structures 34, no. 19 (July 1997): 2497–516. http://dx.doi.org/10.1016/s0020-7683(96)00115-1.

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43

Yang, B., and C. A. Tan. "Transfer Functions of One-Dimensional Distributed Parameter Systems." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 1009–14. http://dx.doi.org/10.1115/1.2894015.

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Distributed parameter systems describe many important physical processes. The transfer function of a distributed parameter system contains all information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. This paper presents a new method for evaluating transfer functions for a class of one-dimensional distributed parameter systems. The system equations are cast into a matrix form in the Laplace transform domain. Through determination of a fundamental matrix, the system transfer function is precisely evaluated in closed form. The method proposed is valid for both self-adjoint and non-self-adjoint systems, and is extremely convenient in computer coding. The method is applied to a damped, axially moving beam with different boundary conditions.

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44

Tran, Thanh H., Quang P. Ha, and Hung T. Nguyen. "Robust Non-Overshoot Time Responses Using Cascade Sliding Mode-PID Control." Journal of Advanced Computational Intelligence and Intelligent Informatics 11, no. 10 (December 20, 2007): 1224–31. http://dx.doi.org/10.20965/jaciii.2007.p1224.

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Overshoot is a serious problem in automatic control systems. This paper presents a new method for elimination of the step response overshoot in a conventional PID-controlled system and enhancement of its robustness by cascading a sliding mode controller in the outer loop. The idea is first to use the cascade control principle to model the under-damped system under PID control with a second-order system. Then, by making use of the sliding mode control outer loop, a robust, reduced-order response can be obtained to suppress the control overshoot. The proposed approach can also deal with time delay systems. Its validity is verified through simulation for some dynamic systems subject to highly nonlinear uncertainties, where overshoot remains an issue.

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45

Asami, Toshihiko, Osamu Nishihara, and Amr M. Baz. "Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems." Journal of Vibration and Acoustics 124, no. 2 (March 26, 2002): 284–95. http://dx.doi.org/10.1115/1.1456458.

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H ∞ and H2 optimization problems of the Voigt type dynamic vibration absorber (DVA) are classical optimization problems, which have been already solved for a special case when the primary system has no damping. However, for the general case including a damped primary system, no one has solved these problems by algebraic approaches. Only the numerical solutions have been proposed until now. This paper presents the analytical solutions for the H∞ and H2 optimization of the DVA attached to the damped primary systems. In the H∞ optimization the DVA is designed such that the maximum amplitude magnification factor of the primary system is minimized; whereas in the H2 optimization the DVA is designed such that the squared area under the response curve of the primary system is minimized. We found a series solution for the H∞ optimization and a closed-form algebraic solution for the H2 optimization. The series solution is then compared with the numerical solution in order to check the accuracy in connection with the truncation error of the series. The exact solution presented in this paper is too complicated to handle by a hand-held calculator, so we proposed an approximate solution for the practical object.

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46

Yang, Yue, Xin Zhao, Weixing Shi, and Jiayue Li. "Optimal Design of Mega-Frame Core Wall Structures Equipped with Viscous Damped Outriggers for Human Comfort Performance under Wind Loading." Shock and Vibration 2021 (May 31, 2021): 1–21. http://dx.doi.org/10.1155/2021/6673682.

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Megatall and supertall buildings often adopt megastructure systems characterized by secondary structure systems, and the serviceability problem caused by wind-induced vibrations often becomes the dominant factor in the structural design. Because the deformation of a supertall building usually presents bending characteristics, a viscous damped outrigger can reduce the wind-induced vibration of a supertall building with the installation of a small number of viscous dampers. However, time history analysis of the prototype model considering the nonlinear characteristics of viscous dampers is time-consuming, which is not conducive for iterative design optimization. Additionally, the conventional simplified model composed of one cantilever beam cannot be used for the analysis and design of a viscous damped outrigger. In this study, a simplified wind-induced vibration prediction model is proposed based on the mechanical characteristics of megastructures. This simplified model is a plane model that includes both core walls and frames whose member size can be extracted from the original structure. Parametric analysis shows that the simplified model has high acceleration prediction accuracy. An optimal design method combined with the simplified model, which aims to minimize the damped outrigger system cost, is proposed. A 600-m supertall building is presented as a case study. The accuracy and effectiveness of the simplified model and the optimal design method proposed in this study are illustrated. Thus, applying this optimal design method in combination with the simplified model can save significant analysis and design time and is conducive to the application of viscous damped outriggers in practical engineering.

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47

Narayanan, S., and S. C. S. Yim. "Modeling and Identification of a Nonlinear SDOF Moored Structure, Part 1—Hydrodynamic Models and Algorithms." Journal of Offshore Mechanics and Arctic Engineering 126, no. 2 (May 1, 2004): 175–82. http://dx.doi.org/10.1115/1.1710875.

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The highly nonlinear responses of compliant ocean structures characterized by a large-geometry restoring force and coupled fluid-structure interaction excitation are of great interest to ocean and coastal engineers. Practical modeling, parameter identification, and incorporation of the inherent nonlinear dynamics in the design of these systems are essential and challenging. The general approach of a nonlinear system technique using very simple models has been presented in the literature by Bendat. In Part 1 of this two-part study, two specific 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 reverse multiple-input/single-output (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 a specific experimental submerged-sphere mooring system under ocean waves exhibiting such highly nonlinear response behaviors. In Part 2, using the measured input wave and output system response data, the algorithms derived based on the MI/SO linear analysis of the reverse dynamic systems are applied to identify the properties of the highly nonlinear system. Practical issues on the application of the R-MI/SO technique based on limited available experimental data are addressed.

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48

Gharra, Kamyar, Karen Khanlari, Jafar Asgari, and Mohammad. "A Simplified Matrix Analysis Approach to Multi Storey Buildings Involving a Friction Damper." Slovak Journal of Civil Engineering 29, no. 3 (September 1, 2021): 1–8. http://dx.doi.org/10.2478/sjce-2021-0015.

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Abstract Damping through friction tends to be one of the most efficient methods to suppress damage to structures from earthquakes. Realizing robust structures is therefore highly dependent on designing for the dynamic forces of friction- damped structures and exploring their reliability against natural disasters. This paper presents a simplified matrix analysis algorithm for multi-storey friction- damped buildings. We have analyzed the behavior of friction- damped systems more accurately by modeling the master-slave degree of freedom of the joints. First, the formulation of the problem is discussed, and a condensed general equation is derived. Then, an end- to- end solution is proposed to find the responses of structures. The displacement response of each storey has been carried out in both condensed and non-condensed general equations, and the results clearly show the accuracy of the proposed method. The numerical analysis and the results of the simulation of various friction- damped structures depicts the proposed approach consists with the commercial finite element method and is applicable for the analysis various types of structures. It is noted that the acceleration and displacement responses of the structures investigated under the proposed method and the traditional finite element method are so consistent that only a 1.5% difference is observed. Moreover, as a result of the proper allocation of degrees of freedom during the analysis, this method yields a reduction in computational costs especially in large buildings.

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49

Kounadis, A. N. "Chaoslike phenomena in the non-linear dynamic stability of discrete damped or undamped systems under step loading." International Journal of Non-Linear Mechanics 26, no. 3-4 (January 1991): 301–11. http://dx.doi.org/10.1016/0020-7462(91)90060-7.

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50

Chu, Zhaobi, Yuanyuan Pan, Haiyan Tang, Min Zhu, and Xueping Dong. "A Robust Direct Parameter Identification of Exponentially Damped Low-Frequency Oscillation in Power Systems." Journal of Sensors 2020 (August 1, 2020): 1–11. http://dx.doi.org/10.1155/2020/2315610.

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Low-frequency oscillations in power systems can be modeled as an exponentially damped sinusoid (EDS) signal. Its frequency, damping factor, and amplitude are identified by the robust algorithm proposed in this paper. Under the condition of no noise, the exponentially convergent property of the proposed identification is proved by the use of time scale change, variable transformation, slow integral manifold, averaging method, and Lyapunov stability theorem in sequence. Under the condition of bounded additive noise, the antinoise performance of the identification of each parameter is investigated by the perturbed system theorem and error synthesis principle. The robustness of the proposed method is embodied in the following aspects: the exponential convergence for EDS signal with a wide range of frequency, especially with a rather low frequency; the boundary values of identification errors resulting from high-frequency sinusoidal noise of both frequency and damping factor can be adjusted by tuning the design parameters; and the different effects of the four design parameters on tracking performance and antinoise performance of each parameter identification. Simulation results demonstrate the performance of the algorithm and validate the conclusions.

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