Relevant bibliographies by topics / Under-damped Systems

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Under-damped Systems'

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Published: 6 September 2023

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Journal articles on the topic "Under-damped Systems"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Under-damped Systems"

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Qiao, Guandong. "Identification of physical parameters of biological and mechanical systems under whole-body vibration." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5982.

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The identification of the physical parameters (mass, stiffness, and damping) of structural, mechanical, and biomechanical systems is a major challenge in many applications, especially when dealing with old systems and biological systems with heavy damping and where environmental noises are presented. This work presents a novel methodology called eigenvector phase correction (EVPHC) to solve for the physical parameters of structural and biomechanical systems even with the existence of a significant amount of noise. The method was first tested on structural/mechanical systems and showed superior results when compared with an iterative method from the literature. EVPHC was then developed and used to identify the physical parameters of supine humans under vertical whole-body vibration. Modal parameters of fifteen human subjects, in the supine position, were first identified in this work using experimentation under vertical whole-body vibration. EVPHC was then used to solve an inverse modal problem for the identification of the stiffness and damping parameters at the cervical and lumbar areas of supine humans. The results showed that the resulting physical parameters were realistically close to those presented in the literature. The proposed human model was able to predict the time histories of the acceleration at the head, chest, pelvis, and legs very closely to those of the experimental measured values. A scaling methodology is also presented in this work, where an average human model was scaled to an individual subject using the body mass properties.
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Books on the topic "Under-damped Systems"

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Boudreau, Joseph F., and Eric S. Swanson. Nonlinear dynamics and chaos. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0013.

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Simple maps and dynamical systems are used to explore chaos in nature. The discussion starts with a review of the properties of nonlinear ordinary differential equations, including the useful concepts of phase portraits, fixed points, and limit cycles. These notions are developed further in an examination of iterative maps that reveal chaotic behavior. Next, the damped driven oscillator is used to illustrate the Lyapunov exponent that can be used to quantify chaos. The famous KAM theorem on the conditions under which chaotic behavior occurs in physical systems is also presented. The principle is illustrated with the Hénon-Heiles model of a star in a galactic environment and billiard models that describe the motion of balls in closed two-dimensional regions.
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Book chapters on the topic "Under-damped Systems"

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Amarir, Imane, Hamid Mounir, Abdellatif El Marjani, and Zakaria Haji. "Numerical Simulation of Damped Welded Profiles Under Variable Amplitude Loading." In Algorithms for Intelligent Systems, 659–67. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-3246-4_51.

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Amarir, Imane, Hamid Mounir, and Abdellatif El Marjani. "Durability Analysis of Welded Rectangular Profiles Under Damped Loads for Automotive Utilization." In Advanced Intelligent Systems for Sustainable Development (AI2SD’2020), 896–919. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-90639-9_73.

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Iawphniaw, Francis, Samrat Dey, and Shantu Saikia. "Dependence of Particle Current and Diffusion on the System Parameters in a Model Under-damped Inhomogeneous Periodic Potential System." In Springer Proceedings in Physics, 73–83. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5141-0_8.

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Rajasekaran, S. "Free vibration of single-degree-of-freedom systems (under-damped) in relation to structural dynamics during earthquakes." In Structural Dynamics of Earthquake Engineering, 43–67. Elsevier, 2009. http://dx.doi.org/10.1533/9781845695736.1.44.

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"Single Degree of Freedom Forced Vibration System." In Structural Dynamics and Static Nonlinear Analysis From Theory to Application, 41–79. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-4399-3.ch002.

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This chapter concerns the study of forced vibration of a single degree of freedom system, treating undamped and damped system under harmonic, periodic, and arbitrary loading with different cases and examples. Passing by all components of the general solution of an undamped forced system, which are a transient solution, depends only on initial conditions, transient solution due to the load at the end the stationary solution. In this chapter, a study of the dynamic influence factor depends on the ration between load frequency and structure one is presented.
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Bose, Goutam Kumar, Pritam Ghosh, and Debashis Pal. "Analytical and Numerical Modelling of Liquid Penetration in a Closed Capillary." In Process Analysis, Design, and Intensification in Microfluidics and Chemical Engineering, 114–35. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-7138-4.ch004.

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The chapter explores the dynamics of liquid penetration in a closed end vertical capillary. This model is very important for impedance spectroscopy methodology where oxidized porous silicon provides an in vitro medium, and one important criteria of this methodology is the liquid penetration depth inside the silicon pores as the impedance is greatly affected by this penetration depth. This problem is also important in order to understand how the presence of entrapped air inside a micro pore can influence the dynamics of capillary flow. For this purpose, the model is studied both analytically and numerically. In this study, different pore size (500 nm and 2 µm diameter) with equal pore depth (~10 µm) have been used. Finally, the analytical solution is compared with the numerical results. In addition, the linearization of the system is also investigated and found the critical viscosity of which demarcates the over-damped and under-damped regimes. Further, this study is extended by incorporating the dynamic contact angle effects on the meniscus dynamics.
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Koch, Christof. "Linearizing Voltage-Dependent Currents." In Biophysics of Computation. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195104912.003.0016.

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We hinted several times at the fact that a small excitatory synaptic input in the presence of voltage-dependent channels will lead to a local depolarization, followed by a hyperpolarization. Those of us who built our own radios will recognize such an overshooting response as being indicative of so-called RLC circuits which include resistances, capacitances as well as inductances. As a reminder, a linear inductance is defined as a circuit element whose instantaneous I—V relationship is, where L is the inductance measured in units of henry (abbreviated as H). Although neurobiology does not possess any coils or coillike elements whose voltage is proportional to the current change, membranes with certain types of voltage- and time-dependent conductances can behave as (/they contained inductances. We talk of a phenomenological inductance, a phenomenon first described by Cole (1941) and Cole and Baker (1941) in the squid axon (see Cole, 1972). Under certain circumstances, discussed further below, such damped oscillations can become quite prominent. This behavior can be obtained in an entirely linear system, as can be observed when reducing (in numerical simulations) the amplitude of the synaptic input (or step current): even though the voltage excursion around steady-state becomes smaller and smaller, the overshoot persists. It is not due to any amplification inherent in such a membrane but is caused by its time- and voltage-dependent nature. Such a linear membrane, whose constitutive elements do not depend on either voltage or time, and which behaves like a bandpass element, has been called quasi-active (Koch, 1984) to distinguish it from a truly active, that is, nonlinear membrane. In this chapter, we will explain in considerable detail how an inductance-like behavior can arise from these membranes by linearizing the Hodgkin-Huxley equations. Experimentally, this can be done by considering the small-signal response of the squid giant axon and comparing it against the theoretical predicted value, a further test of the veracity of the Hodgkin-Huxley equations, which they passed with flying colors.
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Conference papers on the topic "Under-damped Systems"

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Aravind M. A., K. Rajanna, and Dinesh N. S. "Application of EMPC for under-damped Type-1 systems." In 2017 3rd International Conference on Control, Automation and Robotics (ICCAR). IEEE, 2017. http://dx.doi.org/10.1109/iccar.2017.7942741.

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de la Barra, Bernardo A. Leon, and Magnus Mossberg. "Identification of under-damped second-order systems using finite duration rectangular pulse inputs." In 2007 American Control Conference. IEEE, 2007. http://dx.doi.org/10.1109/acc.2007.4282520.

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Rebolledo-Herrera, Lucio-Fidel, and FV Guillermo Espinosa. "Novel parameter tuned methodology for under-damped stochastic resonance applied to EEG signal enhancement." In 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2016. http://dx.doi.org/10.1109/smc.2016.7844554.

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Dincel, Emre, Ugur Yildirim, and Mehmet Turan Soylemez. "Modeling and control of under-damped second order systems with dead-time and inverse response." In 2013 IEEE International Conference on Control System, Computing and Engineering (ICCSCE). IEEE, 2013. http://dx.doi.org/10.1109/iccsce.2013.6719984.

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Radisavljevic, Verica, and Dobrila Skataric. "Exact Decoupling of Non-Classically Damped Matrix Second-Order Linear Mechanical Systems." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-13056.

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Matrix second-order damped linear dynamic systems are frequently encountered in mechanical, structural, civil, aerospace engineering, and related fields. This class of systems is also obtained by approximating dynamics of systems described by partial differential equations (distributed parameter systems). There are many papers in the engineering literature on analysis and control of matrix second-order linear damped systems. They provide either approximate (simplified) analytical results or accurate numerical results (usually computationally involved). In this paper, we show how to decouple exactly a matrix second-order linear system into scalar second-order subsystems and study exactly the corresponding system dynamics at the subsystem level using simple analytical tools. Conditions are established under which the presented procedure is applicable. An example is included to demonstrate the efficiency of the proposed technique.
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Zhang, Haopeng, and Nathan Schutte. "Performance Study of a Bat Searching Algorithm From System Dynamics Perspective." In ASME 2019 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/dscc2019-9017.

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Abstract In this paper, the performance of a bat searching algorithm is studied from system dynamics point of view. Bat searching algorithm (BA) is a recently developed swarm intelligence based optimization algorithm which has shown great success when solving complicated optimization problems. Each bat in the BA has two main states: velocity and position. The position represents the solution of the optimization problems while the velocity represents the searching direction and step size during each iteration. Due to the nature of the update equations, the dynamics of the bats are formulated as a group of second-order discrete-time systems. In this paper, the performance of the algorithm is analyzed based on the nature of the responses in the second-order systems. The over-damped response, under-damped responses are studied and the parameters requirements are derived. Moreover, unstable scenarios of the bats are also considered when examining the performance of the algorithm. Numerical evaluations are conducted to test different choices of the parameters in the BA.
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Förster, Alwin, Lars Panning-von Scheidt, and Jörg Wallaschek. "Approximate Solution of the Fokker-Planck Equation for a Multi-Degree of Freedom Frictionally Damped Bladed Disk Under Random Excitation." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75755.

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Bladed Disks are subjected to different types of excitations, which cannot in any case be described in a deterministic manner. Fuzzy factors, such as slightly varying airflow or density fluctuation, can lead to an uncertain excitation in terms of amplitude and frequency, which has to be described by random variables. The computation of frictionally damped blades under random excitation becomes highly complex due to the presence of nonlinearities. Only a few publications are dedicated to this particular problem. Most of these deal with systems of only one or two degrees of freedom and use computational expensive methods, like finite element method (FEM) or finite differences method (FDM), to solve the determining differential equation. The stochastic stationary response of a mechanical system is characterized by the joint probability density function (JPDF), which is driven by the Fokker-Planck equation (FPE). Exact stationary solutions of the FPE only exist for a few classes of mechanical systems. This paper presents the application of a semi-analytical Galerkin-type method to a frictionally damped bladed disk under influence of Gaussian white noise (GWN) excitation in order to calculate its stationary response. One of the main difficulties is the selection of a proper initial approximate solution, which is applicable as a weighting function. Comparing the presented results with those from the FDM, Monte-Carlo Simulation (MCS) as well as analytical solutions proves the applicability of the methodology.
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Huang, Jihua, and Masayoshi Tomizuka. "Degraded Mode Vehicle Lateral Control Under Fault in Rear Sensors." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41713.

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This paper is concerned with vehicle lateral control for Automated Highway Systems (AHS) studied as a part of the California PATH (Partners for Advanced Transit and Highways) Program. In the PATH lateral control system, magnetometers are installed under both the front and the rear bumpers of the vehicle; these magnetometers measure the lateral deviation of the vehicle relative to the magnets buried along the centerline of each automated lane. Lateral controllers have been designed and tested successfully provided that there is no fault in magnetometers. It has been argued that these controllers are NOT tolerant to the fault in magnetometers. The focus of this paper is the degraded mode lateral control under fault in rear magnetometers. The aim of the controller design is to accomplish adequate performance with the remaining set of magnetometers: the front magnetometers. The effects of the fault are examined, and the significance of the linear time varying (LTV) property of the front magnetometer based vehicle lateral dynamics is recognized. Popular control methods for LTV systems generally involve gain scheduling by switching between several LTI controllers. Such controllers are complicated and it is difficult to prove the stability of the switching mechanism. To derive a simple, effective LTV controller, feedback linearization is applied to approximately cancel out the time varying terms in the plant and to function as a gain scheduler. However, due to the weakly damped zeros of the plant, feedback linearization with state feedback or matched observer state feedback results in weakly damped internal dynamics. In order to tune the internal dynamics, a mismatched observer is designed based on H-infinity optimal control techniques. Experimental results are presented to show the effectiveness of the controller design.
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Radisavljevic, Verica, Dobrila Skataric, and Wu-Chung Su. "Subsystem Level Optimal Control and Filtering of Non-Classically Damped Matrix Second-Order Linear Mechanical Stochastic Systems." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-13053.

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Matrix second-order damped linear dynamic systems are frequently encountered in mechanical, structural, civil, aerospace engineering, and related fields. In this paper, we show how to optimally control matrix second-order systems using locally optimal Kalman filters corresponding to scalar second-order subsystems and how to find the corresponding filter and linear-quadratic (LQ) controller optimal gains at the subsystem level. The globally optimal linear-quadratic controller and the globally optimal Kalman filter and obtained in terms of locally optimal LQ controllers and locally optimal scalar second-order parallel Kalman filters. Conditions are established under which the presented procedure is applicable. Examples are included to demonstrate the efficiency of the proposed technique.
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Farooq, Umar, and Brian F. Feeny. "Output-Only Modal Analysis of Randomly Excited Systems Using Smooth Orthogonal Decomposition." In ASME 2008 Dynamic Systems and Control Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/dscc2008-2218.

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Modal parameter estimation in terms of natural frequencies and mode shapes is studied using smooth orthogonal decomposition (SOD) for randomly excited vibration systems. This work shows that under certain conditions, the SOD eigenvalue problem formulated from white noise induced response data can be tied to the unforced structural eigenvalue problem, and thus can be used for modal parameter estimation. Using output response ensembles only, the generalized eigenvalue problem is formed to estimate modal frequencies and modal vectors for a sixteen-degree-of-freedom lightly damped vibratory system. The estimated frequencies are compared against system frequencies obtained from the structural eigenvalue problem and estimated modal vectors are checked using the modal assurance criterion. Simulations show that for light damping, satisfactory results are obtained for estimating both system frequencies and modal vectors even in presence of sensor noise.
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