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Gotowe bibliografie tematyczne / Under-damped Systems

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Artykuły w czasopismach

Gotowa bibliografia na temat „Under-damped Systems”

Autor: Grafiati

Data publikacji: 6 września 2023

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Artykuły w czasopismach na temat "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 (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 (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 (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 (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 (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 (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 (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 (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 (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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