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Nonlinear Dynamics, 2021
Vortex-induced vibrations are one of the major factors in fatigue failure of power transmission lines and can be mitigated using vibration absorbers in the form of Stockbridge dampers. Since power transmission lines play an important role in modern infrastructure, a thorough understanding of the nonlinear dynamical interactions between conductors ...
Sunit K. Gupta +2 more
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Vortex-induced vibrations are one of the major factors in fatigue failure of power transmission lines and can be mitigated using vibration absorbers in the form of Stockbridge dampers. Since power transmission lines play an important role in modern infrastructure, a thorough understanding of the nonlinear dynamical interactions between conductors ...
Sunit K. Gupta +2 more
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Nonlinear Vibration of Cylindrical Shells
AIAA Journal, 1975The large amplitude vibrations of a thin-walled cylindrical shell are analyzed using the Donnell's shallow-shell equations. A perturbation method is applied to reduce the nonlinear partial differential equations into a system of linear partial differential equations.
Chen, Jay C., Babcock, Charles D.
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Localized Nonlinear Vibrations
2014The description of various phenomena in solid state physics, the physics of waves and vibrations, biophysics, and engineering is based on models of (quasi-one-dimensional) molecular lattice dynamics. The study of linear quasi-periodic structures has allowed the explanation of many properties of systems consisting of a large number of interacting ...
Lev N. Lupichev +2 more
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Nonlinear Forced Vibrations of Beams
Journal of Applied Mechanics, 1985An iterative procedure for computing periodic solutions of nonlinear vibrating beams is presented. The nonlinear partial differential equation is replaced by a coupled system of equations. The contraction mapping principle is then applied to generate a method of successive approximations.
Countryman, M., Kannan, R.
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Applied Mathematics and Computation, 1996
This note is concerned with the approximate solution of initial value problems for nonlinear second-order equations of type: \(u''+ \alpha g(u, u')+ \beta h(u)= f(t)\). In physical terms, these equations arise in nonlinear oscillations where \(g\) and \(h\) represent the damping and the restoring forces and \(f\) the external force. The author proposes
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This note is concerned with the approximate solution of initial value problems for nonlinear second-order equations of type: \(u''+ \alpha g(u, u')+ \beta h(u)= f(t)\). In physical terms, these equations arise in nonlinear oscillations where \(g\) and \(h\) represent the damping and the restoring forces and \(f\) the external force. The author proposes
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Nonlinear vibrations of buried landmines
The Journal of the Acoustical Society of America, 2005The seismo-acoustic method is one of the most promising emerging techniques for the detection of landmines. Numerous field tests have demonstrated that buried landmines manifest themselves at the surface through linear and nonlinear responses to acoustic/seismic excitation. The present paper describes modeling of the nonlinear response in the framework
Dimitri, Donskoy +3 more
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Vibrational control of nonlinear systems: Vibrational stabilizability
IEEE Transactions on Automatic Control, 1986In this paper, the theory of vibrational stabilizability for nonlinear systems is developed. Criteria for stabilizability of nonlinear systems by linear multiplicative vibrations, by almost periodic forcing and by vector additive vibrations. It is shown that, unlike a linear system where only t-stabilizability may take place, in the nonlinear situation
Bellman, Richard E. +2 more
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2014
Nonlinear systems have a range of behaviour not seen in linear vibrating systems. In this chapter the phenomena associated with nonlinear vibrating systems are described in detail. In the absence of exact solutions, the analysis of nonlinear systems is usually undertaken using approximate analysis, numerical simulations and geometrical techniques. This
David Wagg, Simon Neild
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Nonlinear systems have a range of behaviour not seen in linear vibrating systems. In this chapter the phenomena associated with nonlinear vibrating systems are described in detail. In the absence of exact solutions, the analysis of nonlinear systems is usually undertaken using approximate analysis, numerical simulations and geometrical techniques. This
David Wagg, Simon Neild
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Nonlinear piezoelectric vibration absorbers
Smart Materials and Structures, 1996The effect nonlinear electrical shunts on the performance of piezoelectric vibration absorbers for linear systems is presented. The equations of motion are derived in a format suitable for perturbation analysis. An electrical shunt containing cubic and quadratic elements is coupled to the structure via the piezoelectric effect.
Gregory S Agnes, Daniel J Inman
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Nonlinear active vibration damping
IEEE Transactions on Automatic Control, 1994Summary: A multivariable nonlinear controller is investigated for vibration suppression of flexible structures. The closed-loop gain matrix consists of a varying term added to a constant term. The varying term is proportional to the measured signal, providing rapid cancellation of large deflections and maintaining low noise sensitivity.
Kanestrøm, R. K., Egeland, O.
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