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1.
Gzal M. Fang B. Vakakis A. F. Bergman L. A. Gendelman O. V. 《Nonlinear dynamics》2020,101(4):2087-2106
Nonlinear Dynamics - This paper describes a rapid and efficient nonlinear non-resonance mechanism for low-to-high-frequency energy scattering, which is referred to as intermodal targeted energy... 相似文献
2.
Seismic base isolation by nonlinear mode localization 总被引:1,自引:0,他引:1
Y. Wang D. M. McFarland A. F. Vakakis L. A. Bergman 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,74(5-6):387-414
Summary In this paper, the performance of a nonlinear base-isolation system, comprised of a nonlinearly sprung subfoundation tuned
in a 1∶1 internal resonance to a flexible mode of the linear primary structure to be isolated, is examined. The application
of nonlinear localization to seismic isolation distinguishes this study from other base-isolation studies in the literature.
Under the condition of third-order smooth stiffness nonlinearity, it is shown that a localized nonlinear normal mode (NNM)
is induced in the system, which confines energy to the subfoundation and away from the primary or main structure. This is
followed by a numerical analysis wherein the smooth nonlinearity is replaced by clearance nonlinearity, and the system is
excited by ground motions representing near-field seismic events. The performance of the nonlinear system is compared with
that of the corresponding linear system through simulation, and the sensitivity of the isolation system to several design
parameters is analyzed. These simulations confirm the existence of the localized NNM, and show that the introduction of simple
clearance nonlinearity significantly reduces the seismic energy transmitted to the main structure, resulting in significant
attenuation in the response.
This work was supported in part by the National Science Foundation Grant CMS 00-00060. The authors are grateful for this support. 相似文献
3.
Gaetan?KerschenEmail author Alexander?F.?Vakakis Young?S.?Lee D.?Michael?Mcfarland Jeffrey?J.?Kowtko Lawrence?A.?Bergman 《Nonlinear dynamics》2005,42(3):283-303
The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator
weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are
encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in
terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic
orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly
and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that
this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric
study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink.
Finally, the results of experimental measurements supporting the theoretical developments are discussed.
This study was carried out while the author was a postdoctoral fellow at the National Technical University of Athens and at
the University of Illinois at Urbana-Champaign. 相似文献
4.
We present a design procedure for enhancing nonlinear energy pumping from a mode of a linear-damped substructure to a weakly coupled, essentially nonlinear oscillator. By this we denote the one way, irreversible passive transfer of vibrational energy from the mode to the nonlinear attachment. The design relies in the asymptotic expansion for large energies of a nonlinear normal mode of the underlying conservative system that provides an analytic estimate of the level of the amplitude reached by the nonlinear attachment in the energy pumping regime. The analytical findings are validated by direct numerical simulations. 相似文献
5.
Analytic Approximation of the Homoclinic Orbits of the Lorenz System at σ = 10, b = 8/3 and ρ = 13.926... 总被引:1,自引:0,他引:1
We present an iterative technique to analytically approximate the homoclinic loops of the Lorenz system for = 10, b = 8/3 and = H = 13.926.... First, the local structure of the homoclinic solution for t 0 ± and t ± is analyzed. Then, global approximants are used to match the local expansions. The matching procedure resembles the one used in Padé approximations. The accuracy of the approximation is improved iteratively, with each iteration providing estimates for the initial conditions of the homoclinic orbit, the value of H, and three undetermined constants in the local expansions. Within three iterations the error in H falls to the order of 0.1%. Comparisons with numerical integrations are made, and a discussion on ways to extend the technique to other types of homoclinic or heteroclinic orbits, and to improve its accuracy, is given. 相似文献
6.
F. Nucera A. F. Vakakis D. M. McFarland L. A. Bergman G. Kerschen 《Nonlinear dynamics》2007,50(3):651-677
In the field of seismic protection of structures, it is crucial to be able to diminish ‘as much as possible’ and dissipate
‘as fast as possible’ the load induced by seismic (vibration-shock) energy imparted to a structure by an earthquake. In this
context, the concept of passive nonlinear energy pumping appears to be natural for application to seismic mitigation. Hence, the overall problem discussed in this paper can be formulated
as follows: Design a set of nonlinear energy sinks (NESs) that are locally attached to a main structure, with the purpose of passively
absorbing a significant part of the applied seismic energy, locally confining it and then dissipating it in the smallest possible
time. Alternatively, the overall goal will be to demonstrate that it is feasible to passively divert the applied seismic energy
from the main structure (to be protected) to a set of preferential nonlinear substructures (the set of NESs), where this energy
is locally dissipated at a time scale fast enough to be of practical use for seismic mitigation. It is the aim of this work to show that the concept of nonlinear energy pumping is feasible for seismic mitigation. We consider
a two degree-of-freedom (DOF) primary linear system (the structure to be protected) and study seismic-induced vibration control
through the use of Vibro-Impact NESs (VI NESs). Also, we account for the possibility of attaching to the primary structure additional alternative NES configurations
possessing essential but smooth nonlinearities (e.g., with no discontinuities). We study the performance of the NESs through
a set of evaluation criteria. The damped nonlinear transitions that occur during the operation of the VI NESs are then studied
by superimposing wavelet spectra of the nonlinear responses to appropriately defined frequency – energy plots (FEPs) of branches
of periodic orbits of underlying Conservative systems. 相似文献
7.
Alexander F. Vakakis 《Nonlinear dynamics》1992,3(2):123-143
The fundamental and subharmonic resonances of a two degree-of-freedom oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-seales averaging analysis. The system is in a 1–1 internal resonance, i.e., it has two equal linearized eigenfrequencies, and it possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies. The analytical results are verified by a numerical integration of the equations of motion, and a discussion of the effects of the mode bifurcation on the dynamics of the system is given. 相似文献
8.
A time-domain nonlinear system identification method based on multiscale dynamic partitions 总被引:1,自引:0,他引:1
Young S. Lee Stylianos Tsakirtzis Alexander F. Vakakis Lawrence A. Bergman D. Michael McFarland 《Meccanica》2011,46(4):625-649
Based on a theoretical foundation for empirical mode decomposition, which dictates the correspondence between the analytical
and empirical slow-flow analyses, we develop a time-domain nonlinear system identification (NSI) technique. This NSI method
is based on multiscale dynamic partitions and direct analysis of measured time series, and makes no presumptions regarding
the type and strength of the system nonlinearity. Hence, the method is expected to be applicable to broad classes of applications
involving time-variant/time-invariant, linear/nonlinear, and smooth/non-smooth dynamical systems. The method leads to nonparametric
reduced order models of simple form; i.e., in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous
terms representing nonlinear modal interactions. Key to our method is a slow/fast partition of transient dynamics which leads
to the identification of the basic fast frequencies of the dynamics, and the subsequent development of slow-flow models governing
the essential dynamics of the system. We provide examples of application of the NSI method by analyzing strongly nonlinear
modal interactions in two dynamical systems with essentially nonlinear attachments. 相似文献
9.
K. R. Jayaprakash Yuli Starosvetsky Alexander F. Vakakis Maxime Peeters Gaetan Kerschen 《Nonlinear dynamics》2011,63(3):359-385
We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular
beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation
of Rosenberg (Adv. Appl. Mech. 9:155–242, 1966), we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs
that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite
extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify
the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly
affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification
of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides
a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders
or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover,
it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted
disturbances. 相似文献
10.