Energy Transfer from High-Frequency to Low-Frequency Modes in Structures

Nayfeh, A. H.; Mook, Dean T.

doi:10.1115/1.2836454

Cited by 28 publications

(28 citation statements)

References 13 publications

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“…In the course of studying the dynamics of multi-degree-of-freedom nonlinear systems, three energy transfer mechanisms between modes were identi®ed [1]. They were attributed to either internal resonances, combination resonances, or energy exchange among widely spaced modes.…”

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A review of development and implementation of an active nonlinear vibration absorber

Oueini

Nayfeh

Pratt

1999

Archive of Applied Mechanics (Ingenieur Archiv)

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We present an account of an implementation of an active nonlinear vibration absorber that we have developed. The control technique exploits the saturation phenomenon that is known to occur in quadratically-coupled multi-degree-of-freedom systems subjected to primary excitation and possessing a two-to-one internal resonance. The technique is based on introducing an absorber and coupling it with the structure through a sensor and an actuator, where the feedback and control signals are quadratic. First, we consider the case of controlling the vibrations of a single-degree-of-freedom system. We develop the equations governing the response of the closed-loop system and use the method of multiple scales to obtain an approximate solution. We investigate the performance of the control strategy by studying its steady-state and transient characteristics. Additionally, we compare the performance of the quadratic absorber with that of a linear absorber. Then, we present theoretical and experimental results that demonstrate the versatility of the technique. We design an electronic circuit to emulate the absorber and use a variety of sensors and actuators to implement the active control strategy. First, we use a motor and a potentiometer to control the vibration of a rigid beam. We develop a plant model that includes Coulomb friction and demonstrate that the closed-loop system exhibits the saturation phenomenon. Second, we extend the strategy to multi-degree-of-freedom systems. We use PZT ceramics and strain gages to suppress vibrations of¯exible steel beams when subjected to single-and simultaneous two-mode excitations. Third, we employ Terfenol-D, a nonlinear actuator, and accelerometers to control the vibrations of exible beams. In all instances, the technique is successful in reducing the response amplitude of the structures.

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A review of development and implementation of an active nonlinear vibration absorber

Oueini

Nayfeh

Pratt

1999

Archive of Applied Mechanics (Ingenieur Archiv)

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“…This is observed in many experimental research results and also theoretical results [14,[19][20][21][22][23]. The interaction between amplitudes and phases of different modes in nonlinear systems with many degrees of freedom as well as in free and forced multi frequency regimes of deformable bodies with infinite number of vibration frequencies, is observed theoretically by averaging asymptotic method of Krilov-Bogoliyubov-Mitropolskiy [2,[15][16][17][18].…”

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“…Also, we can conclude that discontinuity in the elastic layer is the source for energy transfer between all eigen amplitude modes with infinite number frequency time component processes. By using the model of a double plate system with viscoelastic layer (similar to that in [3], or [20]) we can consider the energy transfer between plates. For that reason we use corresponding partial differential equations and corresponding analytical results and expressions for solutions of the transversal displacements of the both plates vibrations.…”

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Energy transfer in double plate system dynamics

Hedrih

2008

Acta Mech Sin

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The study of energy transfer between coupled subsystems in a hybrid system is very important for applications. This paper presents an analytical analysis of energy transfer between plates of a visco-elastically connected double-plate system in free transversal vibrations. The analytical analysis shows that the visco-elastic connection between plates is responsible for the appearance of two-frequency regime in the time function, which corresponds to one eigen amplitude function of one mode, and also that time functions of different vibration modes are uncoupled, but energy transfer between plates in one eigen mode appears. It was shown for each shape of vibrations. Series of the two Lyapunov exponents corresponding to the one eigen amplitude mode are expressed by using the energy of the corresponding eigen amplitude time component.Keywords Energy transfer between subsystems · Double plate system · Multifrequency transversal vibrations · Analytical solution · Rayleigh function of dissipation IntroductionPlates, beams and belts have been extensively used as structural elements in many industrial applications. Investigation of vibrations of plates dates back to the nineteenth century. The interest in the study of coupled systems [1-13] as newThe English text was polished

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“…For such systems, energy transfer may occur when the lower mode frequency is equal to one-half of the higher mode response may exponentially increase while the higher mode response may decrease due to the energy transfer between the modes. Nayfeh and Mook [4] performed an extensive study on the energy transfer from low-to high-frequency modes. They showed the in#uence of internal resonance on this energy transfer.…”

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confidence: 99%