Axial Vibration Confinement in Nonhomogenous Rods

Choura, Slim; El-Borgi, Sami; Nayfeh, Ali H.

doi:10.1155/2005/514824

Cited by 6 publications

(2 citation statements)

References 24 publications

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“…This method still requires full state feedback in the form of acceleration feedback; however, the states that are not being measured need to be estimated by a dynamic observer in order to meet practical issues. A case study on the axial vibration confinement of the rods using this method is presented in [33]. A similar method for linear time varying systems is reported in [34].…”

Section: Normal Mode Localization and Vibration Cancellationmentioning

confidence: 99%

A Review on Eigenstructure Assignment Methods and Orthogonal Eigenstructure Control of Structural Vibrations

Rastgaar

Ahmadian

Southward

2009

Shock and Vibration

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Abstract. This paper provides a state-of-the-art review of eigenstructure assignment methods for vibration cancellation. Eigenstructure assignment techniques have been widely used during the past three decades for vibration suppression in structures, especially in large space structures. These methods work similar to mode localization in which global vibrations are managed such that they remain localized within the structure. Such localization would help reducing vibrations more effectively than other methods of vibration cancellation, by virtue of confining the vibrations close to the source of disturbance. The common objective of different methods of eigenstructure assignment is to provide controller design freedom beyond pole placement, and define appropriate shapes for the eigenvectors of the systems. These methods; however, offer a large and complex design space of options that can often overwhelm the control designer. Recent developments in orthogonal eigenstructure control offers a significant simplification of the design task while allowing some experience-based design freedom. The majority of the papers from the past three decades in structural vibration cancellation using eigenstructure assignment methods are reviewed, along with recent studies that introduce new developments in eigenstructure assignment techniques.

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Section: Normal Mode Localization and Vibration Cancellationmentioning

confidence: 99%

A Review on Eigenstructure Assignment Methods and Orthogonal Eigenstructure Control of Structural Vibrations

Rastgaar

Ahmadian

Southward

2009

Shock and Vibration

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“…It has the potential to confine the vibrational energy, to reduce the control effort, and to optimize the required sensors and actuators. Choura et al [8] proposed a design methodology for vibration confinement in nonhomogeneous rods. They established conditions for selecting the rod's material and geometrical properties by constructing positive Lyapunov functions whose derivative with respect to the space variable is required to be negative.…”

Section: Introductionmentioning

confidence: 99%

Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

Gafsi

Najar

Choura³

et al. 2014

Shock and Vibration

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In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

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