Active Mode Localization in Distributed Parameter Systems with Consideration of Limited Actuator Placement, Part 2: Simulations and Experiments

Shelley, Franz J.; Clark, William W.

doi:10.1115/1.568454

Cited by 24 publications

(15 citation statements)

References 4 publications

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“…The right eigenvector assignment algorithm used in this paper is an extension of the studies of Tang and Wang 9,10 , which is an improvement over the traditional eigenvector assignment via singular value decomposition technique that was first proposed by Cunningham 11 and utilized by Corr and Clark 12 and Shelley and Clark 13,14 .…”

Section: System Model and Eigenvector Assignment Methodsmentioning

confidence: 98%

Vibration isolator design via energy confinement through eigenvector assignment and piezoelectric networking

Wang

2004

Smart Structures and Materials 2004: Damping and Isolation

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The objective of this research is to investigate the feasibility of utilizing eigenvector assignment and piezoelectric networking for enhancing vibration isolator design through energy confinement. For a classical periodic isolator structure, the material discontinuity creates stop bands that could suppress the wave propagation of external excitation in a particular frequency range. While effective, such method can not always create wide enough stop bands such that all the disturbance frequencies are covered. In this study, the eigenvector assignment technique and piezoelectric networks are utilized to reduce the transmissibility of the isolator modes near the boundary of the stop bands, and therefore widen the effective frequency range and enhance the performance of the isolator.The eigenvector assignment principle is to alter the mode shapes of the system so that the modal components have smaller amplitude in concerned coordinates than in other parts of the system. By applying the eigenvector assignment method on the spatially tailored periodic isolator structure, the attenuated end (the end of the isolator designed to have small vibration) response amplitude at resonant frequencies near the stop band can be reduced, which enhances the vibration isolation performance in the frequency range of interest. On the other hand, piezoelectric networks connecting to the isolator structure increase the degrees of freedom of the integrated system, and enlarge the design space for achievable eigenvectors. The right eigenvectors of this integrated system are selected such that the modal energy in the concerned area is minimized by using the Rayleigh Principle. The integrated system with assigned eigenvectors will re-distribute vibratory energy of the complete electromechanical system. Small vibration at the attenuated end of the isolator is achieved since the energy is confined in the circuitry and other parts of the isolator.Numerical simulations are performed to evaluate the effectiveness of the proposed method on vibration confinement for isolator designs. Frequency responses of the different generalized coordinates in the selected frequency range are illustrated. It is shown that with the piezoelectric networking and eigenvector assignment, the system energy is redistributed and confined in the unconcerned areas, which can greatly enhance the performance of the vibration isolation system.

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Section: System Model and Eigenvector Assignment Methodsmentioning

confidence: 98%

Vibration isolator design via energy confinement through eigenvector assignment and piezoelectric networking

Wang

2004

Smart Structures and Materials 2004: Damping and Isolation

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“…[19][20][21][22][23] The following is a brief overview of eigenstructure assignment that follows closely the work presented by Jiang et al, 13 but it is extended for augmented systems and includes the option for the direct output feedback of Juang et al 11 (as opposed to full state feedback). Consider Eq.…”

Section: Eigenstructure Assignment Via Singular Value Decompositionmentioning

confidence: 99%

Sensitivity enhancement for damage detection in linear systems using optimal feedback auxiliary signals and system augmentation

D’Souza

Epureanu

2008

SPIE Proceedings

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Recently, a sensitivity enhancement technique for damage detection using eigenstructure assignment has been extended from linear to nonlinear systems. Nonlinearities have been accounted for by forming (higher dimensional) augmented systems, which are designed for each trajectory of the nonlinear system, and are characterized by a specific forcing that ensures that the augmented systems follow that trajectory (when projected onto the original, lower dimensional space). The use of system augmentation for damage detection has several benefits beyond its ability to handle nonlinearities. For example, sensitivity can be increased compared to existing linear techniques through nonlinear feedback auxiliary signals because the constraint that the system is stable during its interrogation has to be applied only to the linearized closed loop system, while the augmented linear system does not have that constraint. In this work, the various benefits of nonlinear feedback auxiliary signals are explored for damage detection in linear systems. System augmentation is used in a linear system because a nonlinear controller is employed to enhance sensitivity. In addition to the increased sensitivity, fewer controller actuator points and sensors are required compared to existing linear techniques due to the efficient use of added (augmented) equations. Numerical simulations for a linear mass-spring and a linear mass-spring-damper system are used to validate the approach and discuss the effects of noise.

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“…SVD-eigenvector shaping uses Moore-Penrose generalized left inverse and produces the closest eigenvector in least square sense to the desired ones, since it minimizes Euclidean 2-norm error. The result of applying this method to a simply supported beam, as a distributed parameter system, is presented in [27].…”

Section: Normal Mode Localization and Vibration Cancellationmentioning

confidence: 99%

“…Therefore, not only the number of required pairs of actuators and sensors for continuous systems is infinite but also a large number of actuators and sensors are needed for their linearly discretized models. SVD-eigenvector shaping, a modification of the former method, introduced as a solution to the problem of limited pairs of actuators and sensors [27]. This method is a combination of authors' earlier method and Cunningham [10] approach.…”

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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Active Mode Localization in Distributed Parameter Systems with Consideration of Limited Actuator Placement, Part 2: Simulations and Experiments

Cited by 24 publications

References 4 publications

Vibration isolator design via energy confinement through eigenvector assignment and piezoelectric networking

Vibration isolator design via energy confinement through eigenvector assignment and piezoelectric networking

Sensitivity enhancement for damage detection in linear systems using optimal feedback auxiliary signals and system augmentation

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

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