A new method of passive modifications for partial frequency assignment of general structures

Belotti, Roberto; Ouyang, Huajiang; Richiedei, Dario

doi:10.1016/j.ymssp.2017.06.043

Cited by 24 publications

(20 citation statements)

References 41 publications

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“…Hence, several approaches have been proposed to solve the task of eigenstructure assignment (EA), by exploiting either passive modifications of the system parameters (such as masses or stiffnesses) through dynamic structural modification (see e.g. Jihong and Weihong 2006;Hernandes and Suleman 2014;Belotti et al 2016;Belotti et al 2018b;Thomas et al 2020), or active control (see e.g. Schulz and Inman 1994, Triller and Kammer 1997, Kim et al 1999, Zhang et al 2014.…”

Section: Performance Optimization Through Concurrent Mechanical and Cmentioning

confidence: 99%

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Belotti

Richiedei

Trevisani

2020

Struct Multidisc Optim

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The paper proposes a multi-domain approach to the optimization of the dynamic response of an underactuated vibrating linear system through eigenstructure assignment, by exploiting the concurrent design of the mechanical properties, the regulator and state observers. The approach relies on handling simultaneously mechanical design and controller synthesis in order to enlarge the set of the achievable performances. The underlying novel idea is that structural properties of controlled mechanical systems should be designed considering the presence of the controller through a concurrent approach: this can considerably improve the optimization possibilities. The method is, first, developed theoretically. Starting from the definition of the set of feasible system responses, defined through the feasible mode shapes, an original formulation of the optimality criterion is proposed to properly shape the allowable subspace through the optimal modification of the design variables. A proper choice of the modifications of the elastic and inertial parameters, indeed, changes the space of the allowable eigenvectors that can be achieved through active control and allows obtaining the desired performances. The problem is then solved through a rank-minimization with constraints on the design variables: a convex optimization problem is formulated through the “semidefinite embedding lemma” and the “trace heuristics”. Finally, experimental validation is provided through the assignment of a mode shape and of the related eigenfrequency to a cantilever beam controlled by a piezoelectric actuator, in order to obtain a region of the beam with negligible oscillations and the other one with large oscillations. The results prove the effectiveness of the proposed approach that outperforms active control and mechanical design when used alone.

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Section: Performance Optimization Through Concurrent Mechanical and Cmentioning

confidence: 99%

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Belotti

Richiedei

Trevisani

2020

Struct Multidisc Optim

Self Cite

View full text Add to dashboard Cite

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“…A cantilever beam¯nite element model whose benchmark was presented in some recent papers 32,33 is considered in this numerical experiment. The system matrices The in°uence matrices computed for the state feedback and state derivative feedback were subsequently obtained as follows: :…”

Section: Experiments 2: Control Of Cantilever Beammentioning

confidence: 99%

No Spillover Eigenvalues Assignment of Second-Order Systems with Dense Force Actuators Matrices Using Brauer’s Theorem

Araújo

Santos

2019

Int. J. Str. Stab. Dyn.

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This paper presents an approach for eigenvalue assignment in second-order linear systems with no spillover property. Second-order differential equations arise from dynamical modeling of vibrating structures by finite element or lumped parameter first principles approach in several practical problems. Certain structures can face practical issues when subjected to external perturbation forces, as resonance or flutter type vibrations. The control of excessive vibrations can be attempted by techniques of active vibration control using linear feedback. To change only a few eigenvalues and eigenvectors that cause excessive vibrations, the requirement of no spillover property is a somewhat attractive issue. Furthermore, only the part of the eigenstructure whose eigenvalues must be reassigned is necessary to be known for an efficient parametrization of the feedback matrices. Brauer’s theorem, a milestone result of linear algebra, as well as some recent related results, is applied here to achieve partial eigenvalue assignment using dense force actuator (influence) matrices. The proposal can be applied to general systems with no restriction on the mass, damping, and stiffness with symmetry or definiteness. The procedures to implement the proposal are synthesized in a step-by-step form, and some numerical examples are given to illustrate its application.

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“…Consider the cantilever beam model with 6 degrees-of-freedom (DOFs) given in the literatures 19,24,25…”

Section: Applications In Natural Frequency Assignmentmentioning

confidence: 99%

A multiplicative eigenvalues perturbation and its application to natural frequency assignment in undamped second-order systems

Araújo

Santos

2018

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this article, a novel theorem for eigenvalue perturbation inspired by the results of Brauer is introduced. The new result is valid for single and multiple eigenvalue perturbations, with preservation—no spillover of the remaining spectrum. An application of the proposed results is given since the model updating and the partial eigenvalue assignment problems for second-order linear dynamics have gained crescent attention in the last decades. Furthermore, its effectiveness is illustrated with numerical examples.

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A new method of passive modifications for partial frequency assignment of general structures

Cited by 24 publications

References 41 publications

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

No Spillover Eigenvalues Assignment of Second-Order Systems with Dense Force Actuators Matrices Using Brauer’s Theorem

A multiplicative eigenvalues perturbation and its application to natural frequency assignment in undamped second-order systems

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