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

Araújo, José Mário; Santos, Tito L.M.

doi:10.1177/0959651818771482

Cited by 5 publications

(5 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…20,23 Extensions of Brauer's theorem of interest herein are Rado's theorem 20 and that proposed by Araújo and Santos. 18 Next, these theorems are described.…”

Section: Brauer's Theorem and Related Resultsmentioning

confidence: 99%

“…Theorem 2.2 describes a multiplicative version of Brauer's theorem, and has been successfully applied to solve problems such as model update and partial natural frequency assignments. 18…”

Section: Theorem 22 (Ref 18)mentioning

confidence: 99%

“…[8][9][10][11][12] Nevertheless, for a system with a general structure matrix, that is, not necessarily symmetric or de¯nite, contributions to the PEA problem solution are seldom, 13 and more recently with the receptance approach for systems with asymmetries owing to non-conservative force actions. [14][15][16][17] Recently, the authors have investigated solutions for partial natural frequency assignments in undamped systems, 18 and the no spillover control of vibrating systems by PEA using state feedback with dense in°uence matrices and Brauer's theorem. Brauer's theorem for eigenvalue perturbation is a milestone in the¯eld of linear algebra, and the no-spillover property of the spectrum arises naturally from its application.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…20,23 Extensions of Brauer's theorem of interest herein are Rado's theorem 20 and that proposed by Araújo and Santos. 18 Next, these theorems are described.…”

Section: Brauer's Theorem and Related Resultsmentioning

confidence: 99%

“…Theorem 2.2 describes a multiplicative version of Brauer's theorem, and has been successfully applied to solve problems such as model update and partial natural frequency assignments. 18…”

Section: Theorem 22 (Ref 18)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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.

Self Cite

View full text Add to dashboard Cite

show abstract

“…It offers an opportunity to devise a robust solution to the problem by exploiting the arbitrary nature of the parameters. Inspired by the research results of Brauer, 10 Araújo et al 11 propose an eigenvalue perturbation theorem and apply it to the partial eigenvalue assignment of second-order linear dynamic systems. This method employs multiplicative perturbation and introduces static output feedback of system acceleration to solve the partial eigenvalue assignment problem and is applicable to static acceleration output feedback in an undamped second-order system.…”

Section: Introductionmentioning

confidence: 99%

A new general method for assigning frequencies with low spillover through structural modifications

Liu

Pang

Ouyang

et al. 2023

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

By modifying the mass and stiffness parameters of a structure, a subset of its natural frequencies can be assigned. However, such an assignment is usually accompanied with changes of the remaining frequencies, known as ‘spillover’. Eigenvalue or frequency spillover often needs to be avoided in engineering. In this paper, a new and general method is proposed for assigning a subset of the natural frequencies of a structure with a low level of spillover through structural modifications. The method combines a multi-population genetic algorithm and a radial basis function neural network and is implemented in a MATLAB-PYTHON-ABAQUS data interaction system. It is suitable for theoretical models (for example, finite element models) of general structures. By means of three numerical examples, the ability of the method to assign subsets of frequencies to discrete and discretised continuous structures while maintaining low spillover is demonstrated.

show abstract

“…Zhang et al [32][33][34] presented some algorithms to solve the partial eigenvalue assignment for high-order systems by single-input control or multi-input control. Many researchers [35][36][37] also studied this problem based on various feedback signals, such as the sound pressure signal, displacement feedback signal, and acceleration feedback signal.…”

Section: Introductionmentioning

confidence: 99%

Partial Frequency Assignment for Torsional Vibration Control of Complex Marine Propulsion Shafting Systems

Chen

Ouyang

et al. 2019

Applied Sciences

View full text Add to dashboard Cite

With the large-scale and complexity of ship propulsion shafting, it is more difficult to analyze and control the torsional vibration of shafting. Therefore, an effective control method for the torsional vibration of shafting is of great significance in the field of ship engineering. The main strategy of torsional vibration control adopted in this paper is to keep the natural frequency of a shaft system away from the excitation frequency through structural modifications. In addition, because the basic parameters of much of the equipment in engineering applications cannot be changed, this restriction cannot be ignored when seeking solutions related to structural modifications. This paper studies the partial eigenvalue assignment for the torsional vibration control of complex ship propulsion shafting using the gradient flow method, which can shift a “dangerous” natural frequency to a safe value, while satisfying complex physical constraints. The models of a ship propulsion system and a diesel generator set are established to demonstrate several different desired modification schemes and constraint conditions in practice. In particular, close frequencies are shifted. The numerical simulation results demonstrate that it is effective and feasible to make a partial frequency assignment of torsional vibration, which provides a reliable approach for the control of torsional vibration for complex shaft systems in practical engineering.

show abstract

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

Cited by 5 publications

References 23 publications

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

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

A new general method for assigning frequencies with low spillover through structural modifications

Partial Frequency Assignment for Torsional Vibration Control of Complex Marine Propulsion Shafting Systems

Contact Info

Product

Resources

About