An Inverse Eigenvalue Formulation for Optimizing the Dynamic Behaviour of Pin-Jointed Structures

Djoudi, M. S.; Bahai, H.; Esat, I.I.

doi:10.1006/jsvi.2001.4068

Cited by 13 publications

(8 citation statements)

References 14 publications

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“…Based on these methods, many studies were carried out for developing approximate solutions to direct and inverse eigenvalue problems. Djoudi et al [6] established a relationship between geometric and material properties of pin-jointed truss structures and their eigenvalues in order to relocate natural frequencies of structures to a specified level. Bahai and Aryana [7,8] used the first-and second-order approximations of Taylor expansion for performing sensitivity analysis on two-dimensional plane structures.…”

Section: Introductionmentioning

confidence: 99%

A new method for finding the first‐ and second‐order eigenderivatives of asymmetric non‐conservative systems with application to an FGM plate actively controlled by piezoelectric sensor/actuators

Mirzaeifar

Bahai

Shahab

2008

Numerical Meth Engineering

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SUMMARYIn this paper, a new method for computing eigenvalue and eigenvector derivatives of asymmetric nonconservative systems with distinct eigenvalues is presented. Several approaches have been proposed for eigenderivative analysis of systems with asymmetric and non-positive-definite mass, damping and stiffness matrices. The proposed formulation that is developed by combining the modal and algebraic methods neither have the complications of modal methods in calculating the complex left and right eigenvector derivatives nor suffer from numerical instability problems usually associated with algebraic methods. The method is applied to a functionally graded material (FGM) plate actively controlled by piezoelectric sensor/actuators. In this system, the feedback signal applied to each actuator patch is implemented as a function of the electric potential in its corresponding sensor patch. The use of this closed-loop controlling system leads to a non-self-adjoint system with complex eigenvalues and eigenvectors. A finite element model is developed for static and dynamic analysis of closed-loop controlled FGM plate. The first-and second-order approximations of Taylor expansion are used to estimate the corresponding changes in the plate modal properties due to change in design parameters (the displacement feedback gains and the piezoelectric layer thickness in each S/A pair).

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Section: Introductionmentioning

confidence: 99%

A new method for finding the first‐ and second‐order eigenderivatives of asymmetric non‐conservative systems with application to an FGM plate actively controlled by piezoelectric sensor/actuators

Mirzaeifar

Bahai

Shahab

2008

Numerical Meth Engineering

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“…The structural modification can be also defined as the inverse problem [2,5]. The inverse engineering refers to the problem where the desired response (for example eigenvalue) of the system in known (diagnostics) or decided (modification) but the physical systems is unknown [6].…”

Section: Introductionmentioning

confidence: 99%

“…Such an approach, known as the forward variation [5] approach or design load analysis cycle [1] is expensive, time-consuming and rarely leads to the optimum solution. The simple modification, such as adding a mass or an elastic support can be easily carrying out by determination of the proper receptance in the point where the additional element is added [11,12].…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue based inverse model of beam for structural modification and diagnostics: theoretical formulation

Majkut

2010

Lat. Am. j. solids struct.

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In the work, the problems of the beam structural modification through coupling the additional mass or elastic support, as well as the problem of diagnostics of the beam cracks, are discussed. The common feature for both problems is that the material parameters in each of the discussed cases change only in one point (additional mass, the support in one point, the crack described by the elastic joint). These systems, after determination of the value of additional element and its localization, should have a given natural vibration frequency. In order to solve the inverse problem, i.e. the problem of finding values of the additional quantities (mass, elasticity), the beam inverse model was proposed. Analysis of this model allows finding such a value of additional mass (elasticity) as a function of its localization so that the system has the free vibration frequency, which is desired in the modification problem or measured on the object in the diagnostics.

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“…Structural modification can be also defined as the inverse problem [2,3]. The inverse engineering refers to the problems where the desired response (for example eigenvalue) of the system in known (diagnostics) or decided (modification) but the physical system is unknown [4].…”

Section: Introductionmentioning

confidence: 99%

“…The typical approach to the optimization problem for the system vibration is carrying out a series of modifications of the numerical or analytical model to obtain the required eigenfrequencies [1,3]. Another approach is based on determination the proper receptance in the point where the additional element is added [9,10].…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue based inverse model of beam for structural modification and diagnostics: examples of using

Majkut

2010

Lat. Am. j. solids struct.

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In the work, in order to solve the inverse problem, i.e. the problem of finding values of the additional quantities (mass, elasticity), the beam inverse model was proposed. Analysis of this model allows finding such a value of additional mass (elasticity) as a function of its localization so that the free vibration frequency changes to desirable value. The criteria for choice of the "proper" pair (mass -its position), including the criterion allowing changing the position of the vibration node of the second mode of the free vibrations, were given. Analysis of the influence of uncertainties in the determination of the additional quantity value and its position on the desired free vibration frequency was carried out, too. The proposed beam inverse model can be employing to identification of the beam cracks. In such a case, the input quantity is free vibration frequency measured on the damaged object. Each determined free-vibration frequency allows determining the flexibility curve for the spring modeling crack as a function of its position. The searched parameters of the crack (its depth and position) are indicated by the common point of two arbitrary curves. Accuracy of crack parameters determination depends on accuracy (uncertainty) of frequency measurement. Only some regions containing the searched crack parameters can be obtained in such a situation.

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An Inverse Eigenvalue Formulation for Optimizing the Dynamic Behaviour of Pin-Jointed Structures

Cited by 13 publications

References 14 publications

A new method for finding the first‐ and second‐order eigenderivatives of asymmetric non‐conservative systems with application to an FGM plate actively controlled by piezoelectric sensor/actuators

A new method for finding the first‐ and second‐order eigenderivatives of asymmetric non‐conservative systems with application to an FGM plate actively controlled by piezoelectric sensor/actuators

Eigenvalue based inverse model of beam for structural modification and diagnostics: theoretical formulation

Eigenvalue based inverse model of beam for structural modification and diagnostics: examples of using

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