Natural modes of modified structures

Baldwin, John; Hutton, Stanley G.

doi:10.2514/3.9159

Cited by 65 publications

(34 citation statements)

References 51 publications

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“…In this case 4 =3* and A = A*, i.e the solution of Problem 1 is also the solution of (2). When R is small, the solution of Problem 1 approximates the solution of (2). Hence by minimizing the norm (4) we obtain an optimal approximation.…”

Section: Problem I : Optimal Modificationmentioning

confidence: 99%

“…We also assume that these extracted real modes and corresponding eigenvalues correlate well with the analytical model for the behaviour of the system described by equation ( Since the truncated modal data 0 , and A, do not determine K and M uniquely, it is clear that this cannot be done. In Section 2 we overcome this difficulty by formulating a related optimization problem, which gives an optimal approximation, in some particular sense, to the solution of (2).…”

Section: Introductionmentioning

confidence: 99%

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Mass and stiffness modifications to achieve desired natural frequencies

Sivan

Ram

1996

Commun. Numer. Meth. Engng.

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SUMMARYA method for determining mass and stiffness modifications to achieve desired natural frequencies is presented. The given data are modal testing results, which consist of a truncated set of natural frequencies and mode shapes. The difficulty arising from the incompleteness of data is overcome by solving an optimization problem rather than seeking an exact solution. The obtained modifications are optimal in a Rayleigh-Ritz sense. The case where the mass and stiffness matrices are interrelated is also considered. Numerical examples demonstrating the various results and the sensitivity of the problem to perturbations are presented.

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Section: Problem I : Optimal Modificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mass and stiffness modifications to achieve desired natural frequencies

Sivan

Ram

1996

Commun. Numer. Meth. Engng.

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“…Another method for solution of the inverse-model ambiguity problem is searching for the value of one of the independent variable (for instance mass m a , elasticity k s or flexibility c b ) for the constant fixed value of another independent variable (position x a , x s or x c ) -localized modification [3]. Such calculations (i.e.…”

Section: Inverse Problem In Diagnostics and Structural Modificationmentioning

confidence: 99%

“…In work [3] authors presented detailed review of structural modification methods and classified them into categories of the techniques based on small modification, these based on localized modification, and these based on modal approximation. In the class of small modifications, they described model-updating techniques developed from Rayleigh's principle, eigenvalue derivatives and modal perturbation.…”

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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“…The modal properties of the damped structure are determined by the second-ordei n x n eigenvalue problem (5) which corresponds to the equations of motion in equation (3). The n-vectors Y j are used to obtain the structure's mode shapes aj in the original displacement coordinates x by the relation…”

Section: Effect Of Non-classical Damping O N Modal Propertiesmentioning

confidence: 99%

Dynamic characteristics of non‐classically damped structures

Igusa

1991

Earthq Engng Struct Dyn

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SUMMARYThe equations of motion of a structure in undamped modal coordinates may have non-zero off-diagonal terms in the damping matrix. Although these terms are commonly neglected, studies have shown that they may have a significant influence on the response to dynamic loads. In this paper, two independent criteria are developed to determine when these damping terms will affect the structure's modal properties and response. It is found that even small off-diagonal damping values can be significant if the structure has closely spaced natural frequencies. To quantify and understand the influence of these damping terms, closed-form analytical expressions are derived for the modal properties and harmonic and stochastic response of structures with closely spaced natural frequencies. One conclusion is that off-diagonal damping terms will decrease a modal damping ratio for each pair of closely spaced modes. This is significant, since a response analysis performed by neglecting these off-diagonal terms will underestimate the true response.

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Natural modes of modified structures

Cited by 65 publications

References 51 publications

Mass and stiffness modifications to achieve desired natural frequencies

Mass and stiffness modifications to achieve desired natural frequencies

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

Dynamic characteristics of non‐classically damped structures

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