2013
DOI: 10.1115/1.4025400
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Abstract: In structural dynamics, energy dissipative mechanisms with nonviscous damping are characterized by their dependence on the time-histoiy of the response velocity, which is mathematically represented by convolution integrals involving hereditaiy functions. The widespread Biot damping model assumes that such functions are exponential kernels, which modify the eigenvalues' set so that as many real eigenvalues (named nonviscous eigenvalues) as kernels are added to the system. This paper is focused on the study of a… Show more

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Cited by 15 publications
(15 citation statements)
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“…Consequently, the eigen-modes can be classified into elastic modes related to the 2 Â N complex conjugate eigenvalues and the p nonviscous modes introduced by the non-viscous nature of the damping mechanism. Some authors [56][57][58][59][60][61] studied the dynamic characteristics of viscoelastically damping systems. For stable passive systems, these p extra eigenvalues corresponding to nonviscous modes are negative real eigenvalues, which account for over-critically damped modes and have no oscillatory behavior.…”
Section: Preliminary Concepts and Definitionsmentioning
confidence: 99%
“…Consequently, the eigen-modes can be classified into elastic modes related to the 2 Â N complex conjugate eigenvalues and the p nonviscous modes introduced by the non-viscous nature of the damping mechanism. Some authors [56][57][58][59][60][61] studied the dynamic characteristics of viscoelastically damping systems. For stable passive systems, these p extra eigenvalues corresponding to nonviscous modes are negative real eigenvalues, which account for over-critically damped modes and have no oscillatory behavior.…”
Section: Preliminary Concepts and Definitionsmentioning
confidence: 99%
“…where , * ∈ C, 1 ≤ ≤ , are conjugate complex pairs, corresponding to the modes with oscillatory nature. The rest, ∈ R − , 1 ≤ ≤ , are negative real numbers that represent overcritically damped modes called nonviscous since they are a feature of nonviscous systems particularly of those governed by Biot's exponential kernels [36,37]. Associated with each eigenvalue there exists an eigenvector: we denote u , u * ∈ C , 1 ≤ ≤ to the complex eigenvectors associated with , * , and a ∈ R , 1 ≤ ≤ to the eigenvector associated with the real eigenvalue .…”
Section: Multiple-degree-of-freedom Systemsmentioning
confidence: 99%
“…A fixed‐point iteration method has been developed in the work of Lázaro et al to compute the eigenvalues of a viscoelastic system where the method is only applicable to systems with a proportional, or lightly nonproportional, damping matrix. Lázaro et al have introduced the concept of nonviscous sets, and using that notion, a closed‐form expression that approximates real eigenvalues has been achieved for systems with exponential kernels. It has been established that, for lightly or moderately damped systems, the set of real eigenvalues can be derived solving as many linear eigenvalue problems as exponential kernels .…”
Section: Introductionmentioning
confidence: 99%
“…For instance, additional matrix decompositions are needed for rank deficient damping matrices C j ≠ 0, j = 1, … , n in the work of Wagner et al, 15 while it is not necessary for full rank damping matrices. On the other hand, the level of damping is directly related to the convergence and accuracy of some current numerical methods (see, e.g., other works [18][19][20]. Indeed, damping properties of the viscoelastic system affect the distribution of the real eigenvalues in the intervals I j , j = 1, … , n. It has been proved in our other work 22 that, for full rank matrices C j ≠ 0, j = 1, … , n, we have N eigenvalues in each of these intervals, regardless of the damping level.…”
Section: Introductionmentioning
confidence: 99%
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