2016
DOI: 10.1155/2016/9634103
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Abstract: A novel numerical approach to compute the eigenvalues of linear viscoelastic oscillators is developed. The dissipative forces of these systems are characterized by convolution integrals with kernel functions, which in turn contain a set of damping parameters. The free-motion characteristic equation defines implicitly the eigenvalues as functions of such parameters. After choosing one of them as independent variable, the key idea of the current paper is to obtain a differential equation whose solution can be co… Show more

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Cited by 2 publications
(4 citation statements)
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References 44 publications
(91 reference statements)
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“…The rest of higher-order derivatives σ ″ procedure and using the previously calculated results. In general, it is sufficient to take up the second-order term since this approximation accurately estimates the nonviscous eigenvalues within a wide range of the damping ratios, including lightly and moderately damped structures [15,20]. After obtaining the coefficients σ ′ j (0) and σ ″ j (0), the closed-form expression for σ j remains as follows:…”
Section: Adhikari and Pascual's Methodsmentioning
confidence: 99%
See 2 more Smart Citations
“…The rest of higher-order derivatives σ ″ procedure and using the previously calculated results. In general, it is sufficient to take up the second-order term since this approximation accurately estimates the nonviscous eigenvalues within a wide range of the damping ratios, including lightly and moderately damped structures [15,20]. After obtaining the coefficients σ ′ j (0) and σ ″ j (0), the closed-form expression for σ j remains as follows:…”
Section: Adhikari and Pascual's Methodsmentioning
confidence: 99%
“…The first one due to Adhikari and Pascual [18] approximates the nonviscous eigenvalues with the first iteration of Newton's method applied to the characteristic polynomial. The second one, developed by Lázaro in his PhD Thesis [19] and published in the paper [20], is a perturbation-based approach. Both methods will be described in detail below and can be applied for both single dof systems and multiple dof systems with proportional (or classical) damping.…”
Section: Numerical Computationmentioning
confidence: 99%
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“…Real structures are usually assumed to be lightly damped, that is, dissipative forces can be considered much smaller than inertia and elastic forces. Artificial perturbation of dissipative terms in linear structural dynamics has been successfully applied mainly for the computation of complex frequencies and modes of non-classically viscously [30][31][32][33][34][35] and non-viscously [36][37][38][39][40][41][42] damped structures. In the time domain, techniques based on asymptotic perturbation are very useful to obtain solutions in nonlinear mechanics [43][44][45].…”
Section: Introductionmentioning
confidence: 99%