Approximate critical curves in exponentially damped nonviscous systems

Lázaro, Mario

doi:10.1016/j.ymssp.2018.12.044

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…In ref. [18], it was demonstrated that if D (s)u = 0 (denoting (•) = ∂(•)/∂s), then rank J F,y < n + 1, and therefore, J F,y is non-invertible and the functions s(θ) and u(θ) are not well defined at that point. However, the inverse statement is not true in general; that is, eigensolutions holding D (s)u = 0 might lead to rank J F,y < n + 1.…”

Section: New Results On Critical Damping Of Structures With Viscoelas...mentioning

confidence: 99%

“…For large multiple-dof systems, the general method proposed by Lázaro [9], consisting of eliminating s from Equation (4), cannot be carried out since an analytical expression of the determinant is, in general, not available. Trying to overcome that, Lázaro [18] proposed an approach for systems with multiple degrees of freedom, but the proposal was restricted to problems of one single hereditary kernel.…”

Section: Introductionmentioning

confidence: 99%

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Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

Lázaro

Garcı́a-Raffi

2022

Applied Sciences

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In this paper, a new methodology for the determination of the boundaries between oscillatory and non-oscillatory motion for nonviscously damped nonproportional systems is proposed. It is assumed that the damping forces are expressed as convolution integrals of the velocities via hereditary exponential kernels. Oscillatory motion is directly related to the complex nature of eigensolutions in a frequency domain and, in turn, on the value of the damping parameters. New theoretical results are derived on critical eigenmodes for viscoelastic systems with multiple degrees of freedom, with no restrictions on the number of hereditary kernels. Furthermore, these outcomes enable the construction of a numerical approach to draw the critical curves as solutions of certain parameter-dependent eigenvalue problems. The method is illustrated and validated through two numerical examples, covering discrete and continuous systems.

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Section: New Results On Critical Damping Of Structures With Viscoelas...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

Lázaro

Garcı́a-Raffi

2022

Applied Sciences

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“…In addition, critical damping (Adhikari, 2005;Lázaro, 2019aLázaro, , 2019b, closed-form solution for free vibration (García-Barruetabeña et al, 2012), and other dynamic characteristics of the non-viscous damping linear (Adhikari, 2008) and non-linear (Sieber et al, 2008) system are analyzed by researchers in recent years. Some researchers proposed identification methods such as linear least square method (Adhikari and Woodhouse, 2001), parameter iterative method (Pan and Wang, 2015), and Kalamn filtering method (Reggio et al, 2013) for non-viscous damping system in frequency domain (Su et al, 2019) and in time domain (Shen et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Characteristics of passive vibration control for exponential non-viscous damping system: Vibration isolator and absorber

Shen

Zhou

Lee

2022

Journal of Vibration and Control

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Materials or structures made of polymers or composites often exhibit non-viscous damping behavior. The non-viscous damping forces that depend on the history velocity can be expressed by the exponential non-viscous damping model. Some polymer or composite materials can be used as damping materials for kinetic energy absorption in the dynamic systems. Vibration isolator and absorber are usually considered for shock absorption. In this study, transfer ratios of vibration isolator and absorber with exponential non-viscous damping system are derived by using the Laplace transform. The dimensionless amplitude of vibration absorber with exponential non-viscous damping is derived too. Compared to viscous damping system, transfer ratio and dimensionless amplitude of exponential non-viscous damping system are influenced by the ratio of the relaxation parameter and natural frequency or the frequency of the external load. With the non-viscous damping material used in vibration control, the ratio is therefore a non-negligible factor which should be considered in analysis.

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Critical relationships in nonviscous systems with proportional damping

Lázaro

Garcı́a-Raffi

2020

Journal of Sound and Vibration

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Approximate critical curves in exponentially damped nonviscous systems

Cited by 5 publications

References 23 publications

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

Characteristics of passive vibration control for exponential non-viscous damping system: Vibration isolator and absorber

Critical relationships in nonviscous systems with proportional damping

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