Eigensolutions of non-proportionally damped systems based on continuous damping sensitivity

Lázaro, Mario

doi:10.1016/j.jsv.2015.10.014

Cited by 20 publications

(11 citation statements)

References 29 publications

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“…The example presented above shows that, although the method proposed by Lazaro [19] is an approximate one, its accuracy for systems with proportional damping, including systems with high damping, is very good at least in engineering applications. Using the same model with proportional damping, the efficiency of the method of approximation of the dynamic characteristics of the system depending on the temperature changes, described in Sect.…”

Section: Modal Strain Energy Methodsmentioning

confidence: 99%

“…However, numerical methods have been developed (see, for example [18]). In this paper, the method of which the main assumptions were proposed by Lazaro [19] is presented and used.…”

Section: Nonlinear Eigenproblemmentioning

confidence: 99%

“…This is quite troublesome because, as mentioned earlier, this task can only be solved by iterative methods. However, the use of the Lazaro assumptions [19] enables a direct determination of the course of the natural frequency and the dimensionless damping factor functions within a certain temperature range. Namely, the shift factorα T in Eq.…”

Section: Analysis Of Temperature Influence On Dynamic Characteristicsmentioning

confidence: 99%

“…This type of eigenvalue problem can be solved using the mathematically advanced continuation method [18]. In [19], the method of approximating an eigenvalue problem solution was presented. It was extended in [20] to the case where the viscoelastic properties of the attenuators are described by fractional derivatives.…”

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confidence: 99%

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Approximate method for temperature-dependent characteristics of structures with viscoelastic dampers

Lewandowski

Przychodzki

2018

Arch Appl Mech

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A method for analyzing the influence of temperature on the dynamic characteristics of structures with viscoelastic dampers is proposed in this paper. Dampers which are described by so-called fractional rheological models are considered. The temperature-frequency superposition principle is used to describe the influence of temperature on the dynamic characteristics. The concept of continuous dependence of damping on an artificially introduced parameter is adopted for solving, in an approximate way, the nonlinear eigenvalue problem from which dynamic characteristics are determined. The correctness and effectiveness of the method was verified by means of two examples.

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Section: Modal Strain Energy Methodsmentioning

confidence: 99%

“…However, numerical methods have been developed (see, for example [18]). In this paper, the method of which the main assumptions were proposed by Lazaro [19] is presented and used.…”

Section: Nonlinear Eigenproblemmentioning

confidence: 99%

Section: Analysis Of Temperature Influence On Dynamic Characteristicsmentioning

confidence: 99%

mentioning

confidence: 99%

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Approximate method for temperature-dependent characteristics of structures with viscoelastic dampers

Lewandowski

Przychodzki

2018

Arch Appl Mech

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“…Methods which are devoted to determination of the dynamic properties of VE structures or elastic structures with VE dampers also exist (see, for example, [15][16][17][18][19][20]). For systems with VE elements modeled with the help of classic rheological models, the dynamic characteristics are obtained after solving the quadratic eigenvalue problem [21,22] which can be transformed to the linear eigenvalue problem using the state variables, as shown, for example, in [5,21,23].…”

Section: Introductionmentioning

confidence: 99%

Analysis of dynamic characteristics of viscoelastic frame structures

Lewandowski

Wielentejczyk²

2019

Arch Appl Mech

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Planar frame structures made of a viscoelastic material are considered in the paper. The technically very important structures made of a homogenous material are contemplated. A family of rheological models (classic and fractional) are used to describe the mechanical properties of the viscoelastic material. In particular, the dynamic characteristics of the structures are of interest. A numerically very efficient method is proposed to determine such characteristics. The method requires the solution to the linear eigenvalue problem for corresponding elastic structures and the solution to a nonlinear, algebraic equation. The presented method is much more efficient than other methods where, very often, the continuation method is used to solve the nonlinear eigenvalue problem. The influence of temperature changes on dynamic characteristics is analyzed using the frequency-temperature principle. The results of several parametric analyses are presented and discussed. For the first time, the influence of temperature on the dynamic characteristics of beams has been studied in detail. Keywords Viscoelastic frame structures • Free vibration • Dynamic characteristics • Ordinary and dynamic finite elements • Influences of temperature

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Analysing modal coupling in non-classically damped systems: beyond Rayleigh’s damping hypothesis—a comparative study

Suleiman,

Jaradat,

Benmalek

et al. 2024

Asian J Civ Eng

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Eigensolutions of non-proportionally damped systems based on continuous damping sensitivity

Cited by 20 publications

References 29 publications

Approximate method for temperature-dependent characteristics of structures with viscoelastic dampers

Approximate method for temperature-dependent characteristics of structures with viscoelastic dampers

Analysis of dynamic characteristics of viscoelastic frame structures

Analysing modal coupling in non-classically damped systems: beyond Rayleigh’s damping hypothesis—a comparative study

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