Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers

Kamiński, Marcin; Lenartowicz, Agnieszka; Guminiak, Michał; Przychodzki, Maciej

doi:10.3390/ma15196811

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…where 𝑟 denotes the number of viscoelastic elements, K 𝑣,𝑘 is a location matrix of viscoelastic elements and 𝑔 𝑘 (𝑠) is a function describing the viscoelastic properties of element 𝑘. Structures with viscoelastic elements have already been described in detail, including frame with viscoelastic dampers [29], beam with viscoelastic layers [30], and plates with viscoelastic layers [31] or with viscoelastic dampers [32]. Dynamic behavior of structures with viscoelastic elements can be described by the natural frequency 𝜔 𝑙 and the nondimensional damping ratio 𝛾 𝑙 (for 𝑙 = 1, 2, .…”

Section: Application To Structures With Viscoelastic Elementsmentioning

confidence: 99%

Hob wear prediction based on simulation of friction, heat fluxes, and cutting temperature

Hrytsay,

Stupnytskyy

2023

Archive of Mechanical Engineering

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This paper discusses the different methods used for calculating first-and secondorder sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.

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Section: Application To Structures With Viscoelastic Elementsmentioning

confidence: 99%

Hob wear prediction based on simulation of friction, heat fluxes, and cutting temperature

Hrytsay,

Stupnytskyy

2023

Archive of Mechanical Engineering

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“…One method that enables the incorporation of uncertainties in design parameters is stochastic analysis (Kamiński et al in [22,23]). This approach, particularly when parameters are described as interval numbers, was applied by Muscolino and Sofi in [24] using affine arithmetic.…”

Section: Introductionmentioning

confidence: 99%

“…Advantage: they can be applied when probability distribution is lacking; disadvantages: operations are computationally expensive and results may be less precise than with probabilistic methods.  Methods based on interval analysis [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][23][24][25][26][27][28][29][30][31]35,[42][43][44], where parameters are modeled as intervals. Advantages: they consider the range in which the parameter changes without knowing its exact distribution, allow for the relatively easy determination of the lower and upper bounds of the response function, and are relatively easy to code; disadvantage: the obtained results may be overestimated.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Point Iteration Method for Uncertain Parameters in Dynamic Response of Systems with Viscoelastic Elements

Łasecka-Plura

2024

Applied Sciences

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The paper presents a method for determining the dynamic response of systems containing viscoelastic damping elements with uncertain design parameters. A viscoelastic material is characterized using classical and fractional rheological models. The assumption is made that the lower and upper bounds of the uncertain parameters are known and represented as interval values, which are then subjected to interval arithmetic operations. The equations of motion are transformed into the frequency domain using Laplace transformation. To evaluate the uncertain dynamic response, the frequency response function is determined by transforming the equations of motion into a system of linear interval equations. Nevertheless, direct interval arithmetic often leads to significant overestimation. To address this issue, this paper employs the element-by-element technique along with a specific transformation to minimize redundancy. The system of interval equations obtained is solved iteratively using the fixed-point iteration method. As demonstrated in the examples, this method, which combines the iterative solving of interval equations with the proposed technique of equation formulation, enables a solution to be found rapidly and significantly reduces overestimation. Notably, this approach has been applied to systems containing viscoelastic elements for the first time. Additionally, the proposed notation accommodates both parallel and series configurations of damping elements and springs within rheological models.

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“…The first-and second-order Taylor series expansion was also used in [25], where the solution of the eigenvalue problem and frequency response functions for systems with viscoelastic dampers were analyzed. In [26], uncertainties of a system with viscoelastic dampers were analyzed using a probabilistic approach.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of a Composite Beam with Viscoelastic Layers under Uncertain-But-Bounded Design Parameters

Łasecka-Plura

2023

Applied Sciences

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In this study, dynamic characteristics of a composite beam with uncertain design parameters are analyzed. Uncertain-but-bounded parameters change only within certain specified limits. This study uses interval analysis to investigate a composite beam with viscoelastic layers whose behavior is described using the fractional Zener model. In general, parameters describing both elastic and viscoelastic layers can be uncertain. Several methods have been studied to determine the lower and upper bounds of the dynamic characteristics of a structure. Among them, the vertex method is a comparative method in which the lower and upper bounds of the dynamic characteristics are approximated using the first- and second-order Taylor series expansion. An algorithm to determine the critical combination of uncertain design parameters has also been described. Numerical examples demonstrate the effectiveness of the presented methods and the possibility of applying them to the analysis of systems with numerous uncertain parameters and high uncertainties.

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Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers

Cited by 6 publications

References 18 publications

Hob wear prediction based on simulation of friction, heat fluxes, and cutting temperature

Hob wear prediction based on simulation of friction, heat fluxes, and cutting temperature

Fixed-Point Iteration Method for Uncertain Parameters in Dynamic Response of Systems with Viscoelastic Elements

Dynamic Characteristics of a Composite Beam with Viscoelastic Layers under Uncertain-But-Bounded Design Parameters

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