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1

Modal analysis of frame structures with semi-rigid joints and viscoelastic connections modeled by fractional derivatives

Pawlak Z. M., Łasecka-Plura M., Zak-Sawiak M.

Archives of Mechanics

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2023

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Vol. 75, nr 3

337--363

EN

The paper presents two methods of solving the problem of the dynamics of a frame structure with viscoelastic bonds in nodes. In the first approach, known from the literature, two-node beam elements with three degrees of freedom in each node were used. Exact shape functions were adopted to obtain a stiffness matrix, a consistent mass matrix and a damping matrix for the beam element. These matrices were then modified by introducing rotational viscoelastic constraints at the boundary nodes. In the second approach, a new method of modelling viscoelastic bonds in frame structures was proposed. It consists in removing rigid bonds between elements along selected degrees of freedom and replacing them with a new, additional element with viscoelastic properties. This approach allows the use of any rheological model to describe viscoelastic bonds (i.e. an additional element) without the need to create a new modified finite element. In this work, an advanced rheological model, i.e. the fractional Kelvin model, was used to describe rotational viscoelastic bonds. The use of fractional derivatives to describe the damping properties reduces the number of parameters needed in the model, but leads to a non-linear eigenproblem. In order to solve the eigenvalue problem, the continuation method was used, and the dynamic characteristics of the structure were determined on the basis of the calculated eigenvalues. Selected structures with viscoelastic nodes were analyzed and the obtained results confirm the effectiveness of the proposed approach.

2

Analiza dynamiczna konstrukcji z tłumikami z niedokładnie określonymi parametrami projektowymi

Łasecka-Plura M., Lewandowski R.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2016

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z. 63, nr 1/I

439--446

PL

W pracy został omówiony sposób obliczania charakterystyk dynamicznych ram z niedokładnie określonymi parametrami projektowymi. Analizowano konstrukcje z wbudowanymi pasywnymi tłumikami drgań. Zakłada się, że parametry projektowe mogą się zmieniać, jednak zakres ich zmienności jest znany. Zastosowany rachunek interwałowy pozwala wyrazić parametry projektowe jako tzw. liczby przedziałowe. Przyjęto, że dolna i górna granica szukanych charakterystyk dynamicznych jest przedstawiona jako rozwinięcie w szereg Taylora pierwszego rzędu. W pracy został zamieszczony przykład numeryczny, w którym analizowano ośmiokondygnacyjną, trójprzęsłową ramę z tłumikami. Prezentowana metoda może mieć zastosowanie w praktyce w celu określenia zakresu zmienności charakterystyk dynamicznych przy niedokładnie określonych parametrach projektowych.

EN

In the paper a method for determining dynamic characteristics of frame with uncertain design parameters is described. The structures with built-in passive dampers are considered. The proposed method could be used when the parameters of structures or parameters of dampers are uncertain. The main idea is that values of design parameters could change with respect to values adopted in the design process but the range of their variation is known. The design parameters are expressed as interval values what makes possible calculation of dynamic characteristics of structures by use of interval analysis. In this paper the lower and upper bounds of dynamic characteristics are obtained by use of Taylor series expansion. At the end of the paper a simple numerical example is presented. The eight-storey frame with three bays and three dampers mounted on it is considered. This structure was designed according to EC8 Part 1. The dampers parameters are uncertain. The obtained results are compared with ones determined with a help of the vertex method. This method assumes that it is necessary to calculate end-point combination of uncertain design parameters. The presented method may be applicable in practice in order to predict the limit values of chosen dynamic characteristics of structures with uncertain design parameters.

3

Design sensitivity analysis of frequency response functions and steady-state response for structures with viscoelastic dampers

Łasecka-Plura M., Lewandowski R.

Vibrations in Physical Systems

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2014

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Vol. 26

129--136

EN

In this paper, the design sensitivity of the frequency response function and amplitudes of the steady-state vibration of planar frames with viscoelastic (VE) dampers mounted on them is considered. The dampers are modeled using a five-parameter rheological model with fractional derivatives. The design sentisivity with respect to change of damper parameter is analyzed in detail. The direct method is used to determine the first and the second order sensitivities. Moreover, the results of typical calculations are presented and discussed.

4

The solution of static problem of arch structures by the difference equation method

Rakowski J., Łasecka-Plura M.

Foundations of Civil and Environmental Engineering

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2006

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No. 8

99-110

EN

The solution of a bending problem for a circular arch loaded by nodal forces has been presented herein. The considered structure is divided into a regular mesh of identical finite elements. Equilibrium equations have becnwriiten in the form of three difference equations. The solution has beenobtained in the analytical closed form which does not depend on mesh density.