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1

The vibrations of non-symmetric periodic sandwich beams

Marczak Jakub

Vibrations in Physical Systems

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2020

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Vol. 31, nr 2

art. no. 2020218

EN

Sandwich structures are certain specific type of composites, which are widely used in modern engineering. In this paper the vibration analysis of a specific type of sandwich beam is performed. The considered structure is not only non-symmetric towards its midplane, but also made of periodically varying isotropic materials. As a result, the governing equations of such complicated structure is characterised by periodic, non-continuous and highly oscillating coefficients. With the use of the tolerance averaging technique those equations are transformed into the form with constant coefficients. Eventually, a comparative simulations of free vibration analysis of several sandwich beams were conducted to verify the effectiveness and superiority of proposed calculation method over the FEM.

2

On the modeling of periodic sandwich structures with the use of the broken line hypothesis

Marczak J.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 3

761--773

EN

In this paper a dynamic analysis of sandwich plate with a certain periodic microstructure is considered. The initial system of governing equations is derived basing on the classic broken line hypothesis. As a result of transformations one can obtain a system of three differential equations of motion with periodic, highly oscillating and non-continuous coefficients. In order to derive a system of equations with constant coefficients tolerance averaging technique is applied. Eventually, in the calculation example a free vibration analysis of certain periodic plate strip is performed with the use of both the derived model and a FEM model. It can be observed that the consistency of obtained results is highly dependent on the calculation assumptions.

3

Vibrations of thin functionally graded plates with tolerance-periodic microstructure

Kaźmierczak-Sobińska M., Jędrysiak J.

Vibrations in Physical Systems

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2014

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Vol. 26

99--104

EN

This paper presents a problem of vibrations of thin functionally graded plates. To describe this kind of plates three averaged models are proposed: a tolerance model, an asymptotic model and a combined asymptotictolerance model, cf. [10]. Calculational results obtained for a functionally graded plate band using the proposed models are compared to each other.

4

Efficiency of the needle probe test for evaluation of thermal conductivity of composite materials: two-scale analysis

Łydżba D., Różanski A., Rajczakowska M., Stefaniuk D.

Studia Geotechnica et Mechanica

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2014

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Vol. 36, nr 1

55--62

EN

The needle probe test, as a thermal conductivity measurement method, has become very popular in recent years. In the present study, the efficiency of this methodology, for the case of composite materials, is investigated based on the numerical simulations. The material under study is a two-phase composite with periodic microstructure of “matrix-inclusion” type. Two-scale analysis, incorporating micromechanics approach, is performed. First, the effective thermal conductivity of the composite considered is found by the solution of the appropriate boundary value problem stated for the single unit cell. Next, numerical simulations of the needle probe test are carried out. In this case, two different locations of the measuring sensor are considered. It is shown that the “equivalent” conductivity, derived from the probe test, is strongly affected by the location of the sensor. Moreover, comparing the results obtained for different scales, one can notice that the “equivalent” conductivity cannot be interpreted as the effective one for the composites considered. Hence, a crude approximation of the effective property is proposed based on the volume fractions of constituents and the equivalent conductivities derived from different sensor locations.

5

Asymptotic-tolerance modelling on vibrations of functionally graded thin plates

Kaźmierczak M., Jędrysiak J.

Vibrations in Physical Systems

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2012

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Vol. 25

217--222

EN

In this note there are considered functionally graded plates. To describe vibrations of these plates and take into account the effect of the microstructure, the tolerance averaging method is applied, cf. [7, 8]. There are formulated governing equations of the asymptotic-tolerance model, cf. [8]. Calculational results obtained for a functionally graded plate band using the proposed model, are compared to results by the known – tolerance and asymptotic models.

6

Simplicial modelling of dynamic problems in a micro-periodic composite material

Rychlewska J., Woźniak C.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2003

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Vol. 2, nr 1

159--168

EN

The aim of this paper is to propose a certain new approach to the formulation of both discrete and continuum models for the analysis of dynamic problems in elastic composite solids with a periodic microstructure. The proposed approach is based on a periodic simplicial division of the unit cell and on the assumption of a uniform strain in every simplex. The main feature of the obtained discrete model is the finite-difference form of the governing equations. By applying smoothing operation the continuum models are derived directly from the discrete ones.