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Abstracts of papers for

Previous issue vol. 49, no. 4 (2001)

vol. 50, no. 1-2 (2002)

Next issue vol. 50, no. 3 (2002)

Contents of issue 1-2, vol. 50

1. T. Łodygowski, W. Siekierski : Beam-element model of bridge truss girders regarding joint dimensions
2. T. Orzechowski : Influence of the state of the mating friction elements of the drum brake on the outer thermal field
3. Ji-Huan He : Periodic solutions for a kind of nonlinear oscillations by a new asymptotic approach
4. Ji-Huan He : Nonlinear Mathieu equation and its approximation without a small parameter
5. M. Delyavsky, M. Kravchuk, W. Nagórko, A. Podhorecki : Pure bending of the orthotropic elastic rectangle
6. Z. Wrzesiński : Thermodynamics of a multicomponent gaseous phase as viewed by the balance theory
7. Z. Wrzesiński : The substantial balance of internal energy (IE) for extensive quantities as viewed by the balance theory
8. Z. Wrzesiński : Substantial balance equation of internal energy as viewed by the balance theory

T. Łodygowski, W. Siekierski : Beam-element model of bridge truss girders regarding joint dimensions

The paper concerns modelling of bridge truss girders with regard to joint (gusset plates) dimensions. Modification of the classical beam-element numerical model is presented. It is based on introduction of additional near-node beam elements of lengths corresponding to joint dimensions. Their stiffnesses are determined in the iterative procedure. Results of finite element method analyses of the "accurate" (shell element) and dynamically modified "simplified" (beam element) models of structural joint with a part of connected members are compared. Laboratory tests that verify the iterative procedure are described. The calculated and recorded displacements and internal forces are compared.

Contents

T. Orzechowski : Influence of the state of the mating friction elements of the drum brake on the outer thermal field

The analysis presented below concerns the thermal field of the outer surface of the drum brake registered by means of an AGEMA Series 900LW thermovision camera and the LINY software. Roundness deviations of the inner surface of the drum measured with a TALYROND precise measurement device were compared with the distribution of temperature on the outer surface along the circumference. The results show that these quantities are interdependent and the coefficients of correlation calculated for them are always greater than 0.8. What is more, they are not affected by the type of pressure (i.e. shoe). The distribution of temperature along the generating line of the drum represents the character of the contact between the shoe and the drum. Tests carried out for various arrangements of friction members of the drum brake confirmed the interdependence of the thermal field and the geometry of mating surfaces. A maximum temperature rise of the drum has also been discussed.

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Ji-Huan He : Periodic solutions for a kind of nonlinear oscillations by a new asymptotic approach

This paper proposes a new asymptotic approach to search for the periodic solutions of a kind of nonlinear oscillations. In this method the iteration technique is coupled with the traditional perturbation techniques, yielding a powerful mathematical tool for solving strongly nonlinear equations. Some examples are given to illustrate its effectiveness, convenience and accuracy. Generally, the first iteration leads to a highly accurate approximate solution which is uniformly valid for the whole solution domain. The new asymptotic approach is named the iteration-perturbation method.

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Ji-Huan He : Nonlinear Mathieu equation and its approximation without a small parameter

In this paper, the linear and nonlinear Mathieu equations without a small parameter are considered, which cannot be solved by the perturbation techniques. However, using the variational iteration method, their periodic solutions can be readily obtained with high accuracy. In addition, some special cases have been discussed, where the perturbation solutions are meaningless even when there exists a small parameter.

Contents

M. Delyavsky, M. Kravchuk, W. Nagórko, A. Podhorecki : Pure bending of the orthotropic elastic rectangle

In this contribution, a new method for obtaining the solution to the linear elasticity problem is proposed. An idea of this method is based on certain special expansion of these displacement fields in finite trigonometric series with exponential coefficients. This approach leads to an equivalent problem which requires to derive the exact solution. The proposed method has a mixed analytic-numerical form and has been illustrated by the solution to the boundary value problem for a rectangular region subjected to bending by loads applied on the opposite sides of the region. The numerical results derived have been compared with solutions obtained in the framework of the Euler-Bernoulli beam theory.

Contents

Z. Wrzesiński : Thermodynamics of a multicomponent gaseous phase as viewed by the balance theory

The article presents some formalised definitions of volume density of the molar number of a mixture and a mixture component. With the help of the above definitions, the molar concentration of a mixture component has been determined. An analysis has also been made to define partial volume density. The mass density of a substance component production has been defined and the notion of the referential density of the stream exchange of a substance component has been applied to analyse the movement of substance components in the mixture, whereby defining the notion of a diffusion stream density. Next, with the help of the referential balance equation of a substance component, an analysis has been made of the balance of substance components leading to the definition of an equation of diffusion continuity which in turn, under the accepted constraints, leads to the so-called second Fick's law.

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Z. Wrzesiński : The substantial balance of internal energy (IE) for extensive quantities as viewed by the balance theory

The article presents the balance axiom and the basic balance leading to the referential balances of a scalar and vector extensive quantity (EQ). Next the substantial balance of internal energy (IE) has been done, defining the production part which is the sum of IE creation and annihilation, as well as the exchange part which is the sum of IE inflow and outflow through the boundaries of a substantial system. The substantial balance of internal energy (IE) achieved in this way has been reduced to the balance under the conditions of a reversible change, to obtain finally the balance of IE, commonly referred to as the first principle of thermodynamics for extensive quantities (EQs).

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Z. Wrzesiński : Substantial balance equation of internal energy as viewed by the balance theory

The article defines the microscopic substantial system and elementary first-order increments of elementary third-order increments of internal energy (IE), friction heat and heat exchanged between the substantial microsystem and the exterior. A substantial balance of internal energy (IE) has been presented for extensive quantities (EQ) with reference to a substantial microsystem which has been next transformed into a substantial balance equation of the mass density of internal energy (IE). The substantial balance equation of the mass density of internal energy has been integrated for a substantial system throughout the whole substantial area, obtaining a substantial balance equation of internal energy for intensive quantities related to this area. It has also been defined under what conditions this balance equation can be used in the substantial area. In the case of the reversible change, the substantial balance equation of internal energy (IE) for intensive quantities has been reduced to the equation commonly called the first principle of thermodynamics for intensive quantities.

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Abstracts for 49, 4, 2001 (previous issue)

Abstracts for 50, 3, 2002 (next issue)

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