Abstracts of papers for

Previous issue vol. 43, no. 1 (2002)

vol. 43, no. 2 (2002)

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Contents of issue 2, vol. 43

1. J. Awrejcewicz, G. Kudra and C.-H. Lamarque : Nonlinear dynamics of triple pendulum with impacts
2. R.K. Pramanik, S.C. Pal and M.L. Ghosh : High frequency solution of elastodynamic stress intensity factors due to the diffraction of plane longitudinal wave by an edge crack in a semi-infinite medium
3. J.P. Nowacki, V.I. Alshits and A. Radowicz : Green's function for an infinite piezoelectric strip with a general line defect
4. S. Giambò, B. Maruszewski and L. Restuccia : On a nonconventional thermodynamical model of a defective piezoelectric crystal
5. E. Barbera and S. Giambò : Two-waves nonlinear interactions for hyperbolic systems of balance laws
6. A. Ciarkowski : On Sommerfeld precursor in a Lorentz medium
7. K. Cabańska-Płaczkiewicz and N.D. Pankratova : Vibrations of the complex torsional system with a viscoelastic mass interlayer
8. J. Przeszowski : Vortices and flux quantization in the gauge models of high temperature superconductors

J. Awrejcewicz, G. Kudra and C.-H. Lamarque : Nonlinear dynamics of triple pendulum with impacts

Dynamics of a triple pendulum with damping, external forcing and impacts is analyzed numerically. In this mechanical system periodic, quasi-periodic and chaotic motions are detected. Specially developed numerical methods allow to track nonlinear behaviour of mechanical systems with many degrees of freedom and arbitrarily situated barriers, where an impact occurs.

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R.K. Pramanik, S.C. Pal and M.L. Ghosh : High frequency solution of elastodynamic stress intensity factors due to the diffraction of plane longitudinal wave by an edge crack in a semi-infinite medium

A harmonic in time, plane longitudinal wave is incident on a half-space containing a vertical edge crack. Both the incident field as well as the scattered field have been decomposed into symmetric and antisymmetric fields with respect to the plane of the crack, so that the problem is reduced to the boundary value problem for a 90° wedge. In both the symmetric and antisymmetric problem, incident body waves are at first diffracted by the edge of the crack. For a high frequency solution, the diffracted body wave rapidly decreasing after a few wave-lengths, the significant part of the diffracted wave is the Rayleigh wave which is reflected back from the corner of the wedge giving rise to a Rayleigh wave diffracted by the crack tip. This process of reflection of surface wave from the corner of the wedge and subsequent diffraction by the crack tip continues. Considering the contribution from the incident body waves and all the reflected Rayleigh waves, the stress intensity factors have been determined and their dependence on the frequency and on the angle of incidence has been depicted by means of graphs.

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J.P. Nowacki, V.I. Alshits and A. Radowicz : Green's function for an infinite piezoelectric strip with a general line defect

The 2D electro-elastic fields are found in the piezoelectric strip with the straight general line defect parallel to the surfaces and consisting of the four coinciding sources: the line of forces, the charged line, the dislocation line and its electrostatic analogue. Electrically, the strip is supposed to be placed between two isotropic dielectric media. Mechanically, three boundary conditions are considered: (i) both the surfaces are free; (ii) both the surfaces are clamped; and (iii) one surface is free and the other is clamped. The solutions obtained for a general case of unrestricted anisotropy are presented in the form of convergent Fourier integrals, in terms of the eigenvectors and eigenvalues of the generalized Stroh problem. Determination of these eigenvalues and eigenvectors requires additional computing. Specific features of the derived solutions at infinity are analyzed.

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S. Giambò, B. Maruszewski and L. Restuccia : On a nonconventional thermodynamical model of a defective piezoelectric crystal

The paper deals with an extended thermodynamical description of a defective piezoelectric crystal. Introducing a dislocation core tensor as an internal variable, the body is regarded as homogeneous and isotropic. Liu's theorem is applied to analyze the entropy inequality. The general constitutive relations for the state laws are derived, including all the possible linear and higher order simple and cross-effects which occur in the crystal when thermal, electric, elastic and dislocation fields interact with each other.

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E. Barbera and S. Giambò : Two-waves nonlinear interactions for hyperbolic systems of balance laws

In this paper we study the weakly nonlinear interaction of two waves whose propagation is governed by hyperbolic systems of balance laws. The method used here makes use of nonlinear phase variables and consists in a perturbation analysis. It is applied to an Eulerian gas and to a gas described by extended thermodynamics with thirteen moments.

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A. Ciarkowski : On Sommerfeld precursor in a Lorentz medium

A one-dimensional electromagnetic problem of Sommerfeld precursor evolution, resulting from a finite rise-time signal excitation in a dispersive Lorentz medium is considered. The effect of the initial signal rate of growth as well as of the medium dumping on the precursor shape and its magnitude is discussed. The analysis applied is based on an approach employing uniform asymptotic expansions. In addition, new approximate formulas are given for the location of the distant saddle points which affect local frequency and dumping of the precursor. The results obtained are illustrated numerically and compared with the results known from the literature.

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K. Cabańska-Płaczkiewicz and N.D. Pankratova : Vibrations of the complex torsional system with a viscoelastic mass interlayer

This paper presents an analytical method of solving the free and forced vibrations problems concerning a complex torsional continuous system of two circular shafts connected by a viscoelastic mass interlayer. In the solution of free and forced vibrations, the complex functions of real variable are used. Then, the property of orthogonality of complex modes of free vibrations has been demonstrated which is the basis for solving the free and forced vibrations problem for arbitrary initial conditions. The small torsional vibrations of the complex system with a viscoelastic mass interlayer are excited by the steady-state dynamical loading.

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J. Przeszowski : Vortices and flux quantization in the gauge models of high temperature superconductors

In this brief note different kinds of vortex states in the gauge models of high temperature superconductivity are presented. These theoretical considerations are confronted with a possible future experimental verification.

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