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1
Content available Dynamic characteristics of the structure with viscoelastic dampers combined with inerters and subjected to temperature changes
Pawlak Zdzisław M., Lewandowski Roman
Vibrations in Physical Systems
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2020
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Vol. 31, nr 2
art. no. 2020222
EN
The purpose of the work is dynamic analysis of passive dampers used in structural systems to reduce excessive vibrations caused by wind or earthquakes. Special systems are considered that contain inerter, i.e. device using rotational inertia, in combination with a viscoelastic damper. The so-called fractional models of viscoelastic dampers describe their dynamic behavior in a wide frequency range using a small number of model parameters. To describe material behavior over a wider frequency range, the time-temperature superposition principle is used. The shifting factor is calculated from the well-known William-Landel-Ferry formula. This allows for determination of damper parameters at any temperature based on the parameters obtained at the reference temperature. Laplace transformation of the derived equations of motion leads to the non-linear eigenproblem, which could be solved using the continuation method. The influence of temperature on the dynamic characteristics of the system is examined.
2
Content available On the existence of a nontrivial equilibrium in relation to the basic reproductive number
Wijaya K. P., Sutimin, Soewono E., Götz T.
International Journal of Applied Mathematics and Computer Science
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2017
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Vol. 27, no. 3
623--636
EN
Equilibrium analysis in autonomous evolutionary models is of central importance for developing long term treatments. This task typically includes checks on the existence and stability of some equilibria. Prior to touching on the stability, one often attempts to determine the existence where the basic reproductive number R0 plays a critical role as a threshold parameter. When analyzing a nontrivial equilibrium (e.g., an endemic, boundary, or coexistence equilibrium) where R0 is explicit, we usually come across a typical result: if R0 > 1, then a nontrivial equilibrium exists in the biological sense. However, for more sophisticated models, R0 can be too complicated to be revealed in terms of the involving parameters; the task of relating the formulation of a nontrivial equilibrium to R0 thus becomes intractable. This paper shows how to mitigate such a problem with the aid of functional analysis, adopting the framework of a nonlinear eigenvalue problem. An equilibrium equation is first to be transformed into a canonical equation in a lower dimension, and then the existence is confirmed under several conditions. Three models are tested showing the applicability of this approach.
3
Content available remote Some theorems of Rabinowitz type for nonlinearizable eigenvalue problems
Przybycin J.
Opuscula Mathematica
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2004
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Vol. 24, no. 1
115-121
EN
We discuss the structure of the solution set for nonlinearizable eigenvalue problems in a Hilbert space.
4
Content available remote Investigation of surface wave operators in a nonohomogeneous anisotropic elastic half-space
Klecha T.
Prace Instytutu Podstawowych Problemów Techniki PAN
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2000
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nr 5
3-11
EN
In the paper new alternative approach to surface wave problem in a nonohomogeneous anisotropic elastic semi-space in terms of stress tensor components vanishing on semi-space boundary is presented. This approach alows to perform analysis of surface wave using Green`s function theory similar as is it done for Sturm-Liouville operations in the space of unbounded measure.
5
Content available remote Analysis of Surface Wave Operator in a Nonhomogeneous Isotropic Elastic Semi-space. Part 1
Klecha T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2000
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Vol. 48, nr 4
493-498
EN
In the paper a new alternative approach to surface wave problem in a nonhomogeneous isotropic elastic semi-space is presented. The problem is formulated in terms of stress tensor components vanishing on the boundary of a semi-space. This approach allows us to perform analysis of surface waves using a Green's function theory as well as a Sturm-Liouville operator theory.
6
Content available remote Analysis of Surface Wave Operator in a Nonhomogeneous Anisotropic Elastic Semi-space
Klecha T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2000
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Vol. 48, nr 4
505-511
EN
A new alternative approach to the surface wave problem in a nonhomogeneous anisotropic elastic semi-space in terms of the stress tensor components vanishing on the semi-space boundary is presented. This method allows us to perform an analysis of surface waves using a Green's function theory similar as it is done for Sturm-Liouville operators in the space of unbounded measures.
7
Content available remote Existence of Uniqueness of the Solution to the Problem of Surface Wave Propagation in a Nonhomogeneous Isotropic Elastic Half-space
Klecha T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1999
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Vol. 47, nr 3
221-225
EN
It is shown that in a nonhomogeneous isotropic elastic half-space with constant density and shear modulus and with Poisson ratio being bounded function of half-space depth belonging to the class [formula] the surface wave is unique.
8
Content available remote Propagation of surface waves in a nonhomogeneous anisotropic elastic semi-space
Klecha T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1998
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Vol. 46, nr 2
163-176
EN
In the paper the previous results of the author on the surface waves in a nonhomogeneous isotropic elastic semi-space [4], [6] has been extended to an anisotropic semi-space. It is shown, that the velocity and the amplitude of the surface waves in the non homogeneous anisotropic elastic semi-space, with non homogeneity depending on a semi-space depth, are the analytical functions of the wave number. The branches of the dispersion relation have only algebraic singularities and the singularities are at most countable. Moreover it is demonstrated that for the nonhomogeneous isotropic halfspace with a constant density and a shear modulus, and under the assumption that the Poisson ratio is a bounded function of class C2 [0, [nieskończoność]), there exists at least one solution, and at most finite number of solutions of the dispersion equation.
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