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1

Influence of temperature on dynamic properties of plates with viscoelastic dampers

Lenartowicz Agnieszka, Przychodzki Maciej

Vibrations in Physical Systems

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2020

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Vol. 31, nr 3

art. no. 2020310

EN

The free damped vibrations of thin (Kirchhoff-Love) plates equipped with viscoelastic dampers are considered in the paper. It is assumed that the dampers are described according to the generalized rheological model. Influence of temperature on the parameters of dampers is taken into account using the frequency-temperature correspondence principle. Isotropic and rectangular plates are analysed in numerical tests included in this study. The natural frequencies and non-dimensional damping ratios are determined for these plates by solving the non-linear eigenproblem using the continuation method. The Finite Element Method is used to determine the stiffness matrix and the mass matrix occurring in the considered eigenproblem. The results of exemplary numerical calculations are presented and discussed at the end of this paper.

2

Boundary value problems with solutions

Herzog Gerd, Kunstmann Peer Chr.

Opuscula Mathematica

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2019

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Vol. 39, no. 1

49--60

EN

By means of the continuation method for contractions we prove the existence of solutions of Dirichlet boundary value problems in convex sets. As an application we prove the existence of concave solutions of certain boundary value problems in ordered Banach spaces.

3

Prediction of aircraft lost of control in the flight by continuation, bifurcation, and catastrophe theory methods

Sibilski K., Kowalski M.

Journal of KONES

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2016

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Vol. 23, No. 4

451--460

EN

Lost of Control in Flight (LOC-I) is ordinarily associated with flight outside of the normal flight envelope, with nonlinear behaviours, and with an inability of the pilot to control the aircraft. These results provide a means for analysing accident data to establish whether or not the accident should be classified as LOC-I. Moreover, they help identify when the initial upset occurred, and when control was lost. The analysis also suggests which variables were involved, thereby providing clues as to the underlying mechanism of upset. However, it does not provide direct links to the flight mechanics of the aircraft, so it cannot be used proactively to identify weaknesses or limitations in the aircraft or its control systems. Moreover, it does not explain how departures from controlled flight occur. The complexity of the disaster aetiology stems from both the scale and coupling of the systems (not only the physical aircraft systems but also the organizational systems that support the operation). This complexity creates a pattern of disaster that evolves or it is precipitated through a series of several small failures. The cusp catastrophe model facilitates the mapping of Reason’s latent failure model, providing a descriptive and predictive illustration of the emergence of latent conditions under the trigger of situational factors. The risk of an accident increases as the situational and systematic factors combine to create an inherent instability resulting in the catastrophic event.

4

Application of shape memory alloy in harvesto-absorber system

Kęcik K.

Acta Mechanica et Automatica

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2015

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Vol. 9, no. 3

155--160

EN

This paper presents a conception of the harvester-absorber system consisting of two parts. The first is the pendulum attached to the main system (oscillator), which is suspended on the linear damper and the nonlinear spring made of shape memory alloy. The spring is modelled as a polynomial function based on Landau–Ginzburg theory of phase transitions (similar as ferroelectric and ferromagnets). The obtained results show, that SMA element can increase harvesting energy level, while the absorber effect can be impaired (but not loss). Additionally, introducing SMA element causes changes in dynamics, introduces a new unstable solutions and bifurcations. The analysis was done by classical integration and continuation solution methods.

5

Identification of Formal Fallacies in a Natural Dialogue

Kacprzak M., Sawicka A.

Fundamenta Informaticae

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2014

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Vol. 135, nr 4

403--417

EN

This paper is a continuation of the work [26] in which the LND dialogue system was proposed. LND reconstructs the dialogical logic introduced by Lorenzen using the terminology of persuasion dialogue games as specified by Prakken [18]. The aim of the LND system is to recognize formal fallacies in natural dialogues and remove them. Now we extend this system to include a new protocol enabling the reconstruction of natural dialogues in which parties can commit formal fallacies. We then present the implementation of the protocols applied.

6

A study of the flight dynamics helicopter carrying an external load using bifurcation theory and continuation methods

Sibilski K.

Journal of Theoretical and Applied Mechanics

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2003

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Vol. 41 nr 4

823-852

EN

The paper presents a study of the flight dynamics of a helicopter with an articulated rotor, carrying a suspended load. The aircraft model includes rigid body dynamics, individual flap and blade dynamics, and inflow dynamics. The load is a point mass with a single suspension point. Results are obtained for load masses of up to 1500 kg, with load-to-helocopter mass rations up to 33%, and cable lengths up to 55m. The presence of the external load modifies the flight dynamics and handling quality characteristics of the helicopter because the dynamic and aerodynamic characteristics of the load may make it unstable in certain fight conditions. Maneuvers of this system in wide flight regimes involves non-linear aerodynamics and inertial coupling. In can be stated that the helicopter with the suspended load is a inherently non-linear and time varying system. Theory of dynamical systems provides a methodology for studying such non-linear systems. Bifurcation theory is a part of that theory. It considers changes in the stability of the system which lead to qualitatively different responses of it. In this paper, results from the theory of dynamical systems are used to predict the nature of instabilities caused by bifurcations and the response of the rotorcraft with the suspended load that follow such bifurcations.

PL

W pracy przedstawiono studium dynamiki lotu śmigłowca z przgubowym wirnikiem nośnym, przenoszącego podwieszony pod kadłubem ładunek. W zastosowanym modelu wiropłata uwzględniono stopnie swobody nieodkształcalnego kadłuba, dynamikę wahań i odchyleń łopat wirnika nośnego oraz dynamikę przepływu przez płaszczyznę wirnika nośnego. Założono, że podwieszony ładunek jest punktem materialnym, na który działają siły aerodynamiczne, podwieszonym w jednym punkcie pod kadłubem śmigłowca. Wyniki obliczeń uzyskano dla podwieszonych ładunków o masie do 1500kg (stosunek masy ładunku do masy śmigłowca do 35%), podwieszonych na linie o długości do 55m. Obecność podwieszonego ładunku modyfikuje charakterystyki dynamiczne i osiągi śmigłowca ze względu na silne sprzężenia aerodynamiczne i bezwładnościowe pomiędzy jego ruchem a ruchami śmigłowca. Ze względu na fakt, że układ śmigłowiec-podwieszony ładunek jest opisany za pomocą silnienieliniowych zwyczajnych równań różniczkowych, zastosowanie klasycznej analizy modalnej układu nie zawsze jest możliwe. Doskonałych narzędzi do badania takich równań dostarcza teoria układów dynamicznych i będąca jej częścią teoria bifurkacji. W pracy wykorzystano metodologię teorii układów dynamicznych do prognozowania natury niestabilności spowodowanej występującymi bifurkacjami. Ponadto przeprowadzono symulacje ruchu układu śmigłowiec-podwieszony ładunek po wystąpieniu bifurkacji.

7

A Homotopy Approach to Rational Covariance Extension With Degree Constraint

Enqvist P.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 5

1173-1201

EN

The solutions to the Rational Covariance Extension Problem (RCEP) are parameterized by the spectral zeros. The rational filter with a specified numerator solving the RCEP can be determined from a known convex optimization problem. However, this optimization problem may become ill-conditioned for some parameter values. A modification of the optimization problem to avoid the ill-conditioning is proposed and the modified problem is solved efficiently by a continuation method.