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1

Energy consumption in mechanical systems using a certain nonlinear degenerate model

Jamroziak K., Bocian M., Kulisiewicz M.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 4

827--835

EN

In modern engineering materials used for creating effective ballistic shields, the issues of evaluation of their energy consumption are extremely important. The paper presents a new way of solving this problem using a certain degenerate model with dry friction. This metod involves the use of specially derived identification equations which describe the decrease in potential energy of the system during its vibratory motion induced by a single pulse load. Analytical considerations have been verified using a computer simulation technique for selected examples.

2

The identification of degenerated systems in the impact energy dissipation process

Bocian M., Jamroziak K.

Journal of Achievements in Materials and Manufacturing Engineering

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2013

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Vol. 57, nr 1

23--30

EN

Purpose: The article presents an analysis of impact energy dissipation process with selected non-classical dynamic models. Design/methodology/approach: Identification of impact energy dissipation phenomena in mechanical systems with a layered structure (eg. composite ballistic shields) is quite a challenge, because on the one hand it is sought to the model, whose parameters are as much as possible responsible for the energy dissipation, on the other hand, the number of parameters should be optimized. Searched model should be reduced to a simple description of the whole phenomenon and completely imitate entire mechanical system. Description of the impact energy dissipation was modeled with selected degenerated systems in this case. Models were subjected to hammer extortion the specified impulse of force. The mathematical description of pulsed extortion was carried out by using the energy and balance equation of power. Verification of mathematical identification equations for selected model parameters was performed by computer simulation technique. Findings: This is original analytical method, which uses the degenerated systems in various configurations. It involves the use of specially derived identification equations, which are described by the decrease of potential energy of the system during the vibrations induced by a single impulse load. Research limitations/implications: Method of identification requires the use of appropriate input function. Input function could be a periodic type or a type of step function. Practical implications: Estimation of the energy consumption objects in terms of method of identifying the parameters of the model. Originality/value: Presented work includes the identification of piercing the ballistic shield, and it is a part of work on the implementation of the degenerated models to describe these phenomena.

3

Identification of the selected parameters of the model in the process of ballistic impact

Jamroziak K.

Journal of Achievements in Materials and Manufacturing Engineering

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2011

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Vol. 49, nr 2

305--312

EN

Purpose: Analysis of the process of overshooting the material with high speed refers to the identification of certain properties of elasto-dissipative materials. The result of this identification is to determine the value of deformation on the basis of changes in the speed of the projectile inside the material until it stops or overshoot this material. Design/methodology/approach: On the basis of the proposed dynamic models of piercing the material using energy balance equations, dissipation of the energy of mass which strikes the shield has been described. Findings: Dependence of the values of elastic energy and dissipative energy has been derived based on the energy balance equations whose values determine the sensitivity of the analyzed parameters of the dynamic models of the overshooting process. Research limitations/implications: Dynamic models have been analyzed and the impact energy balance equations have been derived. Those equations were the basis to determine the constants and to show their mathematical and graphical interpretation. Practical implications: Derivation of the dependence for the constants, which are characteristic for the energy balance equations, allowed to describe by dependencies the selected parameters of the model, whose identification may be performed using a special quasi-statistical tests on special stand or in the manner as described. Originality/value: Presented work including the identification of piercing the ballistic shield is a part of work on the implementation of the degenerated models to describe these phenomena.

4

Identification of the elastodamping properties of long bones on a basis of the degenerate models

Panek M.

Vibrations in Physical Systems

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2010

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Vol. 24

313--318

EN

The dynamic load is essential for proper working of the skeletal system. The loads affecting skeleton during practising different kinds of sports and when accidents occur (for example resulting with bone injuries) have dynamic character, often with periodical or pulse shape. Therefore, from the scientific and clinical point of view, assignment of the dynamical properties of bone tissues is necessary. In this paper two degenerate models for description of the bovine bones dynamic properties are presented. The whole femur bone supported as a cantilever beam with additional masson the free end is subject of investigations. The excitation is applied by electro-dynamic shaker. The force sensor is situated between shaker and the bone, and the reaction of the system is measured by acceleration sensor. On the basis the energy balance and the power balance equations the models parameters are identified. In this paper is presented a set of parameters describing chosen models for two cases. In the first case, it is assumed that a value of the additional mass is not known, and in the second case calculations are performed for known value of the substitutional mass. In the first case for both models (built on a basis of the Zener model I and the system basing on the general model of viscoelastic body II), a majority of identified parameters are negative. For a given mass value, in model I every parameter had positive value whereas in model II only the damping parameter was negative. The obtained results indicate that the model I is more suitable to describe of the bone dynamical properties.

PL

Do prawidłowego funkcjonowania układu kostnego niezbędne jest działanie obciążeń o charakterze dynamicznym. Siły działające na kościec podczas uprawiania różnych rodzajów sportu oraz podczas wypadków, np. prowadzących do uszkodzenia kości, także mają charakter dynamiczny, w tym często o przebiegu impulsowym lub okresowym. Dlatego tez z naukowego oraz klinicznego punktu widzenia, istotne jest poznanie własności dynamicznych tkanek kostnych. W niniejszej pracy przedstawiono dwa modele zdegenerowane, mające opisać własności dynamiczne kości wołowych. Badaniom poddano całą kość udową, która mocowana była w układzie belki wspornikowej z dodatkową masą. Wymuszenie realizowane było za pomocą wzbudnika elektro-dynamicznego. Pomiędzy nim a kością umieszczony był czujnik siły, natomiast odpowiedź układu rejestrowana była za pomocą czujnika przyspieszenia. Na tej podstawie za pomocą metody bilansu energii i bilansu mocy identyfikowano wartości parametrów występujących w modelach. Ruch masy dodatkowej zamocowanej na wolnym końcu kości, rozpatrywano jako drgania masy w układzie o jednym stopniu swobody. W pracy przedstawiono zestaw parametrów opisujących wybrane modele dla dwóch przypadków. W pierwszym założono, że wielkość masy dodatkowej nie jest znana, a w drugim obliczenia przeprowadzono dla zadanej wielkości masy zastępczej. W pierwszym przypadku, zarówno układzie w bazującym na modelu Zenera I jak i powstałym na bazie ogólnego modelu ośrodka sprężysto-lepkiego II, większość identyfikowanych parametrów przyjmowała wartości ujemne. Przy zadanej wielkości masy, w modelu I wszystkie parametry przyjmowały wartości dodatnie, natomiast w modelu II tylko parametr tłumienia był ujemny. Na tej podstawie wydaje się, że model l Iepiej nadaje się do opisu właściwości dynamicznych kości.