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Search results for: lagrangian mechanics
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Subharmonic solutions for a class of Lagrangian systems
PublicationWe prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken...
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Homoclinics for singular strong force Lagrangian systems
PublicationWe study the existence of homoclinic solutions for a class of generalized Lagrangian systems in the plane, with a C1-smooth potential with a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin.Under a strong force condition around the singular point ξ, via minimization of an action integral, we will prove the existence of at least two geometrically distinct homoclinic solutions.
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On the existence of homoclinic type solutions of inhomogenous Lagrangian systems
PublicationWe study the existence of homoclinic type solutions for a class of inhomogenous Lagrangian systems with a potential satisfying the Ambrosetti-Rabinowitz superquadratic growth condition and a square integrable forcing term. A homoclinic type solution is obtained as a limit of periodic solutions of an approximative sequence of second order differential equations.
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Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations
PublicationIn this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems.
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Periodic solutions of Lagrangian systems under small perturbations
PublicationIn this paper we prove the existence of mountain pass periodic solutions of a certain class of generalized Lagrangian systems under small perturbations. We show that the found periodic solutions converge to a periodic solution of the unperturbed system if the perturbation tends to 0. The proof requires to work in a rather unusual (mixed) Orlicz–Sobolev space setting, which bears several challenges.
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Homoclinics for singular strong force Lagrangian systems in R^N
PublicationWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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„Eulerian – Eulerian” versus ,,Eulerian –Lagrangean” models of condensation
PublicationLiquid phase in the flowing vapor through stages of the steam turbine is the cause of a lot of failures. Nowadays, due to work of steam turbines at partial load, process of homogeneous and heterogeneous condensation still is current. The formation of drops of condensate under conditions other than nominal operation of turbine is a process still unknown. Engineers and designers involved in the development of power station machines...
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About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
PublicationRecently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether's type Theorem, in particular ([9],Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis...
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Multibody and electromechanical modelling in dynamic balancing of mechanisms for mechanical and electromechanical systems
PublicationPraca prezentuje zagadnienia wspólnego modelowania układu wieloczłonowego i napędu elektrycznego oraz problemy wyrównoważania mechanizmów. Analizowanym układem mechanicznym jest płaski czworobok przegubowy. Analizowany mechanizm zamodelowano jako układ wieloczłonowy z zamkniętymi wielobokami ciał. Do wymuszenia ruchu układu wykorzystano model silnika prądu stałego. Zbadano oddziaływania pomiędzy płytą mocującą czworoboku i otoczeniem....
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Numerical Modeling of Cone Penetration Test in Slightly Overconsolidated Clay with Arbitrary Lagrangian-Eulerian Formulation
PublicationIn this paper the results of the cone penetration test (CPT) modeling with the arbitrary Lagrangian-Eulerian (ALE) formulation provided by Abaqus software package have been presented. The study compares the cone resistance and sleeve friction obtained in numerical analysis with values measured in soundings performed in the uniform layer of clayey soil in the Koszalin area. The clay layer was found to be slightly overconsolidated...
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FE-simulations of dynamic shear localization in granular bodies using an Arbitrary Lagrangian-Eulerian formulation.
PublicationW artykule przedstawiono wyniki symulacji lokalizacji odkształceń w materiałach granulowanych. Obliczenia wykonano przy zastosowaniu nielokalnego modelu hipoplastycznego dla 2 różnych problemów: sciskania dwuosiowego i przepływu silosowego. W obliczeniach wykorzystano sformułowanie ALE.
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Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory
PublicationIterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using...
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Autofagia: mechanizm molekularny, apoptoza i nowotwory = Autophagy: molecular mechanism, apoptosis and cancer
PublicationW pracy omówiono molekularny mechanizm autofagii oraz najważniejsze szlaki sygnałowe uczestniczące w regulacji przebiegu tego procesu w komórkach nowotworowych. Omówiona została również dwojaka rola autofagii w procesie nowotworzenia oraz skutki zarówno indukcji, jak i inhibicji autofagii w terapii przeciwnowotworowej
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Lagrangian model of an isolated dc-dc converter with a 3-phase medium frequency transformer accounting magnetic cross saturation
PublicationThis article presents a nonlinear equivalent circuit model of an isolated dc-dc converter with a 3-phase medium frequency transformer. The model takes into account the magnetic cross saturation of the 3-phase core-type magnetic circuit. The model is suitable in detailed electromagnetic transient simulations of power systems involving isolated dc-dc converters. The model is developed using the Lagrange energy method. It involves...
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On Invariants of Fluid Mechanics Tensors
PublicationThis paper presents physical interpretations of the first and second invariants of tensors of fluid mechanics. Some examples of elementary applications and meanings are also given.
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On mechanics of piezocomposite shell structures
PublicationThis study presents an original and novel investigation into the mechanics of piezo-flexo-magneto-elastic nanocomposite doubly-curved shells (PFMDCSs) and the ability to detect the lower and higher levels of electro-magnetic fields. In this context, by utilizing the first-order shear deformation shell model, stresses and strains are acquired. By imposing Hamilton's principle and the von Kármán approach, the governing equations...
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Fundamentals of classical and analytical mechanics
PublicationThe book is a monographic description of the present attempt to Newtonian and Lagrangian mechanics. But also, it could be found as a supplementary educational material useful for the graduate courses in mechanics taken by students majoring in mechanical engineering, physics or physical science. In the book you can find a brief introduction to concepts and principles of algebra of vectors; Kinematics of particles, mainly focused...
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Probing the structure of quantum mechanics
PublicationWstęp do problemów dotyczących struktury mechaniki kwantowej, a w szczegółności związanych z jej nieliniowością, nielokalnością, a także problemami aks-jomatyzacji i wykorzystaniem zjawisk kwantowych do budowy komuterów.
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Mechanisms positioned in a neighbourhood of their singular positions - velocity amplification in the electromagnetic damping. Part 1 - Background of the mechanical structure modeling
PublicationW pracy przedstawiono metodę modelowania dynamiki drgającego hybrydowego układu mechanicznego złożonego z odkształcalnego podukładu ciągłego oraz z połączonego z nim mechanizmu. U układzie pojawiają się drgania części odkształcalnej. By je wytłumić, ich energia zamieniana jest w energię elektryczną (za pomocą prądnicy prądu stałego) i rozpraszana na oporności obecnej w układzie elektrycznym. Aby przyśpieszyć tłumienie, wprowadzony...
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Applications of Tensor Analysis in Continuum Mechanics
PublicationA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components...
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Biobearings: where mechanics meets biology
PublicationStawy człowieka z punktu widzenia mechaniki są łożyskami ślizgowymi, jednak posiadają zupełnie inne właściwości niż łożyska przemysłowe. Artykuł omawia sposoby implementacji znanych zasad zachowania łożysk ślizgowych dla biołożysk z punktu widzenia materiałowego, uwzględniając te osiągnięcia w zakresie tribologii, biologii, chemii organicznej oraz inżynierii hodowli chrząstek, które są związane z łożyskami synowialnymi.
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Modelling of cutting by means of fracture mechanics
PublicationThe suitability of modern fracture mechanic theory was proved for the estimation of the cutting force and the cutting specific resistance. This paper shows modification of Ernst-Merchant theory and its application for determination some other properties of wood sample. This theory is acceptable for evaluation of shear yield stresses and shear plane angle. Sawing by gang saw machine was used as a process similar to the orthogonal...
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MODELLING OF CUTTING BY MEANS OF FRACTURE MECHANICS
PublicationThe suitability of modern fracture mechanic theory was proved for the estimation of the cutting force and the cutting specific resistance. This paper shows modification of Ernst-Merchant theory and its application for determination some other properties of wood sample. This theory is acceptable for evaluation of shear yield stresses and shear plane angle. Sawing by gang saw machine was used as a process similar to the orthogonal...
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THE METHODS OF TEACHING / LEARNING STRUCTURAL MECHANICS
PublicationStructural mechanics is a key issue to study for engineers. A high rank and high social responsibility profession requires both a high graded and intuitive approach. The evolution of learning / teaching methodology follows the novel technical achievements of every decade. The aim remains the same: to produce a professional to perform advanced relevant analysis and safe, optimal structural design
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Correlation experiments in nonlinear quantum mechanics
PublicationPokazano w jaki sposób należy obliczać wieloczasowe i wielocząstkowe funkcje korelacyjne w nieliniowej mechanice kwantowej, aby zagwarantować lokalność formalizmu.
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Soil mechanics and old buildings foundations
PublicationPraca dotyczy sposobów fundamentowania obiektów zabytkowych. Przeanalizowano historyczny rozwój sposobów posadowienia poczynając od starożytności, poprzez średniowiecze aż do czasów nowożytnych. Omówiono charakterystyczne dla kolejnych okresów historycznych rodzaje fundamentów. Przedstawiono przykłady dobrego i złego fundamentowania.
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Survey of modern trends in analysis of continuum damage mechanics
PublicationW artykule dokonano szerokiego przegladu literatury z zakresu mechaniki zniszczenia izotropowego. Przedstawiono równania stosowane w opisie zniszczenia materiału.
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Innovative rehabilitation lifts – mechanics in medical devices
PublicationMechanical devices are now widely used in physiotherapy and other rehabilitation processes. Particular importance is attached to devices enabling easy and effective transport of disabled people. The article presents innovative designs of rehabilitation lifts offered by the Polish manufacturer of lifts and medical accessories, LeviCare company. Moreover, the main assumptions of the research and development project implemented by...
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Polynomial Chaos Expansion in Bio- and Structural Mechanics
PublicationThis thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair...
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Mechanics of Micro- and Nano-Size Materials and Structures
PublicationNanotechnology knowledge is always looking to expand its boundaries to achieve the mostsignificant benefit to human life and meet the growing needs of today. In this case, we can refer tomicro- and nanosensors in micro/nano-electromechanical systems (MEMS/NEMS). These electricaldevices can detect minimal physical stimuli up to one nanometer in size. Today, micro/nano-sensordevices are widely used in the...
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Polynomial Chaos Expansion in Bio-and Structural Mechanics
PublicationThis monograph presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the...
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Approximation of Covariance Function with Application to Stochastic Mechanics.
PublicationW pracy przedstawiono koncepcję rozwinięć kanonicznych dla funkcji losowych oraz możliwość ich zastosowania w stochastycznej mechanice gruntów. Rozpatrzono rozkład widmowy, rozwinięcia Karhunena-Loevego oraz rozwinięcia ortogonalne zmodyfikowanymi wielomianami Hermite'a. Przeprowadzono analizę błędów dla zagadnienia warstwy gruntu o losowych parametrach sprężystych, uzyskano analityczne rozwiązanie systemu stochastycznego.
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Some Introductory and Historical Remarks on Mechanics of Microstructured Materials
PublicationHere we present few remarks on the development of the models of microstuctured media and the generalized continua.
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From fluid mechanics backgrounds to modern field theory
PublicationOur presentation keeps a historical line of reasoning, since we start from old concepts of fluid mechanics and finish on concepts of modern field theory. We want to show that some facts from the nature phenomena, which have firstly been discovered on the ground of fluid mechanics, were next incorporated into physics and later become the important pattern for whole mathematical physics. Especially, well-known continuum models, which...
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Cosmic-Time Quantum Mechanics and the Passage-of-Time Problem
PublicationA new dynamical paradigm merging quantum dynamics with cosmology is discussed.
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Sawing of wood - mechanics of cutting process, tools and machines.
PublicationW pracy przedstawiono wpływ obciażenia piły na dokładnośc przecinania. Zaprezentowano pilarkę ramową z eliptyczną trajektorią ruchu pił i hybrydowym dynamicznie wyrównoważonym napędem ramy piłowej, jak również wizyjny kontroler ostrzy pił tarczowych.
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A new integrated curriculum for computational methods in mechanics and design
PublicationPrzedstawiono program nowej specjalności na studiach inżynierskich: metody numeryczne w mechanice i projektowaniu, prowadzonej w języku angielskim.
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Mechanical, thermo-mechanical properties of epoxy/glass composites with submicron particles
PublicationIn this research the influence of submicron zinc oxide and silicon dioxide particles on mechanical, thermo-mechanical properties of epoxy matrix composites reinforced with glass fibres was investigated. Composites were fabricated using hand lay-up method. Materials contained 39-41 wt.% of glass fibres. The bending tests, dynamic mechanical analysis and tribological tests were performed on each group of composites and also for...
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Numeryczna mechanika płynów
PublicationNumeryczna mechanika płynów
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Laboratorium Mechaniki Płynów
PublicationKsiążka poświęcona jest zagadnieniom pomiarowym w mechanice płynów. Zawiera opis szeregu ćwiczeń laboratoryjnych związanych z przepływami. Książka przeznaczona jest dla studentów wydziałów mechanicznych i pokrewnych.
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Mechanical Properties of Implants
PublicationW pracy przedstawiono wyniki identyfikacji ortogonalnego modelu matematycznego czterech typów implantów stosowanych w laparoskopowym leczeniu przepukliny brzusznej.
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Katedra Mechaniki Budowli.
PublicationPodano zarys historii Katedry Mechaniki Budowli wraz z omówieniem współpracy naukowo-badawczej i dydaktycznej z zagranicą. Wskazano na aktualne możliwości współpracy z ośrodkami akademickimi, zagranicznymi i polskimi oraz z organizacjami administracyjno-gospodarczymi Regionu Pomorskiego.
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Cartoon computation: Quantum-like algorithms without quantum mechanics
PublicationZaproponowano formalizm prowadzący do algorytmów analogicznych do kwantowych, lecz wykorzystujący jedynie struktury geometryczne. Jako przykład sformułowano odpowiednik kwantowego algorytmu Deutscha-Jozsy.
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P92 steel and inconel 617 alloy welds joint produced using ERNiCr-3 filler with GTAW process: Solidification mechanism, microstructure, mechanical properties and residual stresses
PublicationThe objective of the current study was to analyse the microstructure, mechanical characteristics, and residual stresses of a dissimilar welded joint (DWJ) made of P92 steel and the Inconel alloy 617 (IN617) using the gas tungsten arc welding (GTAW) method. The ERNiCr-3 filler was selected to produce the conventional V groove (VG) and narrow V groove (NVG) butt joint. The filler deficient zones in the weldments, such as the filler...
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A Generalized Framework Towards Structural Mechanics of Three-layered Composite Structures
PublicationThree-layered composite structures find a broad application. Increasingly, composites are being used whose layer thicknesses and material properties diverge strongly. In the perspective of structural mechanics, classical approaches to analysis fail at such extraordinary composites. Therefore, emphasis of the present approach is on arbitrary transverse shear rigidities and structural thicknesses of the individual layers. Therewith...
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Application of Fracture Mechanics for Energetic Effects Predictions While Wood Sawing
PublicationIn the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specific cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, cutting forces (or power - more interesting from energetic point of view) could be considered from a point of view of modern fracture mechanics. Cutting...
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The fundamentals of narrow-kerf sawing; the mechanics and quality of cutting / K. A. Orłowski.
PublicationW pracy przedstawiono ekonomiczne i ekologiczne uwarunkowania dokładnego przecinania drewna za pomocą pił cienkich (o niewielkiej wartości rzazu). Opisano współczesne technologie wykorzystujące cienkie piły: pilarki tarczowe wielopiłowe, pilarki taśmowe i ramowe. W rozdziale drugim omówiono siły skrawania w ujęciu klasycznym, w którym do ich szacowania przyjmuje się przede wszystkim wartości właściwego powierzchniowego oporu skrawania,...
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Influence of meniscus shape in the cross sectional plane on the knee contact mechanics
PublicationWe present a three dimensional finite element analysis of stress distribution and menisci deformation in the human knee joint. The study is based on the Open Knee model with the geometry of the lateral meniscus which shows some degenerative disorders. The nonlinear analysis of the knee joint under compressive axial load is performed. We present results for intact knee, knee with partial and complete radial posterior meniscus root...
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Application of fracture mechanics for energetic effects predictions while wood sawing
PublicationIn the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specific cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, cutting forces (power) could be considered from a point of view of modern fracture mechanics. Cutting forces may be employed to determine not only toughness...
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J. FE modelling of cracks in concrete elements within continuum mechanics.
PublicationW artykule przedstawiono wyniki symulacji rys zakrzywionych w elementach betonowych w warunkach mieszanego sposobu obciążenia. Symulacje wykonano przy zastosowaniu 3 różnych modeli: modelu sprężysto-plastycznego, modelu w ramach mechaniki zniszczeniowej i modelu z rysami obracającymi się.