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    Wyświetlanie 1-3 z 3
    Tytuł:
    Fractional calculus for continuum mechanics – anisotropic non-locality
    Autorzy:
    Sumelka, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/201244.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non-local kinematics
    fractional calculus
    anisotropy
    kinematyka
    rachunek ułamkowy
    anizotropia
    Opis:
    In this paper, a generalisation of previous author’s formulation of fractional continuum mechanics for the case of anisotropic non-locality is presented. The discussion includes a review of competitive formulations available in literature. The overall concept is based on the fractional deformation gradient which is non-local due to fractional derivative definition. The main advantage of the proposed formulation is its structure, analogous to the general framework of classical continuum mechanics. In this sense, it allows to define similar physical and geometrical meaning of introduced objects. The theoretical discussion is illustrated by numerical examples assuming anisotropy limited to single direction.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 2; 361-372
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The analysis of non-linear free vibration of FGM nano-beams based on the conformable fractional non-local model
    Autorzy:
    Rahimi, Z.
    Sumelka, W.
    Shafiei, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/201202.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    FGM nano beam
    nonlinear free vibration
    fractional calculus
    integer stress
    non-integer stress
    gradient’s order
    fractional non-local model
    rachunek różniczkowy
    FGM
    drgania swobodne
    Opis:
    Continuum models generalized by fractional calculus are used in different mechanical problems. In this paper, by using the conformable fractional derivative (CFD) definition, a general form of Eringen non-local theory as a fractional non-local model (FNM) is formulated. It is then used to study the non-linear free vibration of a functional graded material (FGM) nano-beam in the presence of von-Kármán non-linearity. A numerical solution is obtained via Galerkin and multiple scale methods and effects of the integer and non-integer (fractional) order of stress gradient (in the non-local stress-strain relation) on the ratio of the non-local non-linear natural frequency to classical non-linear natural frequency of simply-supported (S-S) and clamped-free (C-F) FGM nano-beams are presented.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 5; 737-745
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Determination of hazardous metal ions in the water with resonant MEMS biosensor frequency shift – concept and preliminary theoretical analysis
    Autorzy:
    Rahimi, Z.
    Yazdani, J.
    Hatami, H.
    Sumelka, W.
    Baleanu, D.
    Najafi, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/202229.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    micro-mechanical sensor
    hazardous metals
    resonant frequency shift
    micro mass-sensor
    drinking water
    Opis:
    Heavy metal ions (e.g. cadmium, chromium, copper, nickel, arsenic, lead, zinc) have significantly serious side effects on the human health. They can bind with proteins and enzymes, altering their activity, increasing neurotoxicity, generating reactive oxygen species (ROS), promote cellular stress and resulting in their damage. Furthermore, the size, shape and type of metal are important for considering nano- or microtoxicity. It then becomes clear that the levels of these metals in drinking water are an important issue. Herein, a new micro-mechanical sensor is proposed to detect and measure these hazardous metals. The sensor consists of a micro-beam inside a micro-container. The surface of the beam is coated with a specific protein that may bind heavy metals. The mass adsorbed is measured using the resonant frequency shift of the micro-beam. This frequency shift due to the admissible mass (which is considered acceptable for drinking water based on the World Health Organization (WHO) standard) of manganese (Mn), lead (Pb), copper (Cu) and cadmium (Cd) is investigated for the first, second and third mode, respectively. Additionally, the effects of micro-beam off-center positions inside the micro-container and the mass location and investigated.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 3; 529-537
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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