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Tytuł:
The constituent equations of piezoelectric cantilevered three-layer actuators with various external loads and geometry
Autorzy:
Mieczkowski, G.
Powiązania:
https://bibliotekanauki.pl/articles/279842.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
piezoelectric bender
constitutive equations
deflection
analytical solutions
Opis:
This paper presents test results for deformation conditions of three-layer, piezoelectric cantilever converters subjected to various electrical and mechanical boundary conditions. A general solution has been developed based on implementation of piezoelectric triple segments (PTS) to the beam. A working mechanism and conditions for strain of the PTS segment have been determined. Basing on the general solution, for the cantilever actuator subjected to an external force (of single and dual PTS segments) and a uniform load (of single PTS segment), particular solutions have also been developed. Moreover, dimensionless frequencies of the oscillating motion for the analyzed converters have been determined. In the next step, the influence of such factors as length, quantity and position of PTS segments, their relative stiffness and unit weight on values of the obtained frequencies of vibration have been defined. The resulting analytical solutions have been compared with the developed FEM solution.
Źródło:
Journal of Theoretical and Applied Mechanics; 2017, 55, 1; 69-86
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modeling the Diffusion of Dichlorvos through Human Stomach Lining
Autorzy:
Bello, O. D.
Oluwatusin, O. O.
Powiązania:
https://bibliotekanauki.pl/articles/1193343.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Analytical solutions
Concentration
Dichlorvos
Diffusion
Mathematical modeling
Opis:
Dichlorvos is the main poison in sniper pesticide which has produced negative effects especially among youths in recent times. The poisonous effects of dichlorvos on humans require urgent studies to combat the damaging impacts among humans. However, the limitations of carrying out experiments on human test subjects request the quest for alternative approach. Such approach can be made through modeling the transport of dichlorvos in the human body and the resulting negative effect. Therefore, this work presents mathematical modeling for the diffusion of dichlorvos through the human stomach lining. The model is set up to determine the amount of dichlorvos that leaves the stomach through diffusion alone and the health effects various concentration of the poison has on humans. Two cases are studied in order to captivate the effects of dichlorvos poisoning for two different scenarios. The initial condition is set to 0.05L and different driving forces is used to model the scenarios in spherical coordinates. The governing equation is derived from Fick’s first law and is solved analytically, a numerical solution is obtained using MATLAB’s pdepe solver and graphs are plotted for the two cases. From the results it is observed that about 14.4% of dichlorvos is diffused through the stomach lining in about 60hours for the first case while for the second case, the periodic intake of water along with dichlorvos gradually reduces the dichlorvos concentration in the stomach. These results show consistency with some experimental results from literature. Therefore, the model can be used in addition to the modes of treatment obtained from literature to predict the concentration of dichlorvos in a person and also proffer a life-saving treatment.
Źródło:
World Scientific News; 2021, 154; 34-47
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of higher order Hamiltonian approach to nonlinear vibrating systems
Zastosowanie metody Hamiltona wyższego rzędu w zagadnieniu drgań układów nieliniowych
Autorzy:
Askari, H.
Nia, Z. S.
Yildirim, A.
Yazdi, M. K.
Khan, Y.
Powiązania:
https://bibliotekanauki.pl/articles/279297.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
higher order Hamiltonian approach
Duffing equation
analytical solutions
Opis:
The higher order Hamiltonian approach is utilized to elicit approximate solutions for two nonlinear oscillation systems. Frequency-amplitude relationships and the model of buc kling of a column and mass-spring system are scrutinized in this paper. First, second and third approximate solutions of examples are achieved, and the frequency responses of the systems are verified by exact numerical solutions. According to the numerical results, we can conclude that the Hamiltonian approach is an applicable method for solving the nonlinear equations, and the accuracy of this method in the second and third approximates is very high and reliable. The achieved results of this paper demonstrate that this method is powerful and uncomplicated for solving of sophisticated nonlinear problems.
W pracy przedstawiono zastosowanie metody Hamiltona wyższego rzędu do wyznaczania przybliżonych rozwiązań analitycznych dla dwóch nieliniowych układów drgających. Szczegółowej analizie poddano charakterystyki amplitudowo-częstościowe modelu ściskanej belki oraz dyskretnego układu sprężysto-inercyjnego. Otrzymano przybliżone rozwiązania pierwszego, drugiego i trzeciego rzędu, a odpowiedzi częstościowe układów porównano z dokładnymi rezultatami symulacji numerycznych. Na ich podstawie oceniono, że metoda Hamiltona jest stosowalna dla układów nieliniowych, a przybliżenia drugiego i trzeciego rzędu stanowią rozwiązania analityczne o wysokiej dokładności. Uzyskane w pracy wyniki przekonują, że zaproponowana metoda jest prostym i jednocześnie bardzo skutecznym narzędziem rozwiązywania nieliniowych problemów układów mechanicznych o dużym stopniu złożoności.
Źródło:
Journal of Theoretical and Applied Mechanics; 2013, 51, 2; 287-296
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Calculation of the heat power of a tube heat exchanger
Autorzy:
Rup, Kazimierz
Powiązania:
https://bibliotekanauki.pl/articles/2091366.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
heat power
tube-in-tube exchanger
analytical solutions
numerical calculations
Opis:
In this paper, the logarithmic mean temperature difference method is used to determine the heat power of a tube-in-tube exchanger. Analytical solutions of the heat balance equations for the exchanger are presented. The considerations are illustrated by an example solution of the problem. In particular, the heat power of the tube-in-tube heat exchanger is determined taking into account the variants of work in the co-current and counter-current mode. Apart from the analytical solutions, appropriate numerical calculations in Matlab environment have been carried out.
Źródło:
Archives of Thermodynamics; 2022, 43, 1; 127--140
1231-0956
2083-6023
Pojawia się w:
Archives of Thermodynamics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The application of cumulants to flow routing
Autorzy:
Romanowicz, Renata J.
Doroszkiewicz, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/108562.pdf
Data publikacji:
2019
Wydawca:
Instytut Meteorologii i Gospodarki Wodnej - Państwowy Instytut Badawczy
Tematy:
open channel flow
linearized St. Venant equation
analytical solutions
moments
cumulants
Opis:
This paper aims to fill a gap between present and past research approaches to modelling flow in open channels. In particular, a history of the analytical solutions of a linearized St. Venant equation is presented. A solution of the linearized St. Venant equation, describing the response of a river channel to a single impulse forcing, the so called Instantaneous Unit Hydrograph (IUH), can be described using cumulants, defined as the moments of a logarithm of a variable. A comparison of analytical and numerical solutions of flood wave propagation under various flow conditions is given. The river reach of Biała Tarnowska is used as an illustration of both approaches. A practical application of simplified solutions to the emulator of a flood wave propagation is suggested showing a link between theory and practice.
Źródło:
Meteorology Hydrology and Water Management. Research and Operational Applications; 2019, 7, 1; 15-21
2299-3835
2353-5652
Pojawia się w:
Meteorology Hydrology and Water Management. Research and Operational Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical and numerical analysis of injection pump (stepped) shaft vibrations using Timoshenko theory
Autorzy:
Noga, Stanisław
Rejman, Edward
Bałon, Paweł
Kiełbasa, Bartłomiej
Smusz, Robert
Szostak, Janusz
Powiązania:
https://bibliotekanauki.pl/articles/2105989.pdf
Data publikacji:
2022
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
modal analysis
natural vibrations
analytical solutions
Timoshenko beam theory
shaft vibrations
Opis:
The free transverse vibrations of shafts with complex geometry are studied using analytical methods and numerical simulations. A methodology is proposed for evaluating the results of a natural transverse vibration analysis as generated by finite element (FE) models of a shaft with compound geometry. The effectiveness of the suggested approach is tested using an arbitrarily chosen model of the injection pump shaft. The required analytical models of the transverse vibrations of stepped shafts are derived based on the Timoshenko thick beam theory. The separation of variables method is used to find the needed solutions to the free vibrations. The eigenvalue problem is formulated and solved by using the FE representation for the shaft and for each shaft-simplified model. The results for these models are discussed and compared. Additionally, the usefulness of the Myklestad–Prohl (MP) method in the field of preliminary analysis of transverse vibration of complex shaft systems is indicated. It is important to note that the solutions proposed in this paper could be useful for engineers dealing with the dynamics of various types of machine shafts with low values of operating speeds.
Źródło:
Acta Mechanica et Automatica; 2022, 16, 3; 215--224
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Coupled lateral-torsional vibrations of a symmetric rotor
Autorzy:
Chiliński, B.
Pakowski, R.
Stanik, Z.
Powiązania:
https://bibliotekanauki.pl/articles/245654.pdf
Data publikacji:
2016
Wydawca:
Instytut Techniczny Wojsk Lotniczych
Tematy:
rotational system
nonlinear differential system of equation
perturbation method
critical states
analytical solutions
Opis:
The paper presents a cross-sectional analysis of dynamics of rotating systems with different characteristics, starting from the search for solutions in an analytical way, and ending with the numerical attempt to verify the results. There is presented a problem of bending and torsional vibrations in rotational systems, using possibly the simplest model of the phenomenon. It is a heavy disk embedded on the deformable massless shaft. The rotor is symmetric and it is assumed that stiffness can be nonlinear. The analysis of vibrations occurring in rotors is made with the use of this model. This is followed by a preliminary discussion on the problem and the conclusions of the pilot studies. There are presented basic problems related to the phenomenon of lateral-torsional coupling in rotational systems with an emphasis on critical states. Formulation of the problem is the conclusion of preliminary part of the paper. Next, there are discussed the selected methods currently used to solve such problems, together with a discussion of their application in this case. In addition, there is discussed a problem of numerical or analytical character of obtained results and the range of using methods in modelling, designing and experimental studies. The next part of the paper focuses on the solution of the model presented in the introduction, using the following analytical or numerical methods: Krylov-Bogolubov, Adams and Runge-Kutta methods. There are presented assumptions, simplifications of the model, technical details of searching for solutions and the results together with a discussion of their correctness. The results, which were obtained from analysis, are polyharmonic. Due to this fact, the spectra of each solution were presented. These aspects are discussed in the context of the solving methods and motion analysis for rotor systems. The whole paper is summarized with a discussion of the results and their confrontation with reality.
Źródło:
Journal of KONES; 2016, 23, 4; 41-47
1231-4005
2354-0133
Pojawia się w:
Journal of KONES
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical determination of the order of stress field singularity in some configurations of multiwedge systems for the case of antiplane deformation
Autorzy:
Makhorkin, M.
Makhorkina, T.
Powiązania:
https://bibliotekanauki.pl/articles/411440.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Oddział w Lublinie PAN
Tematy:
multi-wedge system
antiplane deformation
order of the stress singularities
analytical solutions
composite wedge
Opis:
In this paper, the possibility of constructing the analytical expressions to determine the order of the stress singularities in multi-wedge composites of the most prevalent geometric configurations for the case of antiplane deformation is considered. Particularly, the analytical solutions of the corresponding characteristic equations are constructed for three-wedge systems whose components have such geometric characteristics [wzór] is а half-plane and attached to it wedges with the such apical angles: (in the presence and absence of a slit) [wzór] is а half-plane and attached to it wedges with such apical angles [wzór] (in the presence and absence of the slit with outlet angle to the linear materials interface) [wzór] is а half-plane and attached to it wedges with such apical angles [wzór]. The analytical solutions of characteristic equations for composite wedges composed of [wzór] elements with identical apical angles are constructed as well. Additional studies, the results of which have not been included in the materials of the article due to their inconvenience, indicate to that there are analytical solutions of the characteristic equation for a composite of this type with more elements. The obtained results make it possible to study the stress-strain state in multi-wedge systems of the considered configurations not restricting ourselves only to the vicinity of the wedges convergence point. In addition, the use of analytical solutions of characteristic equations in systems with a large number of wedges having the same apical angles gives the additional possibilities for analysis the angularly functionally graded materials.
Źródło:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2017, 6, 3; 45-51
2084-5715
Pojawia się w:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical solutions for a general mixed boundary value problem associated with motions of fluids with linear dependence of viscosity on the pressure
Autorzy:
Vieru, D.
Fetecau, C.
Bridges, C.
Powiązania:
https://bibliotekanauki.pl/articles/1839812.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
lepkość
płyn newtonowski
przepływ płynu lepkiego
analytical solutions
mixed boundary value problem
pressure dependent viscosity
Opis:
An unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finie Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.
Źródło:
International Journal of Applied Mechanics and Engineering; 2020, 25, 3; 181-197
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical and numerical solving of linear non-homogeneous differential equations of the second-order with constant coefficients by using constant variation method and application of Mathematica program
Rozwiązywanie analityczno-numeryczne liniowych niejednorodnych równań różniczkowych drugiego rzędu o stałych współczynnikach przy użyciu metody wariacji stałej i zastosowaniem programu Mathematica
Autorzy:
Czajkowski, A. A.
Skorny, G. P.
Udała, R.
Powiązania:
https://bibliotekanauki.pl/articles/135888.pdf
Data publikacji:
2017
Wydawca:
Wyższa Szkoła Techniczno-Ekonomiczna w Szczecinie
Tematy:
ordinary differential equations
linear non-homogeneous equations of the second order
constant coefficients
variation constant method
solutions analytical
solutions numerical
Mathematica
równania różniczkowe zwyczajne
równania różniczkowe liniowe niejednorodne drugiego rzędu
stałe współczynniki
metoda wariacji stałej
rozwiązania analityczne
rozwiązania numeryczne
Opis:
Introduction and aim: The paper presents the analytical and numerical algorithm of solving linear nonhomogeneous equations of the second order with constant coefficients. The aim of the work is to show the algorithms for solving equations both analytically and numerically. The additional aim is to show numerical algorithms and graphical interpretation of solutions. Material and methods: For selected equations, from the subject literature, constant variation method has been presented. Results: The paper presents the selected linear non-homogeneous equations of the second order with constant coefficients containing exponential, polynomial and trigonometric functions. Conclusion: Taking into account the constant variation method it is possible to solve the second order linear non-homogeneous differential equations. However, using the Mathematica program for numerical solution, you can quickly get a solution and create a graphical interpretation of solutions.
Wstęp i cel: W pracy pokazano algorytmy analityczny i numeryczny rozwiązywania równań różniczkowych liniowych niejednorodnych drugiego rzędu o stałych współczynnikach. Celem pracy jest pokazanie algorytmu rozwiązywania równań zarówno sposobem analitycznym jak i numerycznych. Ponadto również dodatkowym celem jest pokazanie algorytmów numerycznych oraz interpretacji graficznej rozwiązań. Materiał i metody: Dla wybranych równań, z literatury przedmiotu, zastosowano metodę wariacji stałej. Wyniki: W pracy opracowano wybrane równania różniczkowe liniowe niejednorodne drugiego rzędu o stałych współczynnikach zawierających funkcje wykładnicze, wielomianowe i trygonometryczne. Wniosek: Stosując metodę uzmienniania stałej jest możliwe rozwiązywanie równań różniczkowych liniowych niejednorodnych drugiego rzędu o stałych współczynnikach. Natomiast wykorzystując do numerycznego rozwiązywania program Mathematica można szybko uzyskać rozwiązanie oraz sporządzić interpretację graficzną rozwiązań.
Źródło:
Problemy Nauk Stosowanych; 2017, 7; 19-30
2300-6110
Pojawia się w:
Problemy Nauk Stosowanych
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-10 z 24

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