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Tytuł:
A mathematical analysis of a smart-beam which is equipped with piezoelectric actuators
Autorzy:
Destuynder, P.
Powiązania:
https://bibliotekanauki.pl/articles/205504.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
teoria sterowania
beam theory
control theory
smart structures
Opis:
First of all, a brief reminder on piezoelectric effect is given. Then it is applied to a beam equipped with such actuators. The influence of tile shape and location is discussed. A smart beam model is finally presented and analyzed. The controllability is carefully examined in the framework of the H.U.M. method of Lions (1988). Let us also underline that the asymptotic harmonic behaviour of the structure is videly used.
Źródło:
Control and Cybernetics; 1999, 28, 3; 503-530
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Buckling analysis of short carbon nanotubes based on a novel Timoshenko beam model
Analiza wyboczenia krótkich nanorurek węglowych na podstawie zmodyfikowanego modelu belki Timoszenki
Autorzy:
Hosseini-Ara, R.
Mirdamadi, H. R.
Khademyzadeh, H.
Powiązania:
https://bibliotekanauki.pl/articles/281680.pdf
Data publikacji:
2012
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
short carbon nanotubes
buckling
nonlocal elasticity
Timoshenko beam theory
Opis:
In this paper, we present a novel method to investigate the buckling behavior of short clamped carbon nanotubes (CNTs) with small-scale effects. Based on the nonlocal Timoshenko beam kinematics, the strain gradient theory and variational methods, the higher-order governing equation and its corresponding boundary conditions are derived, which are often not considered. Then, we solve the governing differential equation and determine exact critical buckling loads using a linear polynomial plus trigonometric functions different from the purely trigonometric series. We also investigate the influences of the scale coefficients, aspect ratio and transverse shear deformation on the buckling of short clamped CNTs. Moreover, we compare the critical strains with the results obtained from the Sanders shell theory and validate them with molecular dynamic simulations which are found to be in good agreement. The results show that unlike the other beam theories, this model can capture correctly the small-scale effects on buckling strains of short CNTs for the shell-type buckling.
W pracy zaprezentowano nową metodę analizy problemu wyboczenia krótkich, obustronne zamurowanych nanorurek węglowych (tzw. CTN – Carbon NanoTubes) z uwzględnieniem zjawisk małoskalowych. Na podstawie nielokalnego sformułowania kinematyki belki Timoszenki opracowano teorię gradientu odkształcenia oraz metodę analizy wariacyjnej, wyprowadzono równania konstytutywne wyższego rzędu i odpowiadające im warunki brzegowe, do tej pory z rzadka stosowane w tego typu zagadnieniach. Następnie rozwiązano równania modelu, z których wyznaczono dokładną wartość krytycznego obciążenia prowadzącego do wyboczenia. Użyto w tym celu kombinacji funkcji wielomianowych i trygonometrycznych zamiast szeregów wyłącznie trygonometrycznych. Zbadano również wpływ współczynników skali, proporcji oraz odkształcenia postaciowego na wyboczenie utwierdzonych nanorurek CNT. W trakcie symulacji numerycznych dynamiki molekularnej modelu wykazano dobrą zbieżność otrzymanych wyników z powłokowym modelem Sandersa. Potwierdzono, że – w odróżnieniu od innych teorii belek – zastosowany model dokładnie odzwierciedla efekty małoskalowe przy opisie powłokowego wyboczenia krótkich nanorurek CNT.
Źródło:
Journal of Theoretical and Applied Mechanics; 2012, 50, 4; 975-986
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Free vibration of axially functionally graded Euler-Bernoulli beams
Autorzy:
Kukla, S.
Rychlewska, J.
Powiązania:
https://bibliotekanauki.pl/articles/122752.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
axially functionally graded beams
free vibration
Euler-Bernoulli beam theory
Opis:
In this contribution, free vibration of axially functionally graded beams is analysed within the framework of the Euler-Bernoulli beam theory. The beams with uniaxial variation of the elasticity modulus and mass density are approximated by an equivalent beam with piecewise exponentially varying geometrical and material properties. A numerical example for a beam with pinned ends is presented.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 1; 39-44
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation of boundary condition effects on the stability of FGP beams in thermal environment
Autorzy:
Nasirzadeh, R.
Behjat, B.
Kharazi, M.
Khabazaghdam, A.
Powiązania:
https://bibliotekanauki.pl/articles/281316.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
FGP beam
stability
instability
buckling load
Timoshenko beam theory
non-homogeneous
homogeneous boundary conditions
Opis:
In this paper, stability and instability of Functionally Graded Piezoelectric (FGP) beams is investigated based on the Timoshenko beam theory. The material properties of the beam are considered to change gradually through thickness of the beam by a simple power law. By using the principle of minimum total potential energy, governing equations of the beam are derived. Stability behavior of the beam is predicted by solving the governing equations of the FGP beam. The results show that the homogeneity of boundary conditions plays a critical role in the stability of the FGP beam. While non-homogeneous boundary conditions lead to stable behavior of the FGP beam; homogeneous boundary conditions cause instability in the beam. By solving the eigenvalue equation of the FGP beam, the buckling load of the beam is obtained for the beams that have unstable behavior. Finally, the effects of various parameters on the buckling load of the unstable beam, such as power law index, temperature, applied voltage and aspect ratio are investigated, and the results are compared with the Euler-Bernoulli beam theory.
Źródło:
Journal of Theoretical and Applied Mechanics; 2017, 55, 3; 1003-1014
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
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:
Transient analysis of transversely functionally graded Timoshenko beam (TFGTB) in conjunction with finite element method
Autorzy:
Khafaji, Salwan Obaid Waheed
Al-Shujairi, Mohammed A.
Aubad, Mohammed Jawad
Powiązania:
https://bibliotekanauki.pl/articles/140231.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
FGM beam
transient response
free vibration
fundamental frequency
finite element method
Timoshenko beam theory
Opis:
In this work, transient and free vibration analyses are illustrated for a functionally graded Timoshenko beam (FGM) using finite element method. The governing equilibrium equations and boundary conditions (B-Cs) are derived according to the principle of Hamilton. The materials constituents of the FG beam that vary smoothly along the thickness of the beam (along beam thickness) are evaluated using the rule of mixture method. Power law index, slenderness ratio, modulus of elasticity ratio, and boundary conditions effect of the cantilever and simply supported beams on the dynamic response of the beam are studied. Moreover, the influence of mass distribution and continuous stiffness of the FGM beam are deeply investigated. Comparisons between the current free vibration results (fundamental frequency) and other available studies are performed to check the formulation of the current mathematical model. Good results have been obtained. A significant effect is noticed in the transient response of both simply supported and cantilever beams at the smaller values of the power index and the modulus elasticity ratio.
Źródło:
Archive of Mechanical Engineering; 2020, LXVII, 3; 299-321
0004-0738
Pojawia się w:
Archive of Mechanical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Thermal buckling and free vibration of Euler–Bernoulli FG nanobeams based on the higher-order nonlocal strain gradient theory
Autorzy:
Janevski, G.
Despenić, N.
Pavlović, I.
Powiązania:
https://bibliotekanauki.pl/articles/38444568.pdf
Data publikacji:
2020
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
Euler–Bernoulli beam theory
thermal buckling
vibration
functionally graded materials
higher-order strain gradient theory
Opis:
A size-dependent Euler–Bernoulli beam model is derived within the framework of the higher-order nonlocal strain gradient theory. Nonlocal equations of motion are derived by applying Hamilton’s principle and solved with an analytical solution. The solution is obtained using the Navier solution procedure. In the case of simply supported boundary conditions, the analytical solutions of natural frequencies and critical buckling temperature for free vibration problems are obtained. The paper investigates the thermal effects on buckling and free vibrational characteristics of functionally graded size-dependent nanobeams subjected to various types of thermal loading. The influence of higher-order and lower-order nonlocal parameters and strain gradient scale on buckling and vibration are investigated for various thermal conditions. The obtained results are compared with previous research.
Źródło:
Archives of Mechanics; 2020, 72, 2; 139-168
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams
Autorzy:
Bakhy, S.H.
Al-Waily, M.
Al-Shammari, M.A.
Powiązania:
https://bibliotekanauki.pl/articles/2175761.pdf
Data publikacji:
2021
Wydawca:
Stowarzyszenie Komputerowej Nauki o Materiałach i Inżynierii Powierzchni w Gliwicach
Tematy:
FGMs
sandwich beam
classical beam theory
vibration
FEA
frequency
ANSYS
belka warstwowa
klasyczna teoria belek
wibracje
częstotliwość
Opis:
Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.
Źródło:
Archives of Materials Science and Engineering; 2021, 110, 2; 72--85
1897-2764
Pojawia się w:
Archives of Materials Science and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new approach for buckling analysis of axially functionally graded beams
Autorzy:
Rychlewska, J.
Powiązania:
https://bibliotekanauki.pl/articles/122955.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
functionally graded beams
buckling load
Euler-Bernoulli beam theory
funkcjonalne belki gradientowe
teoria Bernoulliego-Eulera
Opis:
The object of considerations are axially functionally graded (FG) beams, which are loaded by an axial force varying along the length of the beam. The main idea presented here is to approximate FG beams by an equivalent beam with piecewise exponentially varying material properties, geometrical properties and axial load. Numerical solutions of the buckling analysis are obtained for four various types of boundary conditions associated with pinned and clamped ends. The usefulness of the proposed method is confirmed by comparing numerical results with those available for graded beams of special polynomial non-homogeneity.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 2; 95-102
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of isogeometric approach to dynamics of curved beam
Autorzy:
Łasecka-Plura, Magdalena
Białasik, Jan
Kuczma, Mieczysław
Tabrizikahou, Alireza
Powiązania:
https://bibliotekanauki.pl/articles/24201980.pdf
Data publikacji:
2023
Wydawca:
Politechnika Poznańska. Instytut Mechaniki Stosowanej
Tematy:
isogeometric analysis
free-form curved beam
Timoshenko beam theory
vibration analysis
analiza izogeometryczna
belka zakrzywiona
teoria Timoshenki
analiza drgań
Opis:
In the paper dynamics of a free-form Timoshenko curved beam is investigated. The considered problem is solved using isogeometric analysis. Non-uniform rational B-spline (NURBS) basis functions are applied to describe both geometry and displacement field of the considered beam. The Timoshenko beam theory is used to derive the element stiffness and mass matrices. The application of the presented method is shown in numerical examples. The correctness of the presented approach is proved by comparing the obtained results to those available in the literature and calculated by the finite element method. Analysis of convergence is presented for different orders of NURBS basis functions.
Źródło:
Vibrations in Physical Systems; 2023, 34, 1; art. no. 2023117
0860-6897
Pojawia się w:
Vibrations in Physical Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods
Autorzy:
Obara, P.
Gilewski, W.
Powiązania:
https://bibliotekanauki.pl/articles/200456.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Bernoulli-Euler beam theory
Timoshenko beam theory
transverse shear deformation
rotatory inertia
natural frequency
critical force
areas of instability
teoria wiązki Bernoulliego-Eulera
teoria wiązki Tymoszenko
moment bezwładności rotatora
częstotliwość
siła krytyczna
obszary niestabilności
Opis:
The objective of this paper is to determine dynamic instability areas of moderately thick beams and frames. The effect of moderate thickness on resonance frequencies is considered, with transverse shear deformation and rotatory inertia taken into account. These relationships are investigated using the Timoshenko beam theory. Two methods, the harmonic balance method (HBM) and the perturbation method (PM) are used for analysis. This study also examines the influence of linear dumping on induced parametric vibration. Symbolic calculations are performed in the Mathematica programme environment.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 4; 739-750
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mechanical nature of a single walled carbon nanotube using Legendre’s polynomials
Autorzy:
Tiwari, P.
Nagar, P.
Powiązania:
https://bibliotekanauki.pl/articles/279475.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
Euler-Bernoulli’s beam theory
nonlocal elasticity theory
Legendre’s polynomial
aspect ratio
critical buckling load
Winkler and Pasternak elastic constants
Opis:
This paper is concerned with the mechanical response of a single-walled carbon nanotube. Euler-Bernoulli’s beam theory and Hamilton’s principle are employed to derive the set of governing differential equations. An efficient variational method is used to determine the solution of the problem and Legendre’s polynomials are used to define basis functions. Significance of using these polynomials is their orthonormal property as these shape functions convert mass and stiffness matrices either to zero or one. The impact of various parameters such as length, temperature and elastic medium on the buckling load is observed and the results are furnished in a uniform manner. The degree of accuracy of the obtained results is verified with the available literature, hence illustrates the validity of the applied method. Current findings show the usage of nanostructures in vast range of engineering applications. It is worth mentioning that completely new results are obtained that are in validation with the existing results reported in literature.
Źródło:
Journal of Theoretical and Applied Mechanics; 2018, 56, 4; 1153-1162
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite element formulation for the large-amplitude vibrations of FG beams
Sformułowanie metody elementów skończonych dla drgań wielkoamplitudowych w belkach gradientowych
Autorzy:
Javid, M.
Hemmatnezhad, M.
Powiązania:
https://bibliotekanauki.pl/articles/140062.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
large-amplitude vibration
functionally graded materials
functionally graded beams
Euler-Bernoulli beam theory
finite element method
boundary conditions
drgania wielkoamplitudowe
funkcjonalne materiały gradientowe
belki gradientowe
teoria Bernoulliego-Eulera
metoda elementów skończonych
warunki brzegowe
Opis:
On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Kármán type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the powerlaw and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.
W oparciu o teorię Eulera-Bernouliego przeprowadzono analizę wielkoamplitudowych drgań belki gradientowej posługując się metodą elementów skończonych. Związek między odkształceniem i przemieszczeniem, typu von Kármána, zastosowano tam, gdzie końce belki są utwierdzone i mogą poruszać się osiowo. Zakłada się, że właściwości materiału zmieniają się w kierunku poprzecznym (grubości) zgodnie z funkcją potęgową lub sigmoidalną. Metoda elementów skończonych jest zastosowana w celu dyskretyzacji nieliniowych równań sterujących, z których po rozwiązywaniu metodą bezpośredniego całkowania numerycznego wyznacza się częstotliwości drgań nieliniowych belki gradientowej dla różnych warunków brzegowych. Badany jest wpływ wykładnika funkcji, amplitudy drgań, geometrycznych parametrów belki i podparcia końców na częstotliwości drgań swobodnych. Wyniki numeryczne, przedstawione w artykule, zgadzają się dobrze z wynikami podawanymi w dostępnej literaturze.
Źródło:
Archive of Mechanical Engineering; 2014, LXI, 3; 469-482
0004-0738
Pojawia się w:
Archive of Mechanical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Focus shaping of the radially polarized Bessel–Gauss beam with a sine-azimuthal variation wavefront
Autorzy:
Gao, X
Zhang, D.
Mei, T.
Fu, R.
Zhuang, S.
Powiązania:
https://bibliotekanauki.pl/articles/174283.pdf
Data publikacji:
2013
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
Bessel-Gauss beam
wavefront modulation
vector diffraction theory
Opis:
Focusing properties of the radially polarized Bessel–Gauss beam with a sine-azimuthal variation wavefront was investigated by the vector diffraction theory. The wavefront distribution is the sine function of the azimuthal angle with one phase parameter that indicates the phase change frequency. Results show that the focal pattern can be altered by the phase parameter, and many novel focal patterns may occur, such as multiple dark-foci focal pattern, crescent shape, and wheel shape. For case of a higher phase beam, the whole focal pattern turns on a symmetric wheel shape with multiple reduplicate intensity elements. When the phase parameter is an odd number, the number of reduplicate elements equals the phase parameter, while when the phase parameter is an even number, the number of reduplicate elements is two times the phase parameter. In addition, the effect of the phase parameter on the focal pattern is more considerable than that of the beam parameter under low numerical aperture. Under higher numerical aperture, the effect of the beam parameter on the focal pattern gets stronger.
Źródło:
Optica Applicata; 2013, 43, 3; 567-582
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Three-point bending of a beam with non-homogeneous structure in the depth direction
Autorzy:
Magnucki, Krzysztof
Magnucka-Blandzi, Ewa
Witkowski, Dawid
Wittenbeck, Leszek
Powiązania:
https://bibliotekanauki.pl/articles/38912690.pdf
Data publikacji:
2023
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
non-homogeneous beam
shear deformation theory
three-point bending
Opis:
This paper is devoted to the behavior of a non-homogeneous simply supported beam under three-point bending. The individual shear deformation function of a planar cross-section is adopted, and longitudinal displacements, strains, and stresses for two parts of the beam are explained. By applying the principle of stationary potential energy, a system of two differential equations of equilibrium is derived and solved analytically. The positions of the neutral axis, shear coefficients, and deflections are then calculated for three different beam families. Additionally, the bending problem of these beams is studied numerically using the finite element method (FEM). The results of both analytical and numerical calculations are presented in tables and figures. The main contribution of this paper lies in the development of an analytical model incorporating the individual shear deformation function and a numerical FEM model for this beam.
Źródło:
Engineering Transactions; 2023, 71, 4; 645-665
0867-888X
Pojawia się w:
Engineering Transactions
Dostawca treści:
Biblioteka Nauki
Artykuł
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