Ograniczanie wyników
Czasopisma help
Autorzy help
Lata help
Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 25

Liczba wyników na stronie
first rewind previous Strona / 2 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  Timoshenko beam
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 2 next fast forward last
EN
The free vibration model of a steel-polymer concrete beam based on Timoshenko beam theory is presented in this paper. The results obtained on the basis of the model analysis, describing the values of the natural frequencies of the beam vibrations, were compared with the results obtained by the solution of the model formulated on the basis of the classical Euler-Bernoulli beam theory, the finite element model and the results of experimental studies. The developed model is characterized by high compliance with experimental data: the relative error in the case of natural vibration frequencies does not exceed 0.4%, on average 0.2%.
EN
In this paper, a comprehensive study is carried out on the dynamic behaviour of Euler–Bernoulli and Timoshenko beams resting on Winkler type variable elastic foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying along the length direction. The free vibration problem is formulated using Rayleigh-Ritz method and Hamilton’s principle is applied to generate the governing equations. The results are presented as non-dimensional natural frequencies for different material gradation models and different foundation stiffness variation models. Two distinct boundary conditions viz., clamped-clamped and simply supported-simply supported are considered in the analysis. The results are validated with existing literature and excellent agreement is observed between the results.
EN
The purpose of this paper is to study the free vibration and buckling of a Timoshenko nano-beam using the general form of the Eringen theory generalized based on the fractional derivatives. In this paper, using the conformable fractional derivative (CFD) definition the generalized form of the Eringen nonlocal theory (ENT) is used to consider the effects of integer and noninteger stress gradients in the constitutive relation and also to consider small-scale effect in the vibration of a Timoshenko nano-beam. The governing equation is solved by the Galerkin method. Free vibration and buckling of a Timoshenko simply supported (S) nano-beam is investigated, and the influence of the fractional and nonlocal parameters is shown on the frequency ratio and buckling ratio. In this sense, the obtained formulation allows for an easier mapping of experimental results on nano-beams. The new theory (fractional parameter) makes the modeling more flexible. The model can conclude all of the integer and non-integer operators and is not limited to the special operators such as ENT. In other words, it allows to use more sophisticated/flexible mathematics to model physical phenomena.
EN
This paper presents an analysis of the stability of Timoshenko beams which uses Eringen'snonlocal elasticity theory. A numerical algorithm based on the exact solution for the freevibration of segmental Timoshenko beams was formulated. The algorithm enables one tocalculate, with any degree of accuracy, the critical load levels in the beams on the macro andnanoscale. The beams were subjected to conservative and nonconservative static loads. Thelevels of critical loads in the beams were analysed assuming a functional dependence of thenonlocal parameters on the vibrational frequency and the state of stress.
EN
In this study, free vibration characteristics of a functionally graded Timoshenko beam that undergoes flapwise bending vibration is analysed. The energy expressions are derived by introducing several explanotary figures and tables. Applying Hamilton’s principle to the energy expressions, governing differential equations of motion and boundary conditions are obtained. In the solution part, the equations of motion, including the parameters for rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies are calculated and effects of several parameters are investigated.
Logistyka
|
2015
|
nr 3
1750--1754, CD 1
PL
W pracy przedstawiono zastosowanie skończonych elementów przejściowych do modelowania elementów maszyn. W przypadku części o obszarach zróżnicowanych (istotna zmiana geometrii uniemożliwiająca zastosowanie elementów skończonych tego samego typu) zastosowano dwa typy elementów skończonych: belkowe Timoshenki oraz płaskie trójwęzłowe CST. Przedstawiono sposób powiązania siatki MES z zastosowaniem elementu przejściowego. Jako przykład rozpatrzono belkę wspornikową oraz dźwignię. Wyniki obliczeń wykazały, że bardzo istotny jest wybór odpowiednich elementów skończonych dostosowanych do odpowiednich podobszarów, jak również prawidłowe zaprojektowanie elementu przejściowego.
EN
In the paper the application of transition finite elements for modelling machine elements is presented. In the case of diverse areas (significant change in the geometry which prevents the use of the same type finite elements) there are used two types of finite elements: Timoshenko beam and plane CST elements. The procedure of incorporation of the transition element to connect two meshed areas is presented. The transition elements are used to couple structural and continuum elements without using constraint equations. As an examples a cantilever beam and a lever is considered. The calculation results showed that it is very important to choose the appropriate finite element adapted to the corresponding sub-areas, as well as the proper design of the transition element.
7
EN
An analysis of natural frequencies and modes for a cantilever radial rotating beam with end mass is carried out within framework of Timoshenko beam model, on the base of convenient dimensionless equations of motion depended only on two dimensionless parameters. It is shown that the shear deformations at high angular speeds lead to significant changes in the natural modes, and as a consequence – to relevant qualitative effects for the natural frequencies.
EN
We study vehicle models in the form of finite Bernoulli-Euler beams, traveling along a track, which is treated as an infinite beam on a suitable foundation. In the limit, the class of proposed models contains the case of a moving concentrated harmonic force, considered before in several papers. In order to obtain solutions several analytical and numerical techniques are applied. In the range of sub-critical speeds we obtain transient solutions which tend to their known steady counterparts of the concentrated force model.
PL
W niniejszym artykule rozpatruje się modele pojazdu w postaci skończonych belek Bernoulliego-Eulera czy Timoshenki, poruszających się po torze potraktowanym jako nieskończoną belkę na odpowiednim podłożu. Jako graniczny przypadek, klasa modeli zawiera analizowane we wcześniejszych publikacjach wędrujące siły skupione o przebiegu harmonicznym w czasie. W celu otrzymania rozwiązań stosuje się techniki analityczne i numeryczne. W zakresie podkrytycznych prędkości uzyskano rozwiązania przejściowe dążące do znanych rozwiązań ustalonych.
EN
The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defining the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.
PL
W pracy przedstawiono zagadnienie optymalizacji lepko-sprężystego wielowarstwowego podłoża belki Tomoszenki, którą można potraktować jako model szyny kolejowej. Zamodelowano obciążenie rozłożone, w kształcie funkcji Gausa, przemieszczające się wzdłuż belki (szyny) z określoną prędkością liniową. Odkształcenie wywołane tym obciążeniem zależy od parametrów podłoża, min. takich jak grubość warstwy, rodzaj materiału warstwy oraz parametrów obciążenia min. takich jak prędkość przemieszczania i cechy jego rozkładu. Przeprowadzono proces optymalizacji, w którym minimalizowano sumaryczne odkształcenie belki ze względu na wybrane parametry podłoża oraz obciążenia. Model obciążonej belki na podłożu zaimplementowano do aplikacji Comsol Multiphysics, wykorzystującej do rozwiązania problemu metodę elementów skończonych. Minimum funkcji celu poszukiwano przy wykorzystaniu algorytmów genetycznych.
EN
Paper presents the optimization of linear elastic multilayer foundation of the Timoshenko beam, which can be considered as a rail model. The moving load traveling along a beam with particular velocity, which distribution is characterized by Gauss function, is implemented in the model. The displacement caused by the load is dependent on multilayer foundation parameters such as layer thickness, a type of material and load parameters such as moving velocity as well its distribution on a beam. The optimization, i.e. minimization of the total displacement sum, as the result of objective function determined regarding chosen parameters of a foundation and load, as a design variables was carried out. The Comsol Multiphysics is applied in order to solve the beam and moving load problem by using the finite element method. Using genetic algorithm searches the minimum of objective function.
EN
The paper presents a new analytical solution for the dynamic response of an infinitely long Timoshenko beam resting on a nonlinear viscoelastic foundation. Vibrations of the beam are analysed by using Adomian’s decomposition method combined with wavelet based approximation alleviating difficulties related to Fourier analysis and numerical integration. The developed approach allows various parametric analyses leading to full characteristics of the investigated dynamic system.
PL
Artykuł prezentuje nowe analityczne rozwiązanie problemu dynamicznej odpowiedzi nieskończenie długiej belki Timoshenki spoczywającej na nieliniowym lepkosprężystym podłożu, poddanej ruchomemu obciążeniu rozłożonemu na odcinku i harmonicznemu w czasie. Analiza drgań belki została przeprowadzona przy użyciu dekompozycji Adomiana połączonej z aproksymacją falkową pozwalającą ominąć trudności związane z numerycznym całkowaniem oraz zminimalizować niedogodności analizy Fouriera. Uzyskane rozwiązanie daje możliwość parametrycznej analizy badanego układu dynamicznego prowadzącej do opisu jego fizycznych własności. Opracowana metoda wykorzystująca filtry falkowe typu coiflet może być zastosowana do rozwiązania nieliniowych równań różniczkowych opisujących inne układy dynamiczne typu belka-podłoże.
EN
Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C0-continuous semigroups may be applied.
13
Content available remote Continuous model for flexural vibration analysis of a Timoshenko cracked beam
EN
In this paper, a continuous model for vibration analysis of a beam with an open edge crack including the effects of shear deformation and rotary inertia is presented. A displacement field is suggested for the beam and the strain, and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton’s principle. The equation of motion is solved with a modified Galerkin method and the natural frequencies and mode shapes are obtained. A good agreement has been observed between the results of this research and the results of previous work done in this fiels. The results are also compared to results of a similar model with Euler-Bernoulli assumptions to confirm the advantages of the proposed model in the case of short beams.
14
Content available remote Free vibration of a cantilever tapered Timoshenko beam
EN
In this paper the Lagrange multiplier formalism has been used to find a solution of free vibration problem of a cantilever tapered beam. The beam has been circumscribed according to the Timoshenko theory. The sample numerical calculations for the cantilever tapered beam have been carried out and compared with experimental results to illustrate the correctness of the present method.
EN
In the study a free transverse vibration analysis of the simply supported Timoshenko beam on an arbitrary variable Winkler foundation is presented. The analysis is based on the use of the analytical method compared with numerical simulation. The elastic foundation is composed of two arbitrary variable, massless, regions of the Winkler type. At first the general solution of free vibration is derived by the separation of variable method. The natural frequencies of the system under consideration are determined. Then the models of the system formulated by using finite element technique are prepared and eigenvalue problem is solved. Achieved results of calculation are discussed and compared for these models. All needed finite element models are formulated by using ANSYS FE code. It is important to note that the data presented in the article is yielded the practical advice to design engineers.
16
Content available remote Application of Green's matrix method in vibration problems of Timoshenko beams
EN
In the present paper, a Green's matrix used to solve vibration problems of Timoshenko beams is determined. The problem formulation includes beam vibrations which are described by differential equations with variable parameters. To determine the Green's matrix, the power series method was used.
EN
Dynamics of Timoshenko's beam made of a viscoelastic material is studied. Dimensionless equations of motion are obtained, depending only on two parameters, one of which relates to the shear flexibility and the second – to the viscous internal friction. Advantages of the proposed equations are illustrated by solutions to the free and forced oscillation problems for the simplest case of hinged-hinged beams. The influence of the beam shear flexibility and viscous internal friction on the natural frequencies and the dynamic amplification factor is studied.
PL
W pracy analizowano dynamikę belki Timoshenko wykonanej z materiału lepkosprężystego.Wyprowadzono bezwymiarowe równania ruchu zależne jedynie od dwóch parametrów: sztywności ścinania i współczynnika lepkiego tarcia wewnętrznego. Korzyści zaproponowanych równań przedstawiono na przypadkach drgań swobodnych i wymuszonych belki przegubowo podpartej na obu końcach. Analizowano wpływ sztywności ścinania belki i współczynnika lepkiego tarcia wewnętrznego na częstości drgań i dynamiczny współczynnik wzmocnienia.
18
Content available remote New feature of the solution of a Timoshenko beam carrying the moving mass particle
EN
The paper deals with the problem of vibrations of a Timoshenko beam loaded by a travelling mass particle. Such problems occur in a vehicle/track interaction or a power collector in railways. Increasing speed involves wave phenomena with significant increase of amplitudes. The travelling speed approaches critical values. The moving point mass attached to a structure in some cases can exceed the mass of the structure, i.e. a string or a beam, locally engaged in vibrations. In the literature, the travelling inertial load is often replaced by massless forces or oscillators. Classical solution of the motion equation may involve discussion concerning the contribution of the Dirac delta term, multiplied by the acceleration of the beam in a moving point in the differential equation. Although the solution scheme is classical and successfully applied to numerous problems, in the paper the Lagrange equation of the second kind applied to the problem allows us to obtain the final solution with new features, not reported in the literature. In the case of a string or the Timoshenko beam, the inertial particle trajectory exhibits discontinuity and this phenomenon can be demonstrated or proved mathematically in a particular case. In practice, large jumps of the travelling inertial load is observed.
EN
In the paper, a new approach to description of the Timoshenko beam free and forced vibrations by a single equation is proposed. The solution to such an equation is a function of vibration amplitudes. The boundary conditions corresponding to such a description of the beam vibration are also given. It was proved that the form of solution to the differential equation depends on the vibration frequency. The change of the solution form occurs when the frequency crosses a specific value omega = pierwiastek z GkA / (pI). The correctness of proposed description was checked through the analysis of free vibration frequencies and amplitudes of forced vibrations with different boundary conditions as well as comparison with the results of finite element analysis.
PL
W pracy zaproponowano, nowe podejście do opisu drgań własnych i wymuszonych belki Timoshenki przez jedno równanie różniczkowe. Rozwiązaniem takiego równania jest funkcja amplitud drgań. Podano również równania opisujące warunki brzegowe odpowiednie do takiego opisu drgań. Udowodniono, że forma rozwiązania równania różniczkowego zależy od analizowanej częstości drgań. Zmiana formy rozwiązania zmienia się, gdy częstość osiąga określoną w pracy wartość omega = pierwiastek z GkA / (pI). Poprawność zaproponowanego opisu sprawdzono przez analizę częstości drgań własnych i amplitudy drgań wymuszonych belek z różnymi warunkami brzegowymi i porównaniem z wynikami otrzymanymi z analizy MES belki.
PL
Na przykładzie ławy fundamentowej posadowionej na jednorodnym podłożu gruntowym, rozpatrywano modele współpracy konstrukcji i podłoża odkształcalnego. Jako model konstrukcji przyjęto pręt krępy na dwukierunkowym podłozu Winklera. Opisano prętowy element skończony (Timoshenki) umozliwiający uwzględnienie oddziaływania podłoża na spód preta, zaś obciążeń na jego grzbiet. Analizie poddano wpływ modelu konstrukcji (pręt krępy, tarcza) oraz modelu podłoża (w osi, na spodzie) na stan jej przemieszczenia.
EN
The construction and deformable base interaction models were investigated by example of the continuous footing founded on the uniform ground base. A stocky bar on twodirectional Winkler base was assumed to be the construction model. A bar finite (Timoshenko) element was described. It made it possible to accommodate the base action on the bar undersurface and that loads on the bar ridge. The influence of the construction (stocky bar, shield) and the base (in the axis, on the underface) models on the construction displacement was analysed.
first rewind previous Strona / 2 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.