Wyniki wyszukiwania - BazTech

1

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Chajdi Mohcine, Adri Ahmed, El Bikri Khalid, Benamar Rhali

Diagnostyka

|

2021

|

Vol. 22, No. 1

101--112

EN

Geometrically non-linear vibrations of functionally graded Euler-Bernoulli beams with multi-cracks, subjected to a harmonic distributed force, are examined in this paper using a theoretical model based on Hamilton's principle and spectral analysis. The homogenisation procedure is performed, based on the neutral surface approach, and reduces the FG beams analysis to that of an equivalent homogeneous multi-cracked beam. The so-called multidimensional Duffing equation obtained and solved using a simplified method (second formulation) previously applied to various non-linear structural vibration problems. The curvature distributions associated to the multi-cracked beam forced deflection shapes are obtained for each value of the excitation level and frequency. The parametric study performed in the case of a beam and the detailed numerical results are given in hand to demonstrate the effectiveness of the proposed procedure, and in the other hand conducted to analyse many effects such as the beam material property, the presence of crack, the vibration amplitudes and the applied harmonic force on the non-linear dynamic behaviour of FG beams.

2

A new approach for buckling analysis of axially functionally graded beams

Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

|

2015

|

Vol. 14, nr 2

95--102

EN

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.

3

Buckling analysis of axially functionally graded beams

Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

|

2014

|

Vol. 13, nr 4

103--108

EN

In this paper critical buckling loads for axially functionally graded (FG) beams are studied. It is assumed that material properties of the beam vary exponentially through the axial direction. Solutions are derived for three types of boundary conditions: a beam that is clamped at both ends, pinned at both ends and a beam that is clamped at one end and pinned at the other.

4

Finite element formulation for the large-amplitude vibrations of FG beams

Javid M., Hemmatnezhad M.

Archive of Mechanical Engineering

|

2014

|

Vol. LXI, nr 3

469--482

EN

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.

PL

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.

5

An analytical approach to large amplitude vibration and post-buckling of functionally graded beams rest on non-linear elastic foundation

Yaghoobi H., Torabi M.

Journal of Theoretical and Applied Mechanics

|

2013

|

Vol. 51 nr 1

39--52

EN

In this paper, non-linear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) rest on a non-linear elastic foundation subjected to an axial force are studied. Based on Euler-Bernoulli beam theory and von-Karman geometric non-linearity, the partial differential equation (PDE) of motion is derived.Then, this PDE problem is simplified into an ordinary differential equation problem by using the Galerkin method. Finally, the governing equation is analytically solved using the variational iteration metod (VIM). The results from the VIM solution are compared and shown to be in excellent agreement with the available solutions from the open literature. Some new results for the non-linear natural frequencies and buckling load of functionally graded (FG) beams, such as effects of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references.

PL

W pracy przedstawiono analizę drgań nieliniowych i zjawisk następujących po wyboczeniu w belkach wykonanych z funkcjonalnych materiałów gradientowych (FGMs), spoczywających na nieliniowo sprężystym podłożu i jednocześnie poddanych osiowemu ściskaniu. Na podstawie teorii Eulera-Bernoulliego oraz przy uwzględnieniu geometrycznej nieliniowości von Karmana wyprowadzono cząstkowe równanie różniczkowe ruchu takich układów. Równanie to sprowadzono do postaci różniczkowej zwyczajnej za pomocą metody Galerkina. Na koniec, rozwiązano je analitycznie poprzez zastosowanie iteracyjnej metody wariacyjnej (VIM), a uzyskane rozwiązanie porównano z innymi, już istniejącymi i znanymi w literaturze, stwierdzając doskonałą zgodność. Otrzymano również nowe rezultaty w postaci określenia wpływu amplitudy drgań, sprężystości podłoża, wartości siły osiowej, rodzaju podparcia brzegów oraz niejednorodności materiału na częstości własne i obciążenie krytyczne belek gradientowych.

6

Free vibration analysis of functionally graded beams

Kukla S., Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

|

2013

|

Vol. 12, nr 2

39--44

EN

In this paper free vibration of axially functionally graded (FG) beams consisting of two segments is studied. The FG beams under consideration are characterized by axially varying cross-section areas and/or functionally grading material properties. Numerical example for a beam that is clamped at both ends is presented.

7

Nonlinear analysis of functionally graded beams

Tahani M., Torabizadeh M. A., Fereidoon A.

Journal of Achievements in Materials and Manufacturing Engineering

|

2006

|

Vol. 18, nr 1-2

315--318

EN

Purpose: It is the intention of the present study to examine the effect of geometric nonlinearity on displacements and stresses in beams made of functionally graded materials (FGMs) subjected to thermo-mechanical loadings. Design/methodology/approach: The nonlinear strain-displacement relations are used to study the effect of geometric nonlinearity. Temperature distribution through the thickness of the beams in thermal loadings is obtained by solving the one-dimensional heat transfer equation. Then the equilibrium equations are obtained within the framework of the first-order shear deformatyion beam theory (FSDBT) and then solved exactly and also by using a perturbation technique. The results obtained from these two methods are compared for various loadings and boundary conditions. Findings: The numerical results showed that the nonlinearity effect on the displacements and stresses of the beams is significant. Also the effects of material constant n and the boundary conditions on the nonlinear bending behavior of the beams are determined. Research limitations/implications: The exact solution method of nonlinear equilibrium equations can only be developed for composite beams with the same boundary conditions at the ends. Practical implications: It is showed that for the maximum deflections greater than 0.3h a nonlinear solution is required. Originality/value: The paper introduces a new method to obtain analytical solution for nonlinear equilibrium equations. This method can be used in developing higher-order shear deformation and layerwise theories.

8

A new approach for the analysis of functionally graded beams

Mirzababaee M., Tahani M., Zebarjad S. M.

Journal of Achievements in Materials and Manufacturing Engineering

|

2006

|

Vol. 17, nr 1-2

265--268

EN

Purpose: It is the intention of the present study to develope a new beam theory for the analysis of functionally graded compopsite beams to overcome the shortcomings present in the existing beam theories. Design/methodology/approach: Within the displacement field of a first-order shear deformation theory and by using the Hamilton principle the governing equations of motion are obtained for both the new and the existing beam theories. The beams are assumed to have isotropic, two-constituent material distribution through the thickness. Findings: It is found that the procedure used is simple and straightforward and similar to the one used in the development of shear deformation plate and shell theories. It is analytically showed that the new approach yields identical results as those obtained by using the existing first-order shear deformation theory. Research limitations/implications: The new approach can be adopted in developing higher-order shear deformation and layerwise theories. It is believed that the new approach has advantage with respect to the existing beam theories especially for developing beam layerwise theories. Practical implications: The new shear deformation beam theory can be used to develop a new beam element for analysis of practical composite beam structures. Originality/value: The paper introduces an approach to develop a new theory for modeling composite beams. The resulting equations of motion may be solved analytically or by using finite element method.