Wyniki wyszukiwania - Biblioteka Nauki

1

Free vibration of annular plates of stepped thickness resting on Winkler elastic foundation

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Kukla S. , Szewczyk M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2007

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tom Vol. 6, nr 1

109-116

EN

This paper concerns axisymmetric free vibration of annular plates of stepped thickness resting on Winkler elastic foundation. Exact solution to vibration problem was obtained by dividing of considered plate into uniform annular plates and by using the Green's function method. Numerical examples are presented.

2

Free vibration of composite cylindrical shells with orthogonal stiffeners

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Wu Y. , Zhao C. , Liang H. , Yao S. , Xue J. , Xu P.

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2022

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tom Vol. 60 nr 2

239--252

EN

This paper proposes theoretical and numerical approaches to scrutinize the free vibration of orthogonal stiffened cylindrical shells. According to K´arman-Donnell shell theory, the total energy of the stiffened cylindrical shells is derived. Based on the principle of minimum potential energy, the eigenfunction related to the frequency is established and solved by developing a Matlab program. Analytical solutions of the natural frequency for free vibraion of the stiffened cylindrical shells are calculated and are verified against the finite element results from ABAQUS software. On account of the observations from the parametric study, an optimization scheme of the stiffeners is proposed.

3

Free vibration of stepped Timoshenko beams with attachements

100%

Zamorska I.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2008

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tom Vol. 7, nr 1

199-205

EN

In this paper is presented a solution of the free vibration problem of multistepped Timoshenko beam with attachments. The Green's functions method is used to obtain the solution in an form. The presented approach can be used for the vibration analysis of beams consisting of an arbitrary number of segments and an arbitrary number of attached discrete elements.

4

An approach to free vibration analysis of axially graded beams

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Kukla S. , Rychlewska J.

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tom Vol. 54 nr 3

859--870

EN

In this study, the solution to the free vibration problem of axially graded beams with a non-uniform cross-section has been presented. The proposed approach relies on replacing functions characterizing functionally graded beams by piecewise exponential functions. The frequency equation has been derived for axially graded beams divided into an arbitrary number of subintervals. Numerical examples show the influence of the parameters of the functionally graded beams on the free vibration frequencies for different boundary conditions.

5

A modified Fourier-Ritz method for free vibration of rectangular plates with elastic constrains

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Wu T. , Chen Z. B. , Qu J. J.

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tom Vol. 60 nr 1

77--89

EN

In this paper, a modified Fourier-Ritz method is used to study free vibration of a rectangular plate with a set of simply supported opposite sides and another set of arbitrary elastic constraints. The influence of different elastic constraint stiffness values on the modal response of the rectangular plate is also analyzed. In order to avoid that the displacement function of the rectangular plate calculated by the traditional method and its derivative may be discontinuous or non-derivable at the boundary, the displacement function is expressed in the form of the sum of standard cosine series and a periodic polynomial function. Compared with the sine series expansion, the convergence of the result is enhanced. Several sets of numerical examples with different boundary conditions are given in the article, the data shows that the results calculated by this method have good accuracy and fast convergence. In addition, this paper also analyzes the boundary conditions and discusses the influence of different spring stiffness values on the setting of boundary conditions. The results can be applied to the setting of general boundary conditions and the study of vibration control of rectangular plates.

6

Free vibrations analysis of shrouded bladed discs with one loose blade

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Rządkowski R. , Kwapisz L. , Drewczyński M. , Szczepanik R. , Rao J. S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

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tom Vol. 10, No 1

83-95

EN

As a failure of rotor blades in a gas turbine was reported, the rotating-mode shapes of flexible shrouded bladed disc assemblies were calculated using a finite element approach. Rotational effects, such as centrifugal stiffening were accounted for, and all couplings between the flexible parts were allowed. The spin softening effects were neglected. A dynamic analysis of the shrouded bladed disc demonstrated that it was designed with a sufficient safety region of resonance. In case of one blade getting loose, it is vibrating in resonance.

7

Frequencies and modes of rotating flexible shrouded bladed discs-shaft assemblies

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Sokołowski J. , Rządkowski R. , Kwapisz L.

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tom Vol. 7, No 2

215-231

EN

It is now increasingly necessary to predict accurately, at the design stage and without excessive computing costs, the dynamic behaviour of rotating parts of turbomachines, so that resonant conditions at operating speeds are avoided. In this study, global rotating mode shapes of flexible shrouded bladed disc-shaft assemblies are calculated. The rotating modes have been calculated by using a finite element cyclic symmetry approach. Rotational effects, such as centrifugal stiffening have been accounted for, and all the possible couplings between the flexible parts have been allowed. Gyroscopic effects have been neglected. The numerical results have been compared with the experimental. The calculations show the influence of shaft flexibility on the natural frequencies of shrouded bladed discs up to four nodal diameters for the two first frequencies series.

8

Free vibration analysis of point supported rectangular plates using quadrature element method

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Çetkin A. , Orak S.

Journal of Theoretical and Applied Mechanics

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2017

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tom Vol. 55 nr 3

1041--1053

EN

In this study, the hybrid approach of the Quadrature Element Method (QEM) has been employed to generate solutions for point supported isotropic plates. The Hybrid QEM technique consists of a collocation method with the Galerkin finite element technique to combine the high accurate and rapid converging of Differential Quadrature Method (DQM) for effi- cient solution of differential equations. To present the validity of the solutions, the results have been compared with other known solutions for point supported rectangular plates. In addition, different solutions are carried out for different type boundary conditions, different locations and number of point supports. Results for the first vibration modes of plates are also tested using a commercial finite element code, and it is shown that they are in good agreement with literature.

9

Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

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Mercan K. , Demir Ç. , Civalek Ö.

Curved and Layered Structures

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2016

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tom 3

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nr 1

EN

In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love’s first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

10

Linear free vibration of graphene sheets with nanopore via Aifantis theory and Ritz method

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Ziaee S.

Journal of Theoretical and Applied Mechanics

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2017

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tom Vol. 55 nr 3

823--838

EN

This article aims to study the natural frequency of defective graphene sheets since the existence of cut-outs in plates may be essential on the basis of their desired functionality. A combination of the Aifantis theory and Kirchhoff thin plate hypothesis is used to derive governing equations of motion. The Ritz method is employed to derive discrete equations of motion. The molecular structural mechanics method is also employed to specify the effective length scale parameter. In the ‘numerical results’ Section, the effects of different parameters such as boundary conditions and diameter of the hole-to-side length ratio on the fundamental frequency of graphene sheets are studied.

11

Analysis of out-of-plane free vibration of single damaged curved beam based on precise algorithm of structural mechanics

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Li X. , Pan Z. , Guo H.

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tom Vol. 61 nr 2

407--414

EN

Based on a dynamic discrete model of an out-of-plane curved beam with a constant cur- vature, eigen-properties of the spatial curved beam structure in undamaged and damaged configurations are considered in this paper. In the literature, based on the equivalent sec- tion reduction method, a distributed damage modeling method is proposed. Accoding to Euler-Bernoulli beam theory, the stiffness matrix of shear, bending and torsion coupling is derived. Combined with the lumped mass matrix and the characteristic equation of the multi degree of freedom system, natural frequencies of the undamaged and damaged structures are calculated.

12

Efficient free vibration analysis of large structures with close or multiple natural frequencies. P. 1 : Undamped structures

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Lee I. W. , Jung H. J. , Kim M. C.

Computer Assisted Mechanics and Engineering Sciences

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1999

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tom Vol. 6, No. 3-4

403-414

EN

An efficient numerical method which can calculate the eigenproblem for the large structural system with multiple or close natural frequencies is presented. The method is formulated by the accelerated Newton-Raphson method to the transformed problem. The method can calculate the natural frequencies and mode shapes without any numerical instability which may be encountered in the well-known methods such as the subspace iteration method or the determinant search method which has been widely used for solving eigenvalue problem. The efficiency of the method verified by comparing convergence and solution time for numerical examples with those of the subspace iteration method and the determinant search method.

13

Free vibration to a system of cantilever nanobeams

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Ciekot A. , Kukla S.

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2014

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tom Vol. 13, nr 3

29--36

EN

This paper presents a solution to the free vibration problem of a system of two cantilever nanobeams. The nanobeams of the system are axially loaded and coupled by discrete translational springs. The solution of the problem by using the Green’s function method has been obtained. A numerical example shows the effect of the small scale on free vibration frequencies of the nanobeam system considered.

14

Characteristics of vibrating composite stiffened hypars with cut-out at different modes

88%

Sahoo S.

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2019

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tom Vol. 67, iss. 1

75--99

EN

Vibration characteristics of laminated composite stiffened hypar (hyperbolic paraboloid shell bounded by straight edges) with cut-out are analysed in terms of natural frequency and mode shapes. A finite element code is developed for the purpose by combining an eight noded curved shell element with a three noded curved beam element for stiffener. Finite element formulation is based on first order shear deformation theory and includes the effect of cross curvature. The isoparametric shell element used in the present model consists of eight nodes with five degrees of freedom per node while beam element has four degrees of freedom per node. The code is validated by solving benchmark problems available in the literature and comparing the results. The generalised Eigen value solution is chosen for the un-damped free vibration analysis. New results are presented for first five modes of natural frequency by varying boundary conditions, ply orientation and curvature of the shell. The results furnished here may be readily used by practicing engineers dealing with stiffened composite hypars with cut-outs.

15

Timoshenko beam model for vibration analysis of composite steel-polymer concrete box beams

88%

Niesterowicz B. , Dunaj P. , Berczyński S.

Journal of Theoretical and Applied Mechanics

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2020

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tom Vol. 58 nr 3

799--810

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%.

16

Free vibration and buckling analysis of composite laminated shells using the refined zigzag theory

88%

Zhang H. , Gao Y. , He D. , Yang W.

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2022

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tom Vol. 60 nr 3

435--448

EN

In this study, a new composite laminated shell model is proposed for free vibration and stability analysis based on the refined zigzag theory (RZT). In contrast to the published shell models based on the first-order shear deformation theory (FSDT), piecewise-linear zigzag functions are utilized to provide a more realistic representation of deformation states of a transverse shear-flexible shell. In the present formulation, the governing equations and boundary conditions of composite laminated shells are established by d’Alembert’s principle to obtain natural frequencies and critical buckling loadings. In order to evaluate the effectiveness and performance of the present new model for composite laminated shells, examples of free vibration and buckling analysis are carried out for cylindrical and spherical shells involving different lamination schemes and design parameters. The results are compared with the three dimensional (3D) exact, first-order and some high-order solutions in the literature. Numerical results show that the present model not only has high accuracy but also has superior computational efficiency in comparison with high-order models, such that it may show a great potential in engineering applications.

17

Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh's method

88%

Szlachetka O. , Jaworski J. , Chalecki M.

Acta Scientiarum Polonorum. Architectura

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2017

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tom 16

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nr 4

EN

The Rayleigh’s method can be used to determine the first natural frequency of bars (beams or posts) with non-uniform cross-section. The authors have analysed slender bars made of an elastic material and having the shape of a solid of revolution: a curvilinear truncated cone and curvilinear conical pipe. It has been assumed that the bar axis deflected during vibrations has a shape of a beam deflected by a static constant continuous load. The Rayleigh’s method has been applied in the paper in aim to determine the first frequency of free (transverse) vibrations of posts formed as a cantilever bars having the shape of solid and hollow curvilinear truncated cone with the generatrix being a parabola which is convex in relation to the cone axis. The results of calculations are very close to those obtained with finite element method (FEM).

PL

Metodą Rayleigh’a można wyznaczyć pierwszą częstość drgań własnych prętów (belek lub słupów) o zmiennym przekroju poprzecznym. Autorzy analizowali smukłe pręty z materiału sprężystego, które mają kształt bryły obrotowej: krzywoliniowego ściętego stożka oraz krzywoliniowej rury stożkowej. Przyjęto, że oś pręta odkształcona podczas drgań swobodnych ma kształt ugięcia statycznego pod stałym obciążeniem ciągłym. W pracy zastosowano metodę Rayleigh’a do wyznaczenia pierwszej częstości drgań własnych giętnych słupów wspornikowych w kształcie pełnego i wydrążonego krzywoliniowego ściętego stożka, którego tworząca jest parabolą wypukłą w stosunku do osi stożka. Wyniki obliczeń są bardzo bliskie rezultatom otrzymanym przy zastosowaniu metody elementów skończonych (MES).

18

Methods based on the differential quadrature in vibration analysis of plates

88%

Krowiak A.

Journal of Theoretical and Applied Mechanics

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2008

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tom Vol. 46 nr 1

123-139

EN

The paper deals with the methods based on the differential quadrature and their application to the free vibration analysis of plates. The spline-based differential quadrature Method (SDQM) is presented as an alternative to known methods based on the interpolation polynomial (PDQM). The SDQM uses a polynomial piecewise function to approximate the wanted solution of a governing equation. The way of determining the spline functions as well as the way of computing weighting coefficients for the method are presented in the paper. Then the SDQM is applied to determine natural frequencies of plates. The influence of the spline degree, number of nodes and grid point distribution on the accuracy, convergence and stability is investigated in an example. All results are compared with values obtained by the conventional differential quadrature method (PDQM).

PL

Praca dotyczy metod opartych na kwadraturach różniczkowych i ich aplikacji do zagadnienia drgań własnych płyt. W pracy, jako alternatywę do znanych metod kwadratur różniczkowych, opartych na wielomianie interpolacyjnym (PDQM), przedstawiono metodę bazującą na funkcjach sklejanych (SDQM). W SDQM poszukiwane rozwiązanie przybliżane jest funkcją wielomianową, przedziałami zmienną. W pracy przedstawiono sposób wyznaczenia takiej funkcji interpolacyjnej, jak również sposób obliczenia współczynników wagowych, używanych w metodzie kwadratur różniczkowych. Następnie SDQM użyto do wyznaczenia częstości drgań własnych płyt, gdzie analizowano wpływ stopnia wielomianu, liczby węzłów i ich rozmieszczenia na zbieżność, dokładność i stabilność metody. Otrzymane rezultaty porównano z wynikami uzyskanymi przy pomocy konwencjonalnej metody kwadratur różniczkowych (PDQM).

19

Green’s function approach to frequency analysis of thin circular plates

88%

Żur K. K.

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tom Vol. 64, nr 1

181--188

EN

The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green’s functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters. The first ten dimensionless frequencies for eight different natural modes of circular plates are calculated. A part of obtained results have not been presented yet in open literature for thin circular plates. The results of investigation are in good agreement with selected results obtained by other methods presented in literature.

20

Free transverse vibrations of non-uniform beams

88%

Zamorska I.

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tom Vol. 9, nr 2

243-249

EN

In this paper the Green's function method for the free vibration problem of nonuniform Bernoulli-Euler beams is presented. To find the Green's function of the fourth order differential operator, occurring at the beam's equation of motion, the power series method is proposed.