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Article
Publication date: 1 June 1997

Jaroslav Mackerle

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…

Abstract

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 July 2006

B.O. Al‐Bedoor, S. Aedwesi and Y. Al‐Nassar

The purpose of this paper is to validate mathematically the feasibility of extracting the rotating blades vibration condition from the shaft torsional vibration measurement.

Abstract

Purpose

The purpose of this paper is to validate mathematically the feasibility of extracting the rotating blades vibration condition from the shaft torsional vibration measurement.

Design/methodology/approach

A mathematical model is developed and simulated for extracting rotating blades vibration signatures from the shaft torsional vibration signals. The model simulates n‐blades attached to a rigid disk at setting angles and the shaft drives the disk is flexible in torsion. The model is developed using the multi‐body dynamics approach in conjunction with the Lagrangian dynamics. A three‐blade rotor system example is simulated for blades free and forced vibration under stationary and rotating conditions. Frequency spectrums for the shaft torsional and blades bending vibration are represented and studied for analysis verification purposes.

Findings

The torsional vibration frequency spectrums showed blades free and forced vibration signatures. The blade setting angle is shown to reduce the sensitivity of torsional vibration signal to blades vibration signatures as it increases. The torsional vibration signals captured the variation in blades properties and produced broadband frequency components for mistuned system. The shaft torsional rigidity is shown to reduce the sensitivity of torsional vibration signal to blades vibration if increased to extremely high values (approaching rigid shaft). The rotor inertia is shown to have less effect on the torsional vibration signals sensitivity. The method of torsional vibration as a tool for rotating blades vibration measurement, based on the proposed mathematical model and its simulation, is feasible.

Practical implications

There is a growing need for reliable predictive maintenance programs that in turn requires continuous development in methods for machinery health monitoring through vibration data collection and analysis. Turbo machinery and bladed assemblies like fans, marine propellers and wind turbine systems usually suffer from the problem of blades high vibration that is difficult to measure. The proposed new method for blades vibration measurement depends on the shaft torsional vibration signals and can be used also for verifying the signals from other types of bearings sensors for possible blades vibration condition monitoring.

Originality/value

This paper presents a unique mathematical model and simulation results for the rotating blades vibration monitoring. The developed model can be simulated for studying coupled blades vibration problems in the design stage as well as for condition monitoring in maintenance applications.

Details

Journal of Quality in Maintenance Engineering, vol. 12 no. 3
Type: Research Article
ISSN: 1355-2511

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Article
Publication date: 4 July 2016

Marcos Arndt, Roberto Dalledone Machado and Adriano Scremin

The purpose of this paper is devoted to present an accurate assessment for determine natural frequencies for uniform and non-uniform Euler-Bernoulli beams and frames by an…

Abstract

Purpose

The purpose of this paper is devoted to present an accurate assessment for determine natural frequencies for uniform and non-uniform Euler-Bernoulli beams and frames by an adaptive generalized finite element method (GFEM). The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler-Bernoulli beams and frames.

Design/methodology/approach

The variational problem of free vibration is formulated and the main aspects of the adaptive GFEM are presented and discussed. The efficiency and convergence of the proposed method in vibration analysis of uniform and non-uniform Euler-Bernoulli beams are checked. The application of this technique in a frame is also presented.

Findings

The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler-Bernoulli beams and frames. The GFEM, which was conceived on the basis of the partition of unity method, allows the inclusion of enrichment functions that contain a priori knowledge about the fundamental solution of the governing differential equation. The proposed enrichment functions are dependent on the geometric and mechanical properties of the element. This approach converges very fast and is able to approximate the frequency related to any vibration mode.

Originality/value

The main contribution of the present study consisted in proposing an adaptive GFEM for vibration analysis of Euler-Bernoulli uniform and non-uniform beams and frames. The GFEM results were compared with those obtained by the h and p-versions of FEM and the c-version of the CEM. The adaptive GFEM has shown to be efficient in the vibration analysis of beams and has indicated that it can be applied even for a coarse discretization scheme in complex practical problems.

Details

Engineering Computations, vol. 33 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 7 October 2014

V. Kobelev

The purpose of this paper is to address the practically important problem of the load dependence of transverse vibrations for helical springs. At the beginning, the author…

Abstract

Purpose

The purpose of this paper is to address the practically important problem of the load dependence of transverse vibrations for helical springs. At the beginning, the author develops the equations for transverse vibrations of the axially loaded helical springs. The method is based on the concept of an equivalent column. Second, the author reveals the effect of axial load on the fundamental frequency of transverse vibrations and derive the explicit formulas for this frequency. The fundamental natural frequency of the transverse vibrations of the spring depends on the variable length of the spring. The reduction of frequency with the load is demonstrated. Finally, when the frequency nullifies, the side buckling spring occurs.

Design/methodology/approach

Helical springs constitute an integral part of many mechanical systems. A coil spring is a special form of spatially curved column. The center of each cross-section is located on a helix. The helix is a curve that winds around with a constant slope of the surface of a cylinder. An exact stability analysis based on the theory of spatially curved bars is complicated and difficult for further applications. Hence, in most engineering applications a concept of an equivalent column is introduced. The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The transverse vibration is represented by a differential equation of fourth order in place and second order in time. The solution of the undamped model equation could be obtained by separation of variables. The fundamental natural frequency of the transverse vibrations depends on the current length of the spring. Natural frequency is the function of the deflection and slenderness ratio. Is the fundamental natural frequency of transverse oscillations nullifies, the lateral buckling of the spring with the natural form occurs. The mode shape corresponds to the buckling of the spring with moment-free, simply supported ends. The mode corresponds to the buckling of the spring with clamped ends. The author finds the critical spring compression.

Findings

Buckling refers to the loss of stability up to the sudden and violent failure of seed straight bars or beams under the action of pressure forces, whose line of action is the column axis. The known results for the buckling of axially overloaded coil springs were found using the static stability criterion. The author uses an alternative approach method for studying the stability of the spring. This method is based on dynamic equations. In this paper, the author derives the equations for transverse vibrations of the pressure-loaded coil springs. The fundamental natural frequency of the transverse vibrations of the column is proved to be the certain function of the axial force, as well as the variable length of the spring. Is the fundamental natural frequency of transverse oscillations turns to be to zero, is the lateral buckling of the spring occurs.

Research limitations/implications

The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The more accurate model is based on the equations of motion of loaded helical Timoshenko beams. The dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain) is to be derived. Unfortunately, that for the spatial beam models only numerical results could be obtained.

Practical implications

The closed form analytical formulas for fundamental natural frequency of the transverse vibrations of the column as function of the axial force, as well as the variable length of the spring are derived. The practically important formulas for lateral buckling of the spring are obtained.

Originality/value

In this paper, the author derives the new equations for transverse vibrations of the pressure-loaded coil springs. The author demonstrates that the fundamental natural frequency of the transverse vibrations of the column is the function of the axial force. For study of the stability of the spring the author uses an alternative approach method. This method is based on dynamic equations. The new, original expressions for lateral buckling of the spring are also obtained.

Details

Multidiscipline Modeling in Materials and Structures, vol. 10 no. 3
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 4 February 2021

Guichen Zhang, Hongtao Zhang, Heng Peng and Yinghua Liu

High-rise tower structures supported by side frame structure and viscous damper in chemical industry can produce plasticity under dynamic loads, such as wind and…

Abstract

Purpose

High-rise tower structures supported by side frame structure and viscous damper in chemical industry can produce plasticity under dynamic loads, such as wind and earthquake, which will heavily influence the long-term safety operation. This paper aims to systematically study the optimization design of these structures by free vibration and dynamic shakedown analysis.

Design/methodology/approach

The transfer matrix method and Euler–Bernoulli beam vibration are used to study the free vibration characteristic of the simplified high-rise tower structure. Then the extended stress compensation method is used to construct the self-equilibrated stress by using the dynamic load vertexes and the lower bound dynamic shakedown analysis for the structure with viscous damper. Using the proposed method, comprehensive parametric studies and optimization are performed to examine the shakedown load of high-rise tower with various supported conditions.

Findings

The numerical results show that the supported frame stiffness, attached damper or spring parameters influence the free vibration and shakedown characters of high-rise tower very much. The dynamic shakedown load is lowered down quickly with external load frequency increasing to the fundamental natural frequency of the structure under spring supported condition, while changed little with the damping connection. The optimized location and parameter of support are obtained under dynamical excitations.

Research limitations/implications

In this study, the high-rise tower structure is simplified as a cantilever beam supported by a short cantilever beam and a damper under repeated dynamic load, and linear elasticity for solid is assumed for free vibration analysis. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.

Originality/value

This study provides a comprehensive method for the dynamical optimization of high-rise tower structure by combining free vibration and shakedown analysis.

Details

Engineering Computations, vol. 38 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 July 2017

Qingshan Wang, Dongyan Shi, Qian Liang and Fuzhen Pang

The purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels…

Abstract

Purpose

The purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels and shells of revolution with general boundary conditions.

Design/methodology/approach

The modified Fourier series is chosen as the basis function of the admissible functions of the structure to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges, and the vibration behavior is solved by means of the Ritz method. The complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of FG parabolic and circular panels at the common meridian of θ = 0 and 2π. The convergence and accuracy of the present method are verified by other contributors.

Findings

Some new results of FG panels and shells with elastic restraints, as well as different geometric and material parameters, are presented and the effects of the elastic restraint parameters, power-law exponent, circumference angle and power-law distributions on the free vibration characteristic of the panels are also presented, which can be served as benchmark data for the designers and engineers to avoid the unpleasant, inefficient and structurally damaging resonant.

Originality/value

The paper could provide the reference for the research about the moderately thick FG parabolic and circular panels and shells of revolution with general boundary conditions. In addition, the change of the boundary conditions can be easily achieved by just varying the stiffness of the boundary restraining springs along all the edges of panels without making any changes in the solution procedure.

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Article
Publication date: 19 March 2021

Supen Kumar Sah and Anup Ghosh

The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate.

Abstract

Purpose

The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate.

Design/methodology/approach

Equilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate.

Findings

The finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied.

Originality/value

Development and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.

Details

Aircraft Engineering and Aerospace Technology, vol. 93 no. 2
Type: Research Article
ISSN: 1748-8842

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Article
Publication date: 12 November 2019

Zhen Li, Dejian Li, Yao Lu, Kepei Cheng and Qianqiu Wu

The purpose of this paper is to obtain the response time history curves of vertical and lateral acceleration in the span of the main beam under different loads through the…

Abstract

Purpose

The purpose of this paper is to obtain the response time history curves of vertical and lateral acceleration in the span of the main beam under different loads through the finite element time-history analysis method, so as to realize the Serviceability Analysis of a Cable-Supported Footbridge Subjected to Human-Induced Loads, taking the long-span cable-supported footbridge over Dongtan River as an example.

Design/methodology/approach

The finite element method is used for analysis of the footbridge.

Findings

It is found that under the condition of low-density pedestrians walking freely, the response of human vertical vibration acceleration and the load conditions of pedestrian overpasses cannot meet the requirements of normal use. Therefore, the vertical acceleration of the footbridge should be designed to reduce vibration. Under these two loading conditions, the lateral acceleration response meets the requirements of normal use.

Originality/value

On the basis of summarizing the research at home and abroad, the analysis of human-induced vibration is mainly considered from two aspects: frequency regulation and dynamic response control. The walking load models mainly include Fourier series model, self-excitation model, impulse model, stochastic model and more; the crowd load models are divided into groups: low-density crowd walking freely, high-density crowd flowing and more. Therefore, it is very important to calculate the structural vibration response in the design of long-span cable-supported footbridges under pedestrian excitation to meet comfort requirements.

Details

International Journal of Structural Integrity, vol. 11 no. 3
Type: Research Article
ISSN: 1757-9864

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Article
Publication date: 12 October 2015

Amale Mahi, El Abbas Adda Bedia, Abdelouahed Tounsi and Amina Benkhedda

A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides…

Abstract

Purpose

A new simple parametric shear deformation theory applicable to isotropic and functionally graded plates is developed. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The paper aims to discuss these issues.

Design/methodology/approach

Material properties are temperature-dependent and vary continuously through the thickness according to a power law distribution. The plate is assumed to be initially stressed by a temperature rise through the thickness. The energy functional of the system is obtained using Hamilton’s principle. Free vibration frequencies are then calculated using a set of characteristic orthogonal polynomials and by applying Ritz method for different boundary conditions.

Findings

In the light of good performance of the present theory for all boundary conditions considered, it can be considered as an excellent alternative to some two-dimensional (2D) theories for approximating the tedious and time consuming three-dimensional plate problems.

Originality/value

To the best of the authors’ knowledge and according to literature survey, almost all published higher order shear deformation theories have been limited to simply supported boundary conditions and without taking into account the thermal stresses effects. The existing 2D shear deformation theories of Reddy, Karama and Touratier can be easily recovered. Furthermore, this feature can be highly appreciated in an iterative design process where a large number of derived plate models can be tested by selecting only two parameters in a simple polynomial function which is computationally efficient. Finally, new results are presented to show the effect of material variation, and temperature rise on natural frequencies of the FG plate for different boundary conditions.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 3
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 November 1941

Charles B. Lyman

MUCH reference is made in the aeronautical field to the flutter problem and the subject is receiving the attention of many persons engaged in research, testing, and…

Abstract

MUCH reference is made in the aeronautical field to the flutter problem and the subject is receiving the attention of many persons engaged in research, testing, and design. Many aeronautical engineers are well acquainted with some aspect of the problem, and although only a few are concerned with its several phases it is safe to say that all aeronautical men regard it with some degree of interest. It is fitting, therefore, that although it has been adequately treated by many authors from other points of view, a statement be here made summarizing the flutter problem as one of the aeroplane designer. In order that the exact nature of this problem be appreciated it is first necessary that a few of the fundamentals be reviewed.

Details

Aircraft Engineering and Aerospace Technology, vol. 13 no. 11
Type: Research Article
ISSN: 0002-2667

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