Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam

Mei, C.

doi:10.1016/j.compstruc.2007.10.003

Cited by 50 publications

(32 citation statements)

References 14 publications

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“…Since obtaining an exact closed-form solution either seems impossible or involves cumbersome mathematical operations, many researchers have used approximate methods such as the Rayleigh-Ritz method [8], Frobenius series solution [9][10][11][12][13], finite element method [14][15][16][17][18][19][20][21], Galerkin method [22,23] and differential transform method [24][25][26][27]. Hodges [28] proposed an approximate formula for calculating the fundamental natural frequency of a uniform rotating beam clamped at the root.…”

Section: A(x)mentioning

confidence: 99%

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Attarnejad

Shahba

2011

Arab J Sci Eng

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Introducing the concept of basic displacement functions (BDFs), a new beam element is presented for the analysis of rotating tapered beams. BDFs are obtained using the energy method; i.e., the unit-load method. Following the basic principles of structural mechanics, it is shown that the shape functions and consequently the structural matrices can be derived in terms of BDFs. The method is a combination of flexibility and stiffness methods and is considered as the logical extension of the conventional finite element method. The method is employed for both static and free vibration analyses of different types of tapered beams, and the results compare well with those in the literature. Finally, the effects of the taper ratio, hub radius and rotating speed parameter on the natural frequencies and static deflection are investigated. The results obtained are satisfactory even for only a few elements.

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Section: A(x)mentioning

confidence: 99%

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Attarnejad

Shahba

2011

Arab J Sci Eng

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“…It is also shown in [3] that all the solutions to the relativistic harmonic oscillator are periodic. So, we aim in this research to obtain such periodic solutions via differential transformation method (DTM) [5][6][7][8][9][10][11][12][13][14][15][16][17][19][20][21][22][23][24][25][26]. This method was introduced firstly by Zhou in 1986 to study electrical circuits [15].…”

Section: Introductionmentioning

confidence: 99%

Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method

Ebaid

2010

Communications in Nonlinear Science and Numerical Simulation

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“…Ozgumus and Kaya [43] applied DTM to calculate the natural frequency of non-uniform beams. Mei [45] employed DTM for rotating beams. Being very concise and effective in solving non-linear problems is one of the many advantages assigned to DTM.…”

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confidence: 99%

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Talebi

Ariaei

2014

Arch Appl Mech

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An analytical method is presented to determine the vibration characteristics of a rotating Timoshenko beam with variable cross section and intermediate flexible connections using the differential transform method. Based on the application of Timoshenko beam theory on separate beams and the compatibility requirements on each connection point, the correlations between every two adjacent spans are obtained. The formulation is extended to a point where it would be able to evaluate the cases with internal and external flexible connections. The results will be validated against those reported in the literature and compared with the ones from the modal test. A number of parametric studies are conducted to assess the stiffness of elastic connections, rotating speed, hub radius and tapered ratio effects on the beam natural frequencies and mode shapes. It is observed that by changing the stiffness of the intermediate springs, the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams.

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Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam

Cited by 50 publications

References 14 publications

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

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