Hybrid stiff-string–polynomial basis functions for vibration analysis of high speed rotating beams

Gunda, Jagadish Babu; Gupta, Rekha; Ganguli, Ranjan

doi:10.1016/j.compstruc.2008.09.008

Cited by 41 publications

(24 citation statements)

References 48 publications

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“…Tables 3 and 4 show the lowest four nondimensional natural frequencies obtained by the present method and those obtained by Gunda and Ganguli [10] for the uniform rotating beam and by Gunda et al [11] for the tapered rotating beam, respectively. As observed, the present method works well both for high and very high rotating speeds.…”

Section: Un-cracked Rotating Tapered Beamsmentioning

confidence: 86%

“…Gunda and Ganguli [9] then assumed the transverse displacement to vary as a fourth order function and obtained new shape functions that would satisfy the static part of the homogeneous governing differential equation. Later Gunda et al [10,11] proposed a new finite element for free vibration analysis of high-speed rotating beams using shape functions that are a linear combination of the solution of the governing static differential equation of a stiff string and a cubic polynomial. Bazoune [12] investigated the modal characteristics of a rotating tapered Timoshenko beam using the finite element analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vibration analysis of a cracked rotating tapered beam using the p-version finite element method

Cheng

Zhang²,

Wu³

et al. 2011

Finite Elements in Analysis and Design

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Section: Un-cracked Rotating Tapered Beamsmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Vibration analysis of a cracked rotating tapered beam using the p-version finite element method

Cheng

Zhang²,

Wu³

et al. 2011

Finite Elements in Analysis and Design

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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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“…This allows one to see the wave effect in a string, contrary to many more complex systems for example structural elements where it might be either not present or not clearly visible. The analogies between a string and the beams have been considered in papers [5,6,11]. Various aspects of the dynamics response of a string under a moving load have been considered, among others, in the papers [2,4,8,10,[12][13][14][15][18][19][20]22].…”

Section: Introductionmentioning

confidence: 99%

Flexible Complex System of a Double-String Under Extreme Moving Loads

Rusin¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this paper the dynamic response of a complex double-string system traversed by extreme moving load is considered. The paper includes the study of a dynamic behavior of a finite, simply supported double-string flexible complex system subject to moving forces with a constant velocity on the top string. The strings are identical, parallel one upon the other and continuously coupled by a linear Winkler elastic element. The moving loads are around an extreme position of the shear wave velocity of the strings. The classical solution of the response of complex systems subjected to forces moving with a constant velocity has a form of an infinite series. But also it is possible to show that in the considered case part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method to search for a solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The closed solutions take different forms depending if the velocity of a moving force is smaller, equal or larger than the shear wave velocity of the strings. This follows from the fact that in string wave phenomena may occur. The solution for the dynamic response of the composite strings under moving force is important because it can be used also in order to find the solution for other types of moving loads. The double string connected in parallel by linear elastic elements can be studied as a theoretical model of composite system or prestressed structure in which coupling effects and transverse wave effects are taken into account. 5670

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Hybrid stiff-string–polynomial basis functions for vibration analysis of high speed rotating beams

Cited by 41 publications

References 48 publications

Vibration analysis of a cracked rotating tapered beam using the p-version finite element method

Vibration analysis of a cracked rotating tapered beam using the p-version finite element method

Basic Displacement Functions in Analysis of Centrifugally Stiffened Tapered Beams

Flexible Complex System of a Double-String Under Extreme Moving Loads

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