Flapwise bending vibration analysis of double tapered rotating Euler–Bernoulli beam by using the differential transform method

Őzdemir, Őzge; Kaya, Metin O.

doi:10.1007/s11012-006-9012-z

Cited by 102 publications

(27 citation statements)

References 7 publications

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“…2 and 3 into Eqs. 5 and 19 and taking partial derivatives of E k and E s with respect to q ij and q ij , neglecting the higher order non-linear terms, the equation of motion for the tapered beam is formulated using the The trends in the second frequency reported by Ozgumus and Kaya (2006) should exhibit decreasing trend with an increase in taper ratio. However, at τ b = τ h = 0.4, a higher value is reported.…”

Section: Equation Of Motionmentioning

confidence: 99%

“…The results from the present modeling method have been obtained considering ten assumed modes compared with those reported by Ozgumus and Kaya (2006) using the differential transform method. The influence of taper ratios on the first three fundamental frequencies is presented in Tables 1 and 2 and the results are compared. From the data, it has been observed that there is nearly one-to-one correspondence between the results obtained from the current approach and those reported based on the differential transform method.…”

Section: Analysis Of Flapwise Bending Natural Frequenciesmentioning

confidence: 99%

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Flapwise bending vibration analysis of functionally graded rotating double-tapered beams

Maganti

Nalluri

2015

Int J Mech Mater Eng

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Background: During the past decade, many researchers have focused on the vibration characteristics of stationary and rotating functionally graded beams employing various methods of analysis. Hitherto, the studies have been mainly confined to uniform beams. Hence, the present study is aimed at studying the free vibration characteristics of functionally graded double-tapered rotating cantilever beam with symmetric cross section. Material and Method: This paper presents a method which considers the deformation variables to determine flapwise bending vibrations of rotating functionally graded doubletapered beam attached to a rigid hub. The tapered beam is characterized by continuously variable Young's modulus along the thickness direction according to a power law. The equations of motions are derived using hybrid deformation variables employing Lagrange's approach. Rayleigh-Ritz method is used to evaluate the frequencies of the beam. Results: The effect of several parameters such as material composition gradient, taper ratios, hub radius ratio and rotational speed on flapwise bending natural frequencies of tapered beams are investigated. Conclusions: Variation in taper ratios affects the frequency parameters of the beam. The frequency parameters are observed to increase with an increase in hub radius. The power law index has negligible influence on the trend of flapwise bending natural frequencies with an increase in angular speed for different taper ratios.

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Section: Equation Of Motionmentioning

confidence: 99%

Section: Analysis Of Flapwise Bending Natural Frequenciesmentioning

confidence: 99%

Flapwise bending vibration analysis of functionally graded rotating double-tapered beams

Maganti

Nalluri

2015

Int J Mech Mater Eng

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“…The con sequences of centrifugal stiffening have been proven in previous literature to be significant and it is therefore included in this model (Ozgumus and Kaya, 2006;Naguleswaran, 1997Naguleswaran, , 1994. In order to model this effect a geometric stiffness m atrix is added to the original stiffness m atrix.…”

Section: O Ne D Im En Sion Al M Od Elmentioning

confidence: 99%

Fragility analysis of steel and concrete wind turbine towers

Quilligan

O’Connor

Pakrashi

2012

Engineering Structures

140

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“…homotopy analysis [3] or the Green's functions method [4]. However, in most cases, in order to obtain a solution it is necessary to apply approximate methods, such as finite difference method [5], the power series method [6], differential transformation method (DTM) -"improved" Taylor method [5,7,8] or by the use of the Lagrange multiplier formalism [9]. This paper is a continuation of consideration, shown at [10], relating to the use of a matrix and power series methods for solving ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%