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Meccanica
Published in: Meccanica 10/2020

17-09-2020

Natural frequencies of rotating twisted beams: a perturbation method based approach

Authors: Ajinkya Baxy, Abhijit Sarkar

Published in: Meccanica | Issue 10/2020

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Abstract

Structures such as turbomachinery blades, industrial fans, propellers, etc. can be modeled as twisted beams. The study of dynamics of these structures is vital as operational failure of such structures can have catastrophic consequences. As the inclusion of twist and rotation complicates the problem, Finite Element (FE) method is widely used to determine the modal characteristics of rotating twisted beams. In this work, a novel formula is derived to estimate the natural frequencies of rotating twisted beams. The formula is derived using the perturbation method. The twist angle and the rotating speed are treated as the perturbation parameters. In general, the dynamics of rotating twisted beams is coupled in the two transverse planes. However, in the first part of the work the problem is assumed to be uncoupled and it is shown that this assumption is valid under certain cases. In the second part, the problem of general coupled dynamics is solved. Interesting insights based on the formula are presented. The accuracy of the derived formula is verified by comparing it with the literature and FE simulation results. It has been shown that the formula is valid over a fairly large range of twist angles and rotating speeds. In contrast to the detailed FE simulation, the derived analytical formula will be better suited for design iterations in industrial practice.
previous article Modified couple stress theory for three-dimensional elasticity in curvilinear coordinate system: application to micro torus panels

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Appendix
Available only for authorised users
Literature
1.
Banerjee J (2001) Free vibration analysis of a twisted beam using the dynamic stiffness method. Int J Solids Struct 38(38–39):6703–6722CrossRef
2.
Banerjee J, Kennedy D (2014) Dynamic stiffness method for inplane free vibration of rotating beams including coriolis effects. J Sound Vib 333(26):7299–7312CrossRef
3.
Baxy A, Sarkar A (2020) Natural frequencies of a rotating curved cantilever beam: a perturbation method-based approach. Proc Inst Mech Eng Part C J Mech Eng Sci 234(9):1706–1719CrossRef
4.
Cao D, Gao Y (2019) Free vibration of non-uniform axially functionally graded beams using the asymptotic development method. Appl Math Model 40(1):85–96MathSciNet
5.
Cao D, Gao Y, Wang J et al (2019) Analytical analysis of free vibration of non-uniform and non-homogeneous beams: asymptotic perturbation approach. Appl Math Model 65:526–534MathSciNetCrossRef
6.
Carnegie W, Thomas J (1972) The coupled bending–bending vibration of pre-twisted tapered blading. J Eng Ind 94(1):255–266CrossRef
7.
Dawson B (1968) Coupled bending-bending vibrations of pre-twisted cantilever blading treated by the Rayleigh–Ritz energy method. J Mech Eng Sci 10(5):381–388CrossRef
8.
Dawson B, Ghosh N, Carnegie W (1971) Effect of slenderness ratio on the natural frequencies of pre-twisted cantilever beams of uniform rectangular cross-section. J Mech Eng Sci 13(1):51–59CrossRef
9.
10.
Ganguli R (2016) Physics based finite element interpolation functions for rotating beams. Proc Indian Natl Sci Acad 82(2):257–270
11.
Ganguli R (2017) Finite element analysis of rotating beams. Springer, SingaporeCrossRef
12.
Hashemi S, Richard M (2001) Natural frequencies of rotating uniform beams with coriolis effects. J Vib Acoust 123(4):444–455CrossRef
13.
Hodges DH (1981) An approximate formula for the fundamental frequency of a uniform rotating beam clamped off the axis of rotation. Tech. rep, Army Research and Technology Labs Moffett Field CA Aeromechanics Lab
14.
Hsu MH (2009) Vibration analysis of pre-twisted beams using the spline collocation method. J Mar Sci Technol 17(2):106–115
15.
Huseyin K (1973) The multiple-parameter perturbation technique for the analysis of non-linear systems. Int J Non-Linear Mech 8(5):431–443MathSciNetCrossRef
16.
Karami G, Farshad M, Banan M (1991) Pretwisted rods- an efficient finite element modelling. Finite Elem Anal Des 9(1):77–85CrossRef
17.
Kim H, Yoo HH, Chung J (2013) Dynamic model for free vibration and response analysis of rotating beams. J Sound Vib 332(22):5917–5928CrossRef
18.
Kunte M, Sarkar A, Sonti V (2010) Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells. J Sound Vib 329(25):5356–5374CrossRef
19.
Kunte M, Sarkar A, Sonti V (2011) Generalized asymptotic expansions for the wavenumbers in infinite flexible in vacuo orthotropic cylindrical shells. J Sound Vib 330(23):5628–5643CrossRef
20.
Ladde G, Šiljak D (1983) Multiparameter singular perturbations of linear systems with multiple time scales. Automatica 19(4):385–394MathSciNetCrossRef
21.
Lee SY, Kuo YH (1991) Bending frequency of a rotating beam with an elastically restrained root. J Appl Mech 58(1):209–214CrossRef
22.
Lee SY, Sheu JJ (2007) Free vibrations of a rotating inclined beam. J Appl Mech 74(3):406–414CrossRef
23.
Lin S (2001) The instability and vibration of rotating beams with arbitrary pretwist and an elastically restrained root. J Appl Mech 68(6):844–853CrossRef
24.
Lo H, Goldberg J, Bogdanoff J (1960) Effect of small hub-radius change on bending frequencies of a rotating beam. J Appl Mech 27(3):548–550CrossRef
25.
Naguleswaran S (1994) Lateral vibration of a centrifugally tensioned uniform Euler–Bernoulli beam. J Sound Vib 176(5):613–624CrossRef
26.
Nayfeh A (2011) Introduction to perturbation techniques. Wiley, New JerseyMATH
27.
Putter S, Manor H (1978) Natural frequencies of radial rotating beams. J Sound Vib 56(2):175–185CrossRef
28.
Rao J (1991) Turbomachine blade vibration. New Age International, New Delhi
29.
Sarkar K, Ganguli R (2013) Rotating beams and non-rotating beams with shared eigenpair for pinned-free boundary condition. Meccanica 48(7):1661–1676MathSciNetCrossRef
30.
31.
Sisto F, Chang A (1984) A finite element for vibration analysis of twisted blades based on beam theory. AIAA J 22(11):1646–1651CrossRef
32.
Slyper H (1962) Coupled bending vibrations of pretwisted cantilever beams. J Mech Eng Sci 4(4):365–379CrossRef
33.
Swaminathan M, Rao J (1977) Vibrations of rotating, pretwisted and tapered blades. Mech Mach Theory 12(4):331–337CrossRef
34.
Tang AY, Li XF, Wu JX, Lee K (2015) Flapwise bending vibration of rotating tapered Rayleigh cantilever beams. J Constr Steel Res 112:1–9CrossRef
35.
Thomson W (2018) Theory of vibration with applications. CRC Press, Boca RatonCrossRef
36.
37.
Wright A, Smith C, Thresher R, Wang J (1982) Vibration modes of centrifugally stiffened beams. J Appl Mech 49(1):197–202CrossRef
38.
Yardimoglu B, Yildirim T (2004) Finite element model for vibration analysis of pre-twisted timoshenko beam. J Sound Vib 273(4–5):741–754CrossRef
39.
Yoo H, Shin S (1998) Vibration analysis of rotating cantilever beams. J Sound Vib 212(5):807–828CrossRef
40.
Yoo H, Kwak J, Chung J (2001a) Vibration analysis of rotating pre-twisted blades with a concentrated mass. J Sound Vib 240(5):891–908CrossRef
41.
Yoo HH, Park JH, Park J (2001b) Vibration analysis of rotating pre-twisted blades. Comput Struct 79(19):1811–1819CrossRef
42.
ANSYS\(^{\textregistered }\) Academic Research Mechanical, Release 18.1, ANSYS, Inc
Metadata
Title
Natural frequencies of rotating twisted beams: a perturbation method based approach
Authors
Ajinkya Baxy
Abhijit Sarkar
Publication date
17-09-2020
Publisher
Springer Netherlands
Published in
Meccanica / Issue 10/2020
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-020-01238-7

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