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Erschienen in: Archive of Applied Mechanics 4/2018

30.10.2017 | Original

Vibration characteristics of rotating orthotropic cantilever plates using analytical approaches: a comprehensive parametric study

verfasst von: Hamidreza Rostami, Ahmad Rahbar Ranji, Firooz Bakhtiari-Nejad

Erschienen in: Archive of Applied Mechanics | Ausgabe 4/2018

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Abstract

This manuscript is concerned with the free vibration analysis of rotating orthotropic cantilever plates attached with an arbitrary stagger angle to a hub. The general governing equations which include both the centrifugal inertia forces and Coriolis effects are derived using Hamilton’s principle. The results are obtained using extended Kantorovich method and extended Galerkin method which are compared with each other, and available data in the literature and in good agreements are observed. A very detailed study of the influence of varying stiffness ratio, rotation speed, stagger angle, hub radius ratio and aspect ratio on the dynamic characteristics is conducted. These investigations provide complementary results, which leads to improvement in design and appropriate optimization of the material and geometry in this class of problems. The observation of the results shows that the crossing/veering phenomenon is influenced by the stiffness ratio, stagger angle and hub radius ratio. It is found that the centrifugal stiffening rate in the spanwise bending modes is constant, while in the torsion mode is changeable. The plate with the lower stiffness ratio has the higher centrifugal stiffening rate.

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Literatur
1.
Zurück zum Zitat Southwell, R., Gough, B.: The free transverse vibration of airscrew blades. Br. ARC Rep. Memo. 766, 358–369 (1921) Southwell, R., Gough, B.: The free transverse vibration of airscrew blades. Br. ARC Rep. Memo. 766, 358–369 (1921)
2.
Zurück zum Zitat Schilhansl, M.: Bending frequency of a rotating cantilever beam. J. Appl. Mech. Trans. Am. Soc. Mech. Eng. 25, 28–30 (1958)MathSciNetMATH Schilhansl, M.: Bending frequency of a rotating cantilever beam. J. Appl. Mech. Trans. Am. Soc. Mech. Eng. 25, 28–30 (1958)MathSciNetMATH
3.
Zurück zum Zitat Hodges, D.H., Rutkowski, M.J.: Free-vibration analysis of rotating beams by a variable-order finite-element method. AIAA. J. 19, 1459–1466 (1981)CrossRefMATH Hodges, D.H., Rutkowski, M.J.: Free-vibration analysis of rotating beams by a variable-order finite-element method. AIAA. J. 19, 1459–1466 (1981)CrossRefMATH
4.
Zurück zum Zitat Borri, M., Mantegazza, P.: Some contributions on structural and dynamic modeling of helicopter rotor blades. Aerotec. Missili. Spaz. 64(9), 143–154 (1985)MATH Borri, M., Mantegazza, P.: Some contributions on structural and dynamic modeling of helicopter rotor blades. Aerotec. Missili. Spaz. 64(9), 143–154 (1985)MATH
5.
Zurück zum Zitat Yokoyama, T.: Free vibration characteristics of rotating Timoshenko beam. Int. J. Mech. Sci. 30, 743–755 (1988)CrossRefMATH Yokoyama, T.: Free vibration characteristics of rotating Timoshenko beam. Int. J. Mech. Sci. 30, 743–755 (1988)CrossRefMATH
6.
Zurück zum Zitat Vyas, N.S., Rao, J.S.: Equations of motion of a blade rotating with variable angular velocity. J. Sound Vib. 156(2), 327–336 (1992)CrossRefMATH Vyas, N.S., Rao, J.S.: Equations of motion of a blade rotating with variable angular velocity. J. Sound Vib. 156(2), 327–336 (1992)CrossRefMATH
7.
Zurück zum Zitat Naguleswaran, J.S.: Lateral vibration of a centrifugally tensioned uniform Euler–Bernoulli beam. J. Sound Vib. 176, 613–624 (1994)CrossRefMATH Naguleswaran, J.S.: Lateral vibration of a centrifugally tensioned uniform Euler–Bernoulli beam. J. Sound Vib. 176, 613–624 (1994)CrossRefMATH
8.
Zurück zum Zitat Da Silva, M.R.M.C.: A comprehensive analysis of the dynamics of a helicopter rotor blade. Int. J. Solids Struct. 35, 619–635 (1998)CrossRefMATH Da Silva, M.R.M.C.: A comprehensive analysis of the dynamics of a helicopter rotor blade. Int. J. Solids Struct. 35, 619–635 (1998)CrossRefMATH
9.
Zurück zum Zitat Yoo, H.H., Shin, S.H.: Vibration analysis of rotating cantilever beams. J. Sound Vib. 212, 807–828 (1998)CrossRef Yoo, H.H., Shin, S.H.: Vibration analysis of rotating cantilever beams. J. Sound Vib. 212, 807–828 (1998)CrossRef
10.
Zurück zum Zitat Rao, S.S., Gupta, R.S.: Finite element analysis of rotating Timoshenko beams. J. Sound Vib. 242(1), 103–124 (2001)CrossRefMATH Rao, S.S., Gupta, R.S.: Finite element analysis of rotating Timoshenko beams. J. Sound Vib. 242(1), 103–124 (2001)CrossRefMATH
11.
Zurück zum Zitat Chung, J., Yoo, H.H.: Dynamic analysis of a rotating cantilever beam by using the finite element method. J. Sound Vib. 249(1), 147–164 (2002)CrossRef Chung, J., Yoo, H.H.: Dynamic analysis of a rotating cantilever beam by using the finite element method. J. Sound Vib. 249(1), 147–164 (2002)CrossRef
12.
Zurück zum Zitat Marugabandhu, P., Griffin, J.H.: A reduced-order model for evaluating the effect of rotational speed on the natural frequencies and mode shapes of blades. Trans. ASME J. Eng. Gas Turbines Power 125, 772–776 (2003)CrossRef Marugabandhu, P., Griffin, J.H.: A reduced-order model for evaluating the effect of rotational speed on the natural frequencies and mode shapes of blades. Trans. ASME J. Eng. Gas Turbines Power 125, 772–776 (2003)CrossRef
13.
Zurück zum Zitat Banerjee, J.R., Su, H.: Dynamic stiffness formulation and free vibration analysis of a spinning composite beam. Comput. Struct. 84, 1208–1214 (2006)CrossRef Banerjee, J.R., Su, H.: Dynamic stiffness formulation and free vibration analysis of a spinning composite beam. Comput. Struct. 84, 1208–1214 (2006)CrossRef
14.
Zurück zum Zitat Lee, S.Y., Sheu, J.J.: Free vibration of an extensible rotating inclined Timoshenko beam. J. Sound Vib. 304, 606–624 (2007)CrossRefMATH Lee, S.Y., Sheu, J.J.: Free vibration of an extensible rotating inclined Timoshenko beam. J. Sound Vib. 304, 606–624 (2007)CrossRefMATH
15.
Zurück zum Zitat Piovan, M.T., Sampaio, R.: A study on the dynamics of rotating beams with functionally graded properties. J. Sound Vib. 327, 134–143 (2009)CrossRef Piovan, M.T., Sampaio, R.: A study on the dynamics of rotating beams with functionally graded properties. J. Sound Vib. 327, 134–143 (2009)CrossRef
16.
Zurück zum Zitat Li, L., Zhang, D.G., Zhu, W.D.: Free vibration analysis of a rotating hub-functionally graded material beam system with the dynamic stiffening effect. J. Sound Vib. 333, 1526–1541 (2014)CrossRef Li, L., Zhang, D.G., Zhu, W.D.: Free vibration analysis of a rotating hub-functionally graded material beam system with the dynamic stiffening effect. J. Sound Vib. 333, 1526–1541 (2014)CrossRef
17.
Zurück zum Zitat Genta, G., Feng, C., Tonoli, A.: Dynamics behavior of rotating bladed discs: a finite element formulation for the study of second and higher order harmonics. J. Sound Vib. 329, 5289–5306 (2010)CrossRef Genta, G., Feng, C., Tonoli, A.: Dynamics behavior of rotating bladed discs: a finite element formulation for the study of second and higher order harmonics. J. Sound Vib. 329, 5289–5306 (2010)CrossRef
18.
Zurück zum Zitat Chiu, Y.-J., Chen, D.-Z.: The coupled vibration in a rotating multi-disk rotor system. Int. J. Mech. Sci. 53, 1–10 (2011)CrossRef Chiu, Y.-J., Chen, D.-Z.: The coupled vibration in a rotating multi-disk rotor system. Int. J. Mech. Sci. 53, 1–10 (2011)CrossRef
19.
Zurück zum Zitat Dohnal, F., Knopf, E., Nordmann, R.: Efficient modelling of rotor-blade interaction using substructuring. In: Proceedings of the 9th IFToMM ICORD. Mechanism and Machine Science vol. 21, pp. 143–153 (2015) Dohnal, F., Knopf, E., Nordmann, R.: Efficient modelling of rotor-blade interaction using substructuring. In: Proceedings of the 9th IFToMM ICORD. Mechanism and Machine Science vol. 21, pp. 143–153 (2015)
20.
Zurück zum Zitat Dokainish, M.A., Rawtani, R.: Vibration analysis of rotating cantilever plates. Int. J. Numer. Methods Eng. 3(2), 233–248 (1971)CrossRefMATH Dokainish, M.A., Rawtani, R.: Vibration analysis of rotating cantilever plates. Int. J. Numer. Methods Eng. 3(2), 233–248 (1971)CrossRefMATH
21.
Zurück zum Zitat Ramamurti, V., Kielb, R.: Natural frequencies of twisted rotating plates. J. Sound Vib. 97, 429–449 (1984)CrossRef Ramamurti, V., Kielb, R.: Natural frequencies of twisted rotating plates. J. Sound Vib. 97, 429–449 (1984)CrossRef
22.
Zurück zum Zitat Wang, J.T.S., Shaw, D., Mahrenholtz, O.: Vibration of rotating rectangular plates. J. Sound Vib. 112(3), 455–468 (1987)CrossRef Wang, J.T.S., Shaw, D., Mahrenholtz, O.: Vibration of rotating rectangular plates. J. Sound Vib. 112(3), 455–468 (1987)CrossRef
23.
Zurück zum Zitat Rao, J.S., Gupta, K.: Free vibrations of rotating small aspect ratio pretwisted blades. Mech. Mach. Theory 22(2), 159–167 (1987)CrossRef Rao, J.S., Gupta, K.: Free vibrations of rotating small aspect ratio pretwisted blades. Mech. Mach. Theory 22(2), 159–167 (1987)CrossRef
24.
Zurück zum Zitat Yoo, H.H., Kim, S.K.: Free vibration analysis of rotating cantilever plates. AIAA J. 40(11), 2188–2196 (2002)CrossRef Yoo, H.H., Kim, S.K.: Free vibration analysis of rotating cantilever plates. AIAA J. 40(11), 2188–2196 (2002)CrossRef
25.
Zurück zum Zitat Yoo, H.H., Kim, S.K.: Flapwise bending vibration of rotating plates. Int. J. Numer. Methods Eng. 55, 785–802 (2002)CrossRefMATH Yoo, H.H., Kim, S.K.: Flapwise bending vibration of rotating plates. Int. J. Numer. Methods Eng. 55, 785–802 (2002)CrossRefMATH
26.
Zurück zum Zitat Yoo, H.H., Kim, S., Inman, D.: Modal analysis of rotating composite cantilever plates. J. Sound Vib. 258, 233–246 (2002)CrossRef Yoo, H.H., Kim, S., Inman, D.: Modal analysis of rotating composite cantilever plates. J. Sound Vib. 258, 233–246 (2002)CrossRef
27.
Zurück zum Zitat Yoo, H.H., Pierre, C.: Modal characteristic of a rotating rectangular cantilever plate. J. Sound Vib. 259(1), 81–96 (2003)CrossRef Yoo, H.H., Pierre, C.: Modal characteristic of a rotating rectangular cantilever plate. J. Sound Vib. 259(1), 81–96 (2003)CrossRef
28.
Zurück zum Zitat Lim, H.S., Yoo, H.H.: Modal analysis of cantilever plates undergoing accelerated in-plane motion. J. Sound Vib. 297, 880–894 (2006)CrossRef Lim, H.S., Yoo, H.H.: Modal analysis of cantilever plates undergoing accelerated in-plane motion. J. Sound Vib. 297, 880–894 (2006)CrossRef
29.
Zurück zum Zitat Hashemi, S.H., Farhadi, S., Carra, S.: Free vibration analysis of rotating thick plates. J. Sound Vib. 323, 366–384 (2009)CrossRef Hashemi, S.H., Farhadi, S., Carra, S.: Free vibration analysis of rotating thick plates. J. Sound Vib. 323, 366–384 (2009)CrossRef
30.
Zurück zum Zitat Sinha, S.K., Turner, K.E.: Natural frequencies of a pre-twisted blade in a centrifugal force field. J. Sound Vib. 330(11), 2655–2681 (2011)CrossRef Sinha, S.K., Turner, K.E.: Natural frequencies of a pre-twisted blade in a centrifugal force field. J. Sound Vib. 330(11), 2655–2681 (2011)CrossRef
31.
Zurück zum Zitat Sun, J., Kari, L., Arteaga, I.L.: A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton’s principle. J. Sound Vib. 332, 1355–1371 (2013)CrossRef Sun, J., Kari, L., Arteaga, I.L.: A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton’s principle. J. Sound Vib. 332, 1355–1371 (2013)CrossRef
32.
Zurück zum Zitat Sun, J., Arteaga, I.L., Kari, L.: Dynamic modeling of a multilayer rotating blade via quadratic layerwise theory. Compos. Struct. 99, 276–287 (2013)CrossRef Sun, J., Arteaga, I.L., Kari, L.: Dynamic modeling of a multilayer rotating blade via quadratic layerwise theory. Compos. Struct. 99, 276–287 (2013)CrossRef
33.
Zurück zum Zitat Li, L., Zhang, D.G.: Free vibration analysis of rotating functionally graded rectangular plates. Compos. Struct. 136, 493–504 (2016)CrossRef Li, L., Zhang, D.G.: Free vibration analysis of rotating functionally graded rectangular plates. Compos. Struct. 136, 493–504 (2016)CrossRef
34.
Zurück zum Zitat Sinha, S.K., Zylka, R.P.: Vibration analysis of composite airfoil blade using orthotropic thin shell bending theory. Int. J. Mech. Sci. 121, 90–105 (2017)CrossRef Sinha, S.K., Zylka, R.P.: Vibration analysis of composite airfoil blade using orthotropic thin shell bending theory. Int. J. Mech. Sci. 121, 90–105 (2017)CrossRef
35.
Zurück zum Zitat Rostami, H., Rahbar, A.R., Bakhtiari-Nejad, F.: Free in-plane vibration analysis of rotating rectangular orthotropic cantilever plates. Int. J. Mech. Sci. 115–116, 438–456 (2016)CrossRef Rostami, H., Rahbar, A.R., Bakhtiari-Nejad, F.: Free in-plane vibration analysis of rotating rectangular orthotropic cantilever plates. Int. J. Mech. Sci. 115–116, 438–456 (2016)CrossRef
36.
Zurück zum Zitat Kim, H.S., Cho, M., Kim, G.I.: Free-edge strength analysis in composite laminates by the extended Kantorovich method. Compos. Struct. 49, 229–235 (2000)CrossRef Kim, H.S., Cho, M., Kim, G.I.: Free-edge strength analysis in composite laminates by the extended Kantorovich method. Compos. Struct. 49, 229–235 (2000)CrossRef
37.
Zurück zum Zitat Ungbhakorn, V., Singhatanadgid, P.: Buckling analysis of symmetrically laminated composite plates by the extended Kantorovich method. Compos. Struct. 73, 120–128 (2006)CrossRef Ungbhakorn, V., Singhatanadgid, P.: Buckling analysis of symmetrically laminated composite plates by the extended Kantorovich method. Compos. Struct. 73, 120–128 (2006)CrossRef
38.
Zurück zum Zitat Ranji, A.Rahbar, Rostami, H.: A semi-analytical solution for forced vibrations response of rectangular orthotropic plates with various boundary conditions. J. Mech. Sci. Technol. 24, 357–364 (2010)CrossRef Ranji, A.Rahbar, Rostami, H.: A semi-analytical solution for forced vibrations response of rectangular orthotropic plates with various boundary conditions. J. Mech. Sci. Technol. 24, 357–364 (2010)CrossRef
39.
Zurück zum Zitat Ranji, A.R., Rostami, H.: A semi-analytical technique for bending analysis of cylindrical panels with general loading and boundary conditions. J. Mech. Sci. Technol. 26(6), 1711–1718 (2012)CrossRef Ranji, A.R., Rostami, H.: A semi-analytical technique for bending analysis of cylindrical panels with general loading and boundary conditions. J. Mech. Sci. Technol. 26(6), 1711–1718 (2012)CrossRef
40.
Zurück zum Zitat Meirovitch, L.: Principles and Techniques of Vibrations. McGraw Hill, New York (1997) Meirovitch, L.: Principles and Techniques of Vibrations. McGraw Hill, New York (1997)
Metadaten
Titel
Vibration characteristics of rotating orthotropic cantilever plates using analytical approaches: a comprehensive parametric study
verfasst von
Hamidreza Rostami
Ahmad Rahbar Ranji
Firooz Bakhtiari-Nejad
Publikationsdatum
30.10.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 4/2018
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-017-1320-3

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