Nonlinear transient dynamic response of a blade subject to a pulsating load in a decaying centrifugal force field
Source abstract
Abstract
This study is concerned with an analytical solution for the nonlinear transient dynamic response of a rotating blade in a gas turbine engine experiencing dynamic unbalance due to a blade-off scenario leading to rotor unbalance. As a consequence of rotor unbalance, the blade experiences a pulsating load at its tip due to contact with the casing and a decaying centrifugal force field due to the rotor deceleration. The governing equations of motion consider the blade as an elastic Timoshenko beam of varying thickness subject to changing rotational speeds. The analysis takes into account the variation in the thickness of the beam, the coupled axial and lateral displacements of the beam as a result of Coriolis component of acceleration, shear deformation, rotary inertia, and friction resulting from the contact between the blade and the casing. Our findings indicate that the thickness profile of the beam plays a significant role in the transient response. It further reveals that the decaying centrifugal force field leads to a dramatic change in the dynamic response and the resulting forces on the blade.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Dynamics and Control of Mechanical Systems · Bladed Disk Vibration Dynamics · Vibration and Dynamic Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (35)
Show source-provided references
1. Abbas, B.A.: Dynamic stability of a rotating Timoshenko beam with a flexible root. J. Sound Vib. 108(1), 25–32 (1986)10.1016/S0022-460X(86)80308-X ↗
2. Auciello, N.M., Ercolano, A.: A general solution for dynamic response of axially loaded non-uniform Timoshenko beams. Int. J. Solids Struct. 41(18), 4861–4874 (2004)10.1016/j.ijsolstr.2004.04.036 ↗
3. Banerjee, J.R., Su, H.: Development of a dynamic stiffness matrix for free vibration analysis of spinning beams. Comput. Struct. 82(23), 2189–2197 (2004)10.1016/j.compstruc.2004.03.058 ↗
4. Bazoune, A.: Effect of tapering on natural frequencies of rotating beams. Shock Vib. 14(3), 169–179 (2007)10.1155/2007/865109 ↗
5. Chen, C.O., Ho, S.H.: Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform. Int. J. Mech. Sci. 41(11), 1339–1356 (1999)10.1016/S0020-7403(98)00095-2 ↗
6. Datta, P.K., Ganguli, R.: Vibration characteristics of a rotating blade with localized damage including the effects of shear deformation and rotary inertia. Comput. Struct. 36(6), 1129–1133 (1990)10.1016/0045-7949(90)90221-M ↗
7. Esmailzadeh, E., Ohadi, A.R.: Vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads. J. Sound Vib. 236(3), 443–456 (2000)10.1006/jsvi.2000.2999 ↗
8. Fung, E.H., Yau, D.T.: Effects of centrifugal stiffening on the vibration frequencies of a constrained flexible arm. J. Sound Vib. 224(5), 809–841 (1999)10.1006/jsvi.1999.2212 ↗
9. Grant, D.A.: The effect of rotary inertia and shear deformation on the frequency and normal mode equations of uniform beams carrying a concentrated mass. J. Sound Vib. 57(3), 357–365 (1978)10.1016/0022-460X(78)90316-4 ↗
10. Ho, S.H., Chen, C.O.: Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform. Int. J. Mech. Sci. 48(11), 1323–1331 (2006)10.1016/j.ijmecsci.2006.05.002 ↗
11. Hodges, D.Y., Rutkowski, M.Y.: Free-vibration analysis of rotating beams by a variable-order finite-element method. AIAA J. 19(11), 1459–1466 (1981)10.2514/3.60082 ↗
12. Kane, T.R., Ryan, R., Banerjee, A.K.: Dynamics of a cantilever beam attached to a moving base. J. Guid. Control Dyn. 10(2), 139–151 (1987)10.2514/3.20195 ↗
13. Khulief, Y.A.: Vibration frequencies of a rotating tapered beam with end mass. J. Sound Vib. 134(1), 87–97 (1989)10.1016/0022-460X(89)90738-4 ↗
14. Lee, H.P.: Buckling and dynamic stability of spinning pre-twisted beams under compressive axial loads. Int. J. Mech. Sci. 36(11), 1011–1026 (1994)10.1016/0020-7403(94)90024-8 ↗
15. Lee, S.Y., Lin, S.M., Wu, C.T.: Free vibration of a rotating non-uniform beam with arbitrary pretwist, an elastically restrained root and a tip mass. J. Sound Vib. 273(3), 477–492 (2004)10.1016/S0022-460X(03)00506-6 ↗
16. Lee, S.Y., Lint, S.M.: Exact vibration solutions for nonuniform Timoshenko beams with attachments. AIAA J. 30(12), 2930–2934 (1992)10.2514/3.48979 ↗
17. Lempert, G.D., Tsour, A.: Reduction of static friction between surfaces of Ti–6Al–4V and between surfaces of Ti–6Al–4V and Al-7075. Surf. Coat. Technol. 52(3), 291–295 (1992)10.1016/0257-8972(92)90029-A ↗
18. Liao, C.L., Huang, B.W.: Parametric resonance of a spinning pretwisted beam with time-dependent spinning rate. J. Sound Vib. 180(1), 47–65 (1995)10.1006/jsvi.1995.0066 ↗
19. Lin, S.C., Hsiao, K.M.: Vibration analysis of a rotating Timoshenko beam. J. Sound Vib. 240(2), 303–322 (2001)10.1006/jsvi.2000.3234 ↗
20. Luther, H.A.: An explicit sixth-order Runge–Kutta formula. Math. Comput. 22(102), 434–436 (1968)10.1090/S0025-5718-68-99876-1 ↗
21. Meirovitch, L.: Analytical Methods in Vibration. Macmillan, New York (1967)
22. Naguleswaran, S.: Lateral vibration of a centrifugally tensioned uniform Euler–Bernoulli beam. J. Sound Vib. 176(5), 613–624 (1994)10.1006/jsvi.1994.1402 ↗
23. Ozgumus, O.O., Kaya, M.O.: Vibration analysis of a rotating tapered Timoshenko beam using DTM. Meccanica 45(1), 33–42 (2010)10.1007/s11012-009-9221-3 ↗
24. Sarkar, K., Ganguli, R.: Closed-form solutions for non-uniform Euler–Bernoulli free–free beams. J. Sound Vib. 332(23), 6078–6092 (2013)10.1016/j.jsv.2013.06.008 ↗
25. Şimşek, M.: Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load. Compos. Struct. 92(10), 2532–2546 (2010)10.1016/j.compstruct.2010.02.008 ↗
26. Sinha, S.K.: Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end. Int. J. Nonlinear Mech. 40(1), 113–149 (2005)10.1016/j.ijnonlinmec.2004.05.019 ↗
27. Smith, W.G.: Analytic solutions for tapered column buckling. Comput. Struct. 28(5), 677–681 (1988)10.1016/0045-7949(88)90011-9 ↗
28. Tong, X., Tabarrok, B., Yeh, K.Y.: Vibration analysis of Timoshenko beams with non-homogeneity and varying cross-section. J. Sound Vib. 186(5), 821–835 (1995)10.1006/jsvi.1995.0490 ↗
29. Wang, G., Wereley, N.M.: Free vibration analysis of rotating blades with uniform tapers. AIAA J. 42(12), 2429–2437 (2004)10.2514/1.4302 ↗
30. Weaver Jr., W., Timoshenko, S.P., Young, D.H.: Vibration Problems in Engineering. Wiley, London (1990)
31. Yang, J.B., Jiang, L.J., Chen, D.C.: Dynamic modelling and control of a rotating Euler–Bernoulli beam. J. Sound Vib. 274(3), 863–875 (2004)10.1016/S0022-460X(03)00611-4 ↗
32. Yang, S.M., Tsao, S.M.: Dynamics of a pretwisted blade under nonconstant rotating speed. Comput. Struct. 62(4), 643–651 (1997)10.1016/S0045-7949(96)00227-1 ↗
33. Yardimoglu, B., Yildirim, T.: Finite element model for vibration analysis of pre-twisted Timoshenko beam. J. Sound Vib. 273(4), 741–754 (2004)10.1016/j.jsv.2003.05.003 ↗
34. Yuan, S., Ye, K., Xiao, C., Williams, F.W., Kennedy, D.: Exact dynamic stiffness method for non-uniform Timoshenko beam vibrations and Bernoulli–Euler column buckling. J. Sound Vib. 303(3), 526–537 (2007)10.1016/j.jsv.2007.01.036 ↗
35. Zhang, J., Perez, R.J., Lavernia, E.J.: Documentation of damping capacity of metallic, ceramic and metal-matrix composite materials. J. Mater. Sci. 28, 2395–2404 (1993)10.1007/BF01151671 ↗