Module 9 : The Continuous and Finite Element Transverse Vibration Analyses of Simple Rotor Systems

Lecture 4 : Proportional Damping Static and Dynamic Condensations

M. Karthikeyan, and R. Tiwari , 2009, Mechanism and Machine Theory , Detection, localization, and sizing of a structural flaw in a beam based on forced response measurements- An experimental investigation. (Available online: doi:10.1016/j.mechmachtheory.2009.11.003).

Khulief, Y.A., and Mohiuddin, M.A., 1994, “Modal Characteristics of Rotors Using A Conical Shaft Finite Element,” Computer Methods in Applied Mechanics & Engineering, vol. 115, pp. 125-144.

Khulief, Y.A., and Mohiuddin, M.A., 1999, “ Coupled Bending Torsional Vibration of Rotors using Finite Elements,” Journal of Sound & Vibration, Vol. 223(2), pp. 297-316.

Kim, Y.D., and Lee, C.W., 1986, “ Finite Element Analysis of Rotor Bearing Systems Using A Modal Transformation Matrix,” Journal of Sound & Vibration, vol. 111, pp. 441-456.

Ku, D.M, 1998, “ Finite Element Analysis of Whirl Speeds of Rotor-Bearing Systems with Internal Dampimg,” Journal Mechanical Design, Vol. 102, pp. 599-619.

Lund, J.W., 1974, “ Stability of Damped Critical Speeds of a Flexible Rotor on Fluid Film Bearings,” Transactions of the ASME, Journal of Engineering for Industry, Vol. 96, pp.509-517.

McVaugh, J.M., and Nelson, H.D., 1976 , “The Dynamics of Rotor Bearing Systems Using Finite Elements,” Transactions of the ASME, Journal of Engineering for Industry, vol. 98, pp. 593-600.

Meiorvitch, L., 1967, Analytical Methods in Vibrations , MacMillan Book Co., NY.

Meirovitch, L., 1986, Elements of Vibration Analysis , McGraw Hill, Second edition, NY.

Nelson, H.D., 1980, “A Finite Rotating Shaft Element Using Timoshenko Beam Theory,”, Transactions of the ASME, Journal of Mechanical Design, vol.102, pp.793-803.

Nelson, H.D., 1998, Rotordynamic modelling and analysis procedures: a review. JSME International Journal, Series C, Vol. 41, No. 1, 1-12.

Nelson, H.D., and Zorzi, E.S., 1977, “Finite Element Simulation of Rotor Bearing Systems With Internal Damping,” Transactions of the ASME, Journal of Engineering for Power, vol. 99, pp.71-76.

Nelson, H.D., and Zorzi, E.S., 1980, “The Dynamics of Rotor Bearing Systems With Axial Torque - A Finite Element Approach,” Journal of Mechanical Engineering Design, vol.102, 158-161.

Nelson, H.D., Sept. 1977, “A Finite Rotating Shaft Element Using Timoshenko Beam Theory,” Engineering Research Center Report ERC-R-77023, Arizona State University, p. 61.

O'Callahan J. 1989 Seventh International Modal Analysis Conerence, Las Vegas, January, 17-21. A procedure for an improved reduced system (IRS) model.

O'Callahan J., Avitabile P. and Riemer R. 1989 Seventh International Modal Analysis Conerence, Las Vegas, January, 29-37. System equivalent reduction expansion process.

Ozguven, H.N., and Ozkan, Z.L., 1984, “Whirl Speeds & Unbalance Response of Multibearing Rotors Using Finite Elements,” Transactions of the ASME, Journal of Vibration, Acoustics, Stress, and Reliability in Design, vol.106, pp. 72-79.

Paz M., 1984, AIAA Journal, 22 (5), 724-727. Dynamic condensation.

Polk, S.R., May1974, “Finite Element Formulation & Solution of Flexible Rotor – Rigid Disc Systems for Natural Frequencies & Critical Whirl Speeds,” MSE Engineering Report, Arizona State University.

Rao, J. S., Rotor Dynamics, New Age International Publishers, Third Edition, 1996, pp. 209 - 211.

Ruhl, R.L., 1970, “Dynamics of Distributed Parameter Rotor Systems: Transfer Matrix & Finite Element Techniques,” Ph.D. Dissertation, Cornell University, Ithaca, N.Y.

Ruhl, R.L., and Booker, J.F., 1972, “A Finite Element Model for Distributed Parameter Turborotor Systems,” Transactions of the ASME, Journal of Engineering for Industry, vol. 94, pp. 128-132.

Shanmugam, A., Chandramouli P., 2006, A fixed–free interface component mode synthesis method for rotordynamic analysis. Journal of Sound and Vibration 297, 664–679.

Shiau, T.N., and Hwang, J.L., 1989, “A New Approach to the Dynamic Characteristics of Undamped Rotor-Bearing Systems,” ASME, Journal of Vibration, Acoustics, Stress, and Reliability in Design, vol.111, pp. 379-385.

Thorkildsen, T., June 1979, “Solution of a Distributed mass and Unbalanced Rotor Systems using a Consistent Mass Matrix Approach,” MSE Engineering Report, Arizona state University.

Tondl, A., 1965, Some Problems of Rotor Dynamics , Chapman and Hall Ltd., England, pp. 100 –102