==========
REFERENCES
==========

Arafat, H. N., Nayfeh, A. H., and Chin, C-M., 1998,
"Nonlinear Nonplanar Dynamics
of Parametrically Excited Cantilever Beams,"
Nonlinear Dyn., Vol. 15, 31-61.

Benedettini, F., Rega, G., and Alaggio, R., 1995a,
"Experimental Analysis of the Finite Dynamics of a Suspended Cable,"
Proceedings of the 15th ASME
Biennial Conference on Mechanical Vibrations and Noise,
DE Vol. 84-1, 543-552.

Benedettini, F., Rega, G., and Alaggio, R., 1995b,
"Non-Linear Oscillations of
a Four-Degree-of-Freedom Model of a Suspended Cable under
Multiple Internal Resonance Conditions,"
J. Sound Vib., Vol. 182, 775-798.

Chin, C-M. and Nayfeh, A. H., 1996,
"Bifurcation and Chaos in Externally Excited 
Circular Cylindrical Shells,"
J. Appl. Mech., Vol. 63, 565-574.

Chin, C-M. and Nayfeh, A. H., 1997,
"Three-to-One Internal Resonances in Hinged-Clamped Beams,"
Nonl. Dyn., Vol. 12, 129-154.

Chin, C-M., Nayfeh, A. H., and Lacarbonara, W., 1997,
"Two-to-One Internal Resonances in Parametrically Excited Buckled Beams,"
Proceedings of the
AIAA Structures, Structural Dynamics and Materials Conference, 
Vol. 1, 213-223.

Chu, H-N. and Herrmann, G., 1956,
"Influence of Large Amplitudes on Free
Flexural Vibrations of Rectangular Elastic Plates,"
J. Appl. Mech., Vol. 23, 532-540.

Crespo da Silva, M. R. M., 1978,
"Flexural-Flexural Oscillations of Beck's
Column Subjected to a Planar Harmonic Excitation,"
J. Sound Vib., Vol. 60, 133-144.

Crespo da Silva, M. R. M. and Glynn, C. C., 1978a,
"Nonlinear Flexural-Flexural-Torsional Dynamics of
Inextensional Beams, I. Equations of Motion,"
J. Struct. Mech., Vol. 6, 437-448.

Crespo da Silva, M. R. M. and Glynn, C. C., 1978b,
"Nonlinear Flexural-Flexural-Torsional Dynamics of
Inextensional Beams, II. Forced Motions,"
J. Struct. Mech., Vol. 6, 449-461.

Lacarbonara, W., Nayfeh, A. H., and Kreider, W., 1998,
"Experimental Validation
of Reduction Methods for Nonlinear Vibrations of Distributed-Parameter
Systems: Analysis of a Buckled Beam,"
Nonlinear Dyn., Vol. 17, 95-117.

Malkin, I. G., 1956,
"Some Problems in the Theory of Nonlinear Oscillations,"
GITTL, Moscow.

McIvor, I. K., 1966,
"The Elastic Cylindrical Shell under Radial Impulse,"
J. Appl. Mech., Vol. 33, 831-837.

Nayfeh, A. H., 1975,
"Nonlinear Propagation of a Wave Packet in a Hard-Walled Circular Duct,"
J. Acoust. Soc. Am., Vol. 57, 803-809.

Nayfeh, A. H., 1981,
Introduction to Perturbation Techniques, 
Wiley, New York.

Nayfeh, A. H., 1998,
"Reduced-Order Models of Weakly Nonlinear Spatially Continuous Systems,"
Nonlinear Dyn., Vol. 16, 105-125.

Nayfeh, A. H. and Asfar, K. R., 1986,
"Response of a Bar Constrained by a Non-Linear Spring to a Harmonic Excitation,"
J. Sound Vib., Vol. 105, 1-15.

Nayfeh, A. H. and Bouguerra, H., 1990,
"Non-Linear Response of a Fluid Valve,"
Int. J. Non-Linear Mech., Vol. 25, 433-439.

Nayfeh, A. H., Kreider, W., and Anderson, T. J., 1995,
"Investigation of Natural Frequencies and Mode Shapes of Buckled Beams,"
AIAA J., Vol. 33, 1121-1126.

Nayfeh, A. H. and Lacarbonara, W., 1997,
"On the Discretization of
Distributed-Parameter Systems with Quadratic and Cubic Nonlinearities,"
Nonlinear Dyn., Vol. 13, 203-220.

Nayfeh, A. H. and Lacarbonara, W., 1998,
"On the Discretization of Spatially
Continuous Systems with Quadratic and Cubic Nonlinearities,"
JSME Int. J., C41, 510-531.

Nayfeh, A. H., Lacarbonara, W., and Chin, C-M., 1999,
"Nonlinear Normal Modes
of Buckled Beams: Three-to-One and One-to-One Internal Resonances,"
Nonlinear Dyn., in press.

Nayfeh, A. H. and Mook, D. T., 1979,
Nonlinear Oscillations,
Wiley, New York.

Nayfeh, A. H., Nayfeh, J. F., and Mook, D. T., 1992,
"On Methods for
Continuous Systems with Quadratic and Cubic Nonlinearities,"
Nonlinear Dyn., Vol. 3, 145-162.

Nayfeh, S. A. and Nayfeh, A. H., 1993,
"Nonlinear Interactions Between
Two Widely Spaced Modes - External Excitation,"
Int. J. Bif. Chaos, Vol. 3, 417-427.

Nayfeh, A. H. and Nayfeh, S. A., 1995,
"Nonlinear Normal Modes of
a Continuous System with Quadratic Nonlinearities,"
J. Vib. Acoust., Vol. 117, 199-205.

Nayfeh, A. H., Nayfeh, S. A., and Pakdemirli, M., 1995,
"On the Discretization of Weakly Nonlinear Spatially Continuous Systems,"
Nonlinear Dynamics and Stochastic Mechanics,
(W. Kliemann and N. Sri Namachchivaya, eds.), 
CRC Press, Boca Raton, Florida, 175-200.

Pai, P. F. and Nayfeh, A. H., 1990a,
"Non-Linear Non-Planar
Oscillations of a Cantilever Beam under Lateral Base Excitations,"
Int. J. Non-Linear Mech., Vol. 25, 455-474.

Pai, P. F. and Nayfeh, A. H., 1990b,
"Three-Dimensional Nonlinear
Vibrations of Composite Beams- I. Equations of Motion,"
Nonlinear Dyn., Vol. 1, 477-502.

Pakdemirli, M., Nayfeh, S. A., and Nayfeh, A. H., 1995,
"Analysis of
One-to-One Autoparametric Resonances in Cables - Discretization vs.
Direct Treatment,"
Nonlinear Dyn., Vol. 8, 65-83.

Raouf, R. A. and Nayfeh, A. H., 1990a,
"Nonlinear Axisymmetric
Response of Spherical Shells to a Radial Harmonic Excitation,"
Int. J. Non-Linear Mech., Vol. 25, 475-492.

Raouf, R. A. and Nayfeh, A. H., 1990b,
"One-to-One Autoparametric
Resonances in Infinitely Long Cylindrical Shells,"
Comp. Struct., Vol. 35, 163-173.

Rega, G., Lacarbonara, W., Nayfeh, A. H., and Chin, C-M., 1999,
"Multiple Resonances in Suspended Cables: 
Direct versus Reduced-Order Models,"
Int. J. Non-Linear Mech., accepted for publication.

von Karmam, T., 1910,
"Festigkeitsprobleme in Maschinenbau,"
Encyklopadie der Mathematischen Wissenschaften, P. R. Halmos, ed.,
Am. Math. Soc., Vol. 3, 211-385.

Yamamoto, T. 1957,
"On the Vibrations of a Rotating Shaft,"
Mem. Fac. Eng. Nagoya Univ., Vol. 9, 19-115.

Yamamoto, T. 1960,
"Response Curves at the Critical Speeds of Subharmonic
and Summed and Differential Harmonic Oscillations,"
Bull. JSME, Vol. 3, 397-403.