Nonlinear response of cantilever beams to combination and subcombination resonances

Shock and Vibration

Volumn 5, Issue 5-6, 1998, Pages 277-288

  Nayfeh, Ali H ^a   Arafat, Haider N ^a  

^a State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CANTILEVER BEAMS; DYNAMIC RESPONSE; GALERKIN METHODS; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; RESONANCE; SHEAR DEFORMATION; STRUCTURAL ANALYSIS;

COMBINATION RESONANCE; HAMILTON EXTENDED PRINCIPLE; NONLINEAR RESPONSE; PARAMETRIC RESONANCE; PITCHFORK BIFURCATIONS; SUBCOMBINATION RESONANCE;

VIBRATIONS (MECHANICAL);

EID: 0032228873     PISSN: 10709622     EISSN: None     Source Type: Journal    
DOI: 10.1155/1998/181460     Document Type: Article

References (17)

1. T.J. Anderson, B. Balachandran and A.H. Nayfeh, Nonlinear resonances in a flexible cantilever beam, J. Vibration and Acoustics, Trans. ASME 116 (1994), 480-484.
2. K.G. Asmis and W.K. Tso, Combination and internal resonance in a nonlinear two-degrees-of-freedom system, J. Applied Mechanics, Trans. ASME 39 (1972), 832-834.
3. M.P. Cartmell and J.W. Roberts, Simultaneous combination resonances in a parametrically excited cantilever beam, Strain 23 (1987), 117-126.
4. J. Dugundji and V. Mukhopadhyay, Lateral bending - torsion vibrations of a thin beam under parametric excitation, J. Applied Mechanics, Trans. ASME 40 (1973), 693-698.
5. R.C. Kar and T. Sujata, Parametric instability of an elastically restrained cantilever beam, Computers and Structures 34 (1990), 469-475.
6. R.C. Kar and T. Sujata, Dynamic stability of a rotating, pretwisted and preconed cantilever beam including coriolis effects, Computers & Structures 42 (1992), 741-750.
7. A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley-Interscience, New York, 1981.
8. A.H. Nayfeh, Combination resonances in the non-linear response of bowed structures to a harmonic excitation, J. Sound and Vibration 90 (1983), 457-470.
9. A.H. Nayfeh and D.T. Mook, Nonlinear Oscillations, Wiley-Interscience, New York, 1979.
10. A.H. Nayfeh and L.D. Zavodney, The response of two-degree-of-freedom systems with quadratic non-linearities to a combination parametric resonance, J. Sound and Vibration 107 (1986), 329-350.
11. J. Shaw, S.W. Shaw and A.G. Haddow, On the response of the non-linear vibration absorber, Int. J. Non-Linear Mechanics 24 (1989), 281-293.
12. S. Sridhar, A.H. Nayfeh and D.T. Mook, Nonlinear resonances in a class of multi-degree-of-freedom systems, J. Acoustical Society of America 58 (1975), 113-123.
13. D.A. Streit, A.K. Bajaj and C.M. Krousgrill, Combination parametric resonance leading to periodic and chaotic response in two-degree-of-freedom systems with quadratic non-linearities, J. Sound and Vibration 124 (1988), 297-314.
14. S. Timoshenko, Vibration Problems in Engineering, Van Nostrand, New York, 1928.
15. W.K. Tso and K.G. Asmis, Multiple parametric resonance in a non-linear two degree of freedom system, Int. J. Non-Linear Mechanics 9 (1974), 269-277.
16. T. Yamamoto, K. Yasuda and N. Tei, Summed and differential harmonic oscillations in a slender beam, Bulletin JSME 24 (1981), 1214-1222.
17. T. Yamamoto, K. Yasuda and N. Tei, Super summed and differential harmonic oscillations in a slender beam, Bulletin JSME 25 (1982), 959-968.