Vibration and buckling analysis of rectangular plates with nonlinear elastic end restraints against rotation

International Journal of Solids and Structures

Volumn 34, Issue 18, 1997, Pages 2291-2301

  Chang, T P ^a   Chang, H C ^a  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BUCKLING; ELASTICITY; FINITE ELEMENT METHOD; ITERATIVE METHODS; NATURAL FREQUENCIES; STRUCTURAL LOADS; VIBRATIONS (MECHANICAL);

RECTANGULAR PLATES; ROTATIONAL RESTRAINTS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0031164994     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(96)00146-1     Document Type: Article

References (25)

1. Bennouna, M. M. and White, R. G. (1984). The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam. Journal of Sound and Vibration 96, 309-331.
2. Bhaohyam, G. R. and Prathap, G. (1980). Galerkin finite element method for nonlinear beam vibration. Journal of Sound and Vibration 72, 191-203.
3. Chi, M., Dennis, Jr, B. G. and Vossoughi, J. (1984). Transverse and torsional vibrations of an axially loaded beam with elastically constrained ends. Journal of Sound and Vibration 96, 235-241.
4. Den Hartog, J. P. (1936). Forced vibrations in nonlinear systems with various combinations of linear springs. Journal of Applied Mechanics 3, A127-A130.
5. Dokainish, M. A. and Kumar, R. (1971). Experimental and theoretical analysis of the transverse vibrations of a beam having bilinear support. Experimental Mechanics, Journal of SESA. 11(6), 263-270.
6. Evensen, D. A. (1968). Nonlinear vibrations of beams with various boundary conditions. American Institute of Aeronautics and Astronautics Journal 6, 370-372.
7. Gutierrez, R. H., Laura, P. A. A. and Rossi, R. E. (1990). Natural frequencies of a Timoshenko beam of non-uniform cross-section elastically restrained at one end and guided at the other. Journal of Sound and Vibration 141, 174-179.
8. Gutierrez, R. H., Laura, P. A. A. and Rossi, R. E. (1991). Fundamental frequency of vibration of a Timoshenko beam of non-uniform thickness. Journal of Sound and Vibration 145, 341-344.
9. Laura, P. A. A. and Romanelli, E. (1974). Vibrations of rectangular plates elastically restrained against rotation along all edges and subject to a biaxial state of stress. Journal of Sound and Vibration 37, 367-377.
10. Lee, S. Y. and Ke, H. Y. (1990). Free vibrations of a non-uniform beam with general elastically restrained boundary conditions. Journal of Sound and Vibration 136, 425-437.
11. Liu, W. H., Kou, H. S. and Yang, F. S. (1988). Nonlinear vibrations of beams with elastically restrained edges. Journal of Sound and Vibration 121, 375-381.
12. Maurizi, M. J. and Belles, P. M. (1991). General equation of frequencies for vibrating uniform one-span beams under compressive axial loads. Journal of Sound and Vibration 145, 345-347.
13. Maurizi, M. J., Rossi, R. E. and Belles, P. M. (1990). Free vibration of uniform Timoshenko beam with ends elastically restrained against rotation and translation. Journal of Sound and Vibration 141, 359-362.
14. Paslay, P. R. and Gurtin, M. E. (1960). The vibration response of a linear undamped systems resting on a nonlinear spring. Journal of Applied Mechanics, Transactions of the ASME 27, 272-274.
15. Picard, A., Beaulieu, D. and Perusse, B. (1987). Rotational restraint of a simple column base connection. Canadian Journal of Civil Engineering 14, 49-57.
16. Porter, B. and Billet, R. A. (1965). Harmonic and sub-harmonic vibration of a continuous system having nonlinear constraint. International Journal of Mechanical Science 7(6), 431-439.
17. Prathap, G. (1978). Nonlinear vibration of beams with variable axial restraint. American Institute of Aeronautics and Astronautics Journal 16, 622-624.
18. Sarma, B. S. and Varadan, T. K. (1983). Lagrange-type formulation for finite element analysis of nonlinear beam vibration. Journal of Sound and Vibration 86, 61-70.
19. Srinivasan, A. V. (1965). Large amplitude free oscillations of beams and plates. American Institute of Aeronautics and Astronautics Journal 3, 1151-1153.
20. Taucher, T. R. and Ayre, R. S. (1965). Shock response of a simple beam on nonlinear supports. Journal of Engineering Mechanics Division, Proceedings of the ASCE 91-109.
21. Timoshenko, S. P. and Gere, J. M. (1961). Theory of Elastic Stability, 2nd edn. McGraw-Hill, New York.
22. Venkateswara Rao, G. and Rajasekhara Naidu, N. (1994). Free vibration and stability behaviour of uniform beams and columns with nonlinear elastic end rotational restraints. Journal of Sound and Vibration 176, 130-135.
23. Wah, T. (1964). The normal modes of vibration of certain non-linear continuous systems. Journal of Applied Mechanics 7, 139-140.
24. Warburton, G. B. and Edney, S. L. (1984). Vibrations of rectangular plates with elastically restrained edges. Journal of Sound and Vibration 95, 537-552.
25. Woinowsky-Krieger, S. (1950). The effect of an axial force on the vibration of hinged bars. Journal of Applied Mechanics 17, 35-36.