Parametric instability of conical shells by the generalized differential quadrature method

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 6, 1999, Pages 819-837

  Ng, T Y ^a   Hua, Li ^a   Lam, K Y ^a   Loy, C T ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Conical shells; GDQ method; Parametric instability

Indexed keywords

BOUNDARY CONDITIONS; PARTIAL DIFFERENTIAL EQUATIONS; SHEAR STRESS; SHELLS (STRUCTURES); STABILITY;

GENERALIZED DIFFERENTIAL QUADRATURE; PARAMETRIC INSTABILITY;

CONTINUUM MECHANICS;

EID: 0033078196     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990228)44:6<819::AID-NME528>3.0.CO;2-0     Document Type: Article

References (22)

1. V. V. Bolotin, Dynamic Stability of Elastic Systems, Holden-Day, San Francisco, (1964).
2. J. C. Yao, 'Nonlinear elastic buckling and parametric excitation of a cylinder under axial loads', J. Appl. Mech. ASME, 32, 109-115 (1965).
3. A. Vijayaraghavan and R. M. Evan-Iwanowski, 'Parametric instability of circular cylindrical shells', J. Appl. Mech. ASME, 34, 985-990 (1967).
4. L. R. Koval, 'Effect of longitudinal resonance on the parametric stability of an axially excited cylindrical shell', J. Acoust. Soc. Am., 55, 91-97 (1974).
5. K. Nagai and N. Yamaki, 'Dynamic stability of circular cylindrical shells under periodic compressive forces', J. Sound Vib., 58, 425-441 (1978).
6. C. S. Hsu, 'On the parametric excitation of a dynamic system having multiple degrees of freedom', J. Appl. Mech. ASME, 30, 367-372 (1963).
7. C. W. Bert and V. Birman, 'Parametric instability of thick, orthotropic, circular cylindrical shells', Acta Mech., 71, 61-76 (1988).
8. A. Argento, 'Dynamic stability of a composite circular cylindrical shell subjected to combined axial and torsional loading', J. Comp. Mater., 27(18), 1722-1738 (1993).
9. A. Argento and R. A. Scott, 'Dynamic instability of layered anisotropic circular cylindrical shell, part I: theoretical development', J. Sound Vib., 162(2), 311-322 (1993).
10. A. Argento and R. A. Scott, 'Dynamic instability of layered anisotropic circular cylindrical shell. Part II: numerical results', J. Sound Vib., 162(2), 323-332 (1993).
11. C. L. Liao and C. R. Cheng, 'Dynamic stability of stiffened laminated composite plates and shells subjected to in-plane pulsating forces', Int. J. Numer. Meth. Engng., 37, 4167-4183 (1994).
12. A. Kornecki, 'Dynamic stability of truncated conical shells under pulsating pressure', Israel J. Technol., 4, 110-120 (1966).
13. J. Tani, 'Dynamic instability of truncated conical shells under periodic axial loads', Int. J. Solids Struct., 10, 169-176 (1974).
14. J. Tani, 'Influence of deformations prior to instability on the dynamic instability of conical shells under periodic axial load', J. Appl. Mech. ASME, 43, 8-91 (1976).
15. J. Tani, 'Influence of deformation before instability on the parametric instability of conical shells under periodic pressure', J. Sound Vib., 45, 253-258 (1976).
16. J. Tani, 'Dynamic stability of truncated conical shells under pulsating torsion'. J. Appl. Mech. ASME, 48, 391-398 (1981).
17. C. Massalas, A. Dalamangas and G. Tzivanidis, 'Dynamic instability of truncated conical shells, with variable modulus of elasticity, under periodic compressive forces', J. Sound Vib., 79(4), 519-528 (1981).
18. R. E. Bellman and J. Casti, 'Differential quadrature and long-term integration', J. Math. Anal. Appl., 34, 235-238 (1971).
19. C. Shu and B. E. Richards, 'Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations', Int. J. Numer. Meth. Fluids, 15, 791-798 (1992).
20. C. W. Bert and M. Malik, 'Free vibration analysis of thin cylindrical shells by the differential quadrature method', J. Press. Vessel Technol., 118, 1-12 (1996).
21. C. W. Bert, X. Wang and A. G. Striz, 'Static and free vibration analysis of beams and plates by differential quadrature method', Acta Mech., 102, 11-24 (1994).
22. C. T. Loy, K. Y. Lam and C. Shu, 'Analysis of cylindrical shells using generalized quadrature', Shock and Vib., 4, 193-198 (1997).