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Vibration of Stiffened Plates with Cutout Subjected to Partial Edge Loading

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Abstract

The buckling and vibration characteristics of stiffened plates with cutout subjected to in-plane partial edge loadings at the plate boundary are studied using finite element method. Buckling loads and vibration frequencies are determined for different plate and cutout aspect ratios, various boundary conditions, partial edge loading at different locations, cutout ratios, various parameters of stiffeners by varying the number, size and location of the stiffeners. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The buckling and vibration characteristics are discussed and the free vibration results available in the literature for stiffened plates with/without cutout are compared.

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Abbreviations

a:

Plate dimension in longitudinal direction

b:

Plate dimension in the transverse direction

c:

Width extent of partial edge loading at the boundary

t:

Plate thickness

E, G:

Young’s and shear moduli for the plate material

b s , d s :

Web thickness and depth of a x-stiffener

A s :

Cross-sectional area of the stiffener

I s :

Second moment of area of the stiffener cross-section about reference axis

[D P ]:

Rigidity matrix of plate

[D S ]:

Rigidity matrix of stiffener

[K e ], [K S ]:

Stiffness matrix of plate, stiffness matrix of stiffener

[M p ], [M S ]:

Consistent mass matrix of plate, stiffener

[K G ]:

Geometric stiffness matrix

[N] r :

Matrix of a shape function of a node r

P cr :

Critical buckling load

g, d:

Cutout length, cutout width

g/d:

Cutout width ratio

T S , P S :

Torsional constant, polar moment of inertia of the stiffener element

ω, λ:

Frequency parameter, buckling parameter

D:

Plate flexural rigidity

ρ:

Density of the plate material

References

  1. S.M. Dickinson, M.M. Kalidas, Vibration and buckling calculation of rectangular plates subjected to complicated in-plane stress distribution in a Rayleigh–Ritz analysis. J. Sound Vib. 75(2), 151–162 (1981)

    Article  MATH  Google Scholar 

  2. P.K. Deolasi, P.K. Datta, D.L. Prabhakar, Buckling and vibration of rectangular plates subjected to partial edge loading (compression or tension). J. Struct. Eng. 22(3), 135–144 (1995)

    Google Scholar 

  3. P. Sundaresan, G. Singh, G.V. Rao, Buckling of moderately thick rectangular composite plates subjected to partial edge compression. Int. J. Mech. Sci. 40(11), 1105–1117 (1998)

    Article  MATH  Google Scholar 

  4. Y. Yamiki, Buckling of rectangular plate under locally distributed forces applied on the two opposite edges. Report of the Institute of high speed mechanics, (Tohoku University, Sendai, 1953), vol. 26, pp. 71–87 and vol. 27, pp. 89–98

  5. G. Baker, M.N. Pavolic, Elastic stability of simply supported rectangular plates under locally distributed edge forces. J. Appl. Mech. 49, 177–179 (1982)

    Article  Google Scholar 

  6. A.W. Leissa, E.F. Ayoub, Vibration and buckling of simply supported rectangular plate subjected to a pair of in-plane concentrated forces. J. Sound Vib. 127(1), 155–171 (1988)

    Article  MATH  Google Scholar 

  7. C. Mei, T.Y. Yang, Free vibration of finite element plates subjected to complex middle plane force system. J. Sound Vib. 23(2), 145–156 (1972)

    Article  MATH  Google Scholar 

  8. M.Z. Khan, A.C. Walker, Buckling of plates subjected to localized edge loading. Struct. Eng. 50, 225–232 (1972)

    Google Scholar 

  9. C.J. Brown, Elastic stability of plates subjected to concentrated loads. Comput. Struct. 33(5), 1325–1327 (1989)

    Article  Google Scholar 

  10. S. Kukla, B. Skalmierski, Free vibration of rectangular plate loaded by a non-uniform in plane force. J. Sound Vib. 187(2), 339–343 (1995)

    Article  Google Scholar 

  11. A.K.L. Srivastava, P.K. Datta, A.H. Sheikh, Vibration and dynamic instability of stiffened plates subjected to in-plane harmonic edge loading. Int. J. Struct. Stab. Dyn. 2(2), 185–206 (2002)

    Article  MATH  Google Scholar 

  12. I.J. Monahan, P.J. Nemergut, G.E. Maddux, Natural frequencies and mode shapes of plates with interior cutouts. Shock Vib. Bull. 41, 37–49 (1970)

    Google Scholar 

  13. P. Paramsivam, J.K. Sridhar Rao, Free vibration of rectangular plates of abruptly varying stiffnesses. Int. J. Mech. Sci. 11, 885–895 (1969)

    Article  Google Scholar 

  14. R. Ali, S.J. Atwal, Prediction of natural frequencies of rectangular plates with rectangular cutouts. Comput. Struct. 12, 819–823 (1980)

    Article  MATH  Google Scholar 

  15. G. Mundkur, R.B. Bhat, S. Neria, Vibration of plates with cutouts using boundary characteristics orthogonal polynomial functions in the Rayleigh–Ritz method. J. Sound Vib. 176(1), 136–144 (1964)

    Article  Google Scholar 

  16. K.Y. Lam, K.C. Hung, Vibration study on plates with stiffened openings sing orthogonal polynomials and partitioning method. Comput. Struct. 33(3), 295–301 (1990)

    Article  Google Scholar 

  17. H.P. Lee, S.P. Lim, S.T. Chow, Prediction of natural frequencies of rectangular plates with rectangular cutouts. Comput. Struct. 36(5), 861–869 (1990)

    Article  Google Scholar 

  18. S.K. Sahu, P.K. Datta, Dynamic stability of curved panels with cutouts. J. Sound Vib. 251(4), 683–696 (2002)

    Article  Google Scholar 

  19. M. Mukhopadhyay, A. Mukherjee, Finite element buckling analysis of stiffened plates. Comput. Struct. 4(6), 795–803 (1990)

    Article  Google Scholar 

  20. I.E. Harik, M. Guo, Finite element analysis of eccentrically stiffened plates in free vibration. Comput. Struct. 49(6), 1007–1015 (1993)

    Article  MATH  Google Scholar 

  21. G. Aksu, Free vibration analysis of stiffened plates including the effects of in-plane inertia. J. Appl. Mech. Trans. ASME 49, 206–212 (1982)

    Article  MATH  Google Scholar 

  22. H. Zeng, C.W. Bert, A differential quadrature analysis of vibration for stiffened plates. J. Sound Vib. 241(2), 247–252 (2001)

    Article  Google Scholar 

  23. M.D. Olson, C.R. Hazell, Vibration studies of some integral rib stiffened plates. J. Sound Vib. 50, 43–61 (1977)

    Article  Google Scholar 

  24. T.P. Holopainen, Finite element free vibration analysis of eccentrically stiffened plates. Comput. Struct. 56, 100–993 (1995)

    Article  Google Scholar 

  25. C. Ray, S.K. Satsangi, Finite element analysis of laminated hat stiffened plates. J. Reinf. Plast. Compos. 15(12), 1174–1193 (1996)

    Google Scholar 

  26. H.A. Larrondo, D.R. Avalos, P.A.A. Laura, R.E. Rossi, Vibration of simply supported rectangular plates with varying thickness and same aspect ratio cutouts. J. Sound Vib. 244(4), 738–745 (2001)

    Article  Google Scholar 

  27. J.N. Reddy, Large amplitude flexural vibration of layered composite plates with cutouts. J. Sound Vib. 83(1), 1–10 (1982)

    Article  MATH  Google Scholar 

  28. A.N. Nayak, J.N. Bandyopadhyay, Free vibration analysis of laminated stiffened shells. J. Eng. Mech. ASCE 129(11), 1245–1253 (2003)

    Article  Google Scholar 

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  1. Department of Civil Engineering, National Institute of Technology, Jamshedpur, 831014, India

    A. K. L. Srivastava

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Srivastava, A.K.L. Vibration of Stiffened Plates with Cutout Subjected to Partial Edge Loading. J. Inst. Eng. India Ser. A 93, 129–135 (2012). https://doi.org/10.1007/s40030-012-0018-3

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