Corner stress singularity effects on the vibration of rhombic plates with combinations of clamped and simply supported edges

Journal of Sound and Vibration

Volumn 193, Issue 3, 1996, Pages 555-580

  Mcgee, O G ^a,c   Kim, J W ^a   Kim, Y S ^a   Leissa, A W ^b  

^a Georgia Institute of Technology   (United States)

^b Ohio State University   (United States)

^c Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; BENDING (DEFORMATION); BOUNDARY CONDITIONS; LAGRANGE MULTIPLIERS; NATURAL FREQUENCIES; POLYNOMIALS; STRESS ANALYSIS; STRESSES; VIBRATIONS (MECHANICAL);

CORNER STRESS SINGULARITY; HINGED HINGED CORNERS; OBTUSE ANGLES; RITZ METHOD; SKEW RHOMBIC PLATES; THIN PLATE LAGRANGIAN FUNCTIONAL;

PLATES (STRUCTURAL COMPONENTS);

EID: 0030173391     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1996.0302     Document Type: Article

References (33)

1. H. D. CONWAY and K. A. FARNHAM 1965 International Journal of Mechanical Sciences 7, 811-816. The free flexural vibrations of triangular, rhombic and parallelogram plates and some analogies.
2. S. DURVASULA 1969 Journal of Aircraft 6, 66-68. Free vibration of simply supported parallelogrammic isotropic flat plates.
3. P. V. TSYDZIC 1952 Prikl. Mat. Mekh 16(3). Application of the perturbation method to solve problems of the natural vibrations of nearly rectangular plates (in Russian).
4. I. H. TAI and W. A. NASH 1973 Report No. AFOSR-TR-14-0189, Department of Civil Engineering, University of Massachusetts. Vibrations of thin plates - a new approach.
5. I. CHOPRA and S. DURVASULA 1971 International Journal of Mechanical Science 13, 935-944. Natural frequenceis and modes of tapered skew plates.
6. T. SAKATA 1981 International Journal of Mechanical Science 23, 677-685. Natural frequencies of simply supported skew plates.
7. K. NAGAYA 1980 Journal of Sound and Vibration, 68, 35-43. Vibration of a plate with straight line boundaries.
8. D. J. GORMAN 1988 Journal of Sound and Vibration, 125, 281-290. Accurate free vibration analysis of rhombic plates with simply supported and fully clamped edge conditions.
9. D. J. GORMAN 1981 Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics 58, 203-208. Accurate analytical type solutions for the free vibration of simply supported parallelogram plates.
10. C. S. HUANG, O. G. MCGEE, A. W. LEISSA and J. W. KIM 1995 Transactions of the American Society of Mechanical Engineers, Journal of Vibration and Acoustics 117(3a), 245-251. Accurate vibration analysis of simply supported rhombic plates by considering stress singularities.
11. A. W. LEISSA 1969 Vibration of Plates, NASA SP-160. Washington, D.C.: U.S. Government Printing Office. Reprinted, Acoustical Society of America (1993).
12. A. W. LEISSA 1977 Shock and Vibration Digest 9(10), 13-24. Recent research in plate vibrations: classical theory.
13. A. W. LEISSA 1981 Shock and Vibration Digest 13(9), 11-22. Plate vibration research 1976-1980: classical theory.
14. A. W. LEISSA 1987 Shock and Vibration Digest 19(2), 11-18. Recent studies in plate vibrations: 1981-1985: part I - classical theory.
15. K. KANAKA RAJU and E. HINTON 1980 Earthquake Engineering and Structural Dynamics 8, 55-62. Natural frequencies and modes of rhombic Mindlin plates.
16. T. ROCK and E. HINTON 1974 Earthquake Engineering and Structural Dynamics 3, 51-63. Free vibration and transient response of thick and thin plates using the finite element method.
17. S. DURVASULA 1969 Journal of Aircraft 6(1), 66-68. Free vibration of simply supported parallelogrammic plates.
18. P. S. NAIR and S. DURVASULA 1973 Journal of Sound and Vibration 26, 1-19. Vibration of skew plates.
19. S. DURVASULA 1969 American Institute of Aeronautics and Asternautics Journal 7, 1164-1166. Natural frequencies and modes of clamped skew plates.
20. S. F. NG and A. SHARMA 1979 Canadian Aeronautics and Space Journal 25, 372-381. Vibration of thin plates using the Ritz method.
21. R. K. KAUL and V. CADAMBE 1956 Aeronautical Quarterly, 337-352. The natural frequencies of thin skew plates.
22. T. MIZUSAWA, T. KAJITA and M. NARUOKA 1979 Journal of Sound and Vibration 62, 301-308. Vibration of skew plates using B-spline functions.
23. K. M. LIEW and K. Y. LAM 1990 Journal of Sound and Vibration 139, 241-252. Application of two-dimensional orthogonal plate function to flexural vibrations of skew plates.
24. K. M. LIEW, Y. XIANG, S. KITIPORNCHAI and C. M. WANG 1993 Journal of Sound and Vibration 168, 39-69. Vibration of thick skew plates based on Mindlin shear deformation plate theory.
25. N. GANESAN and S. NAGARAJA RAO 1985 Journal of Sound and Vibration 101, 117-119. Vibration analysis of moderately thick skew plates by a variational approach.
26. P. A. LAURA and J. GROSSON 1968 Journal of the Acoustical Society of America 44, 823-824. Fundamental frequency of vibration of rhombic plates.
27. M. L. WILLIAMS 1952 Proceedings of the 1st U.S. National Congress of Applied Mechanics, 325-329. Surface stress singularities resulting from various boundary conditions in angular plates under bending.
28. O. G. MCGEE, A. W. LEISSA and C. S. HUANG 1992 International Journal of Numerical Methods in Engineering 35, 409-424. Vibration of cantilevered skewed plates with corner stress singularities.
29. A. W. LEISSA, O. G. MCGEE and C. S. HUANG 1993 Journal of Applied Mechanics 60, 134-140. Vibration of sectorial plates having corner stress singularities.
30. G. W. STEWART 1970 Introduction to Matrix Computation. New York: Academic Press.
31. J. STOER and R. BULIRSCH 1980 Introduction to Numerical Analysis. New York: Springer-Verlag. See Article 6.7.
32. W. H. PRESS, B. P. FLANNERY, S. A. TEUKOLSKY and W. T. VETTERLING 1986 Numerical Recipes - the Art of Scientific Computing. Cambridge: Cambridge University Press.
33. A. W. LEISSA 1973 Journal of Sound and Vibration 31, 257-293. The free vibration of rectangular plates.