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Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method

Year 2003, Volume: 16 Issue: 1, 43 - 71, 30.06.2003

Ömer Civalek , Hikmet H. Çatal

Abstract

Numerical solution to static and free vibration analysis of thin circular and annular plates having various supports and load conditions are obtained by the method of Harmonic Differential Quadrature (HDQ). Bending moments, normal stress, and deflections of circular plate are found for uniformly distributed, central concentrated, and non-uniformly loads. Both clamped and simply supported edges are considered as boundary conditions. Results are obtained by using various number of grid points. The obtained results are compared with existing solutions available from other numerical methods and analytical results. The method presented gives efficient accurate results for the deflection and bending analysis of circular plates.

Keywords

Harmonic differential quadrature circular plates annular plates free vibration deflection bending moment stress

References

  • [1] Timoshenko S., and Krieger W.S., “Theory Of Plates And Shells”, New York: 2nd Ed. McGraw-Hill, 1959.
  • [2] Civalek Ö. “Finite Element analysis of plates and shells”, Elazığ: Fırat University, (in Turkish)1998.
  • [3] Szilard, R, “Theory and Analysis of Plates: Classical and Numerical Methods”. Prentice-Hall, Englewood cliffs, NJ, 1974.
  • [4] Melerski, E., “Circular Plates Analysis By Finite Differences: Energy Approaches”, J. of Eng. Mech., ASCE, 115, 1205-1225,1989.
  • [5] Pardoen, G.C, and Hagen, R.L., “Symmetrical Bending Of Circular Plates Using Finite Elements”, Computers and Structure, 2, 547-553,1972.
  • [6] Ugural A.C., “Stress In Plates And Shells”, Mc Graw Hill Companies, 1999.
  • [7] Bellman R., Casti J., “Differential Quadrature And Long-Term Integration”, Journal of Math. Analysis and App., 34, 235-238,1971.
  • [8] Bert C.W., Jang S.K., Striz AG., “Two New Approximate Methods For Analyzing Free Vibration Of Structural Components”, AIAA Journal , 26 (5), 612-618,1987.
  • [9] Du H., Lim M.K., Lin, R.M., “Application Of Generalized Differential Quadrature Method To Structural Problems”. Int. J. Numerical Meth. Engng.,37, 1881-1896,1994.
  • [10] Civalek Ö., “Static, Dynamic And Buckling Analysis Of Elastic Bars Using DQ”, XVI. National Technical Engineering Symposium, Ankara, METU, 2001.
  • [11] Civalek, Ö., Çatal, H.H., Stability And Vibration Analysis Of Plates By Harmonic Differential Quadrature, IMO Technical Journal, 2003; Vol. 14 (1), 2835-2852.
  • [12] Jang S.K., Bert C.W., Striz A.G., “Application Of Differential Quadrature To Static Analysis Of Structural Components”, Inter. J. Num. Meth. Engng., 28, 561- 577,1989.
  • [13] Liew K.M., Teo T.M., and Han J.B., “Comparative Accuracy Of DQ And HDQ Methods For Three- Dimensional Vibration Analysis Of Rectangular Plates”, Int. J. Num. Meth. Engng., 45,1831-1848, 1999.
  • [14] Shu C., Richards B.E., “Application Of Generalized Differential Quadrature To Solve Two- Dimensional Incompressible Navier -Stokes Equations”, Inter. J. Numerical Meth. In Fluids,15,791-798, 1992.
  • [15] Civalek, Ö., Çatal,H.H., Dynamic Analysis Of One And Two Dimensional Structures By The Method Of Generalized Differential Quadrature, Türkiye İnşaat Mühendisleri Odası, Mühendislik Haberleri, Sayı 417, s.39-46,2002.
  • [16] Hamming R.W., “Numerical Methods For Scientists And Engineers”, New York, McGraw-Hill, 1973.
  • [17] Björck A., and Pereyra V., “Solution Of Vandermonde System Of Equations”. Math. comput., 24, 893-903,1970.
  • [18] Striz A.G., Wang X., and Bert C.W., “HDQ Method And Applications To Analysis Of Structural Components”, ACTA Mech., 111,85-94,1995.
  • [19] Shu C., Xue H., “Explicit Computations Of Weighting Coefficients In The Harmonic Differential Quadrature”. J. of Sound and Vib., 204(3), 549-555,1997.
  • [20] Zienkiewicz O.C, “The Finite Element Method In Engineering Science”, 3rd edt.: McGraw- Hill; London, 1977.
  • [21] Berktay I., “Theory Of Plates And Its Applications”, Istanbul, Yıldız University Press, 1992(in Turkish).
  • [22] Bert C.W, Malik M. “The differential quadrature method for irregular domains and application to plate vibration”. Inter. J.of Mechanical Science, 1996; 38(6):589-606.
  • [23] Zienkiewicz O. C, Taylor, R.L., “The Finite Element Method”, Vol. 1.: McGraw- Hill; 1989.
  • [24] Wang C.M, Liew K.M, and Alwis W.A.M, “Buckling of Skew Plates and Corner Conditions For Simply Supported Edges”, J.of Eng. Mechanics, 1991, 118, 651-662.
  • [25] Liew K.M, Han J.B, “A Four-Node Differential Quadrature Method For Straight- Sided Quadrilateral Reissner /Mindlin Plates”, Communications in Numerical Methods in Engineering, 1997,13, 73-81.
  • [26] Kim C.S, Dickinson S.M, “On The Free, Transverse Vibration Of Annular And Circular, Thin Sectorial Plates Subject To Certain Complicating Effects”, Journal of Sound and Vibration, 1989,134, 407-415.
  • [27] Leissa, AW, “Vibration of Plates”, NASA, SP-160, 1969.

Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method

Year 2003, Volume: 16 Issue: 1, 43 - 71, 30.06.2003

Ömer Civalek , Hikmet H. Çatal

Abstract

Numerical solution to static and free vibration analysis of thin circular and annular plates having various supports and load conditions are obtained by the method of Harmonic Differential Quadrature (HDQ). Bending moments, normal stress, and deflections of circular plate are found for uniformly distributed, central concentrated, and non-uniformly loads. Both clamped and simply supported edges are considered as boundary conditions. Results are obtained by using various number of grid points. The obtained results are compared with existing solutions available from other numerical methods and analytical results. The method presented gives efficient accurate results for the deflection and bending analysis of circular plates.

Keywords

Harmonic differential quadrature circular plates annular plates free vibration deflection bending moment stress

References

  • [1] Timoshenko S., and Krieger W.S., “Theory Of Plates And Shells”, New York: 2nd Ed. McGraw-Hill, 1959.
  • [2] Civalek Ö. “Finite Element analysis of plates and shells”, Elazığ: Fırat University, (in Turkish)1998.
  • [3] Szilard, R, “Theory and Analysis of Plates: Classical and Numerical Methods”. Prentice-Hall, Englewood cliffs, NJ, 1974.
  • [4] Melerski, E., “Circular Plates Analysis By Finite Differences: Energy Approaches”, J. of Eng. Mech., ASCE, 115, 1205-1225,1989.
  • [5] Pardoen, G.C, and Hagen, R.L., “Symmetrical Bending Of Circular Plates Using Finite Elements”, Computers and Structure, 2, 547-553,1972.
  • [6] Ugural A.C., “Stress In Plates And Shells”, Mc Graw Hill Companies, 1999.
  • [7] Bellman R., Casti J., “Differential Quadrature And Long-Term Integration”, Journal of Math. Analysis and App., 34, 235-238,1971.
  • [8] Bert C.W., Jang S.K., Striz AG., “Two New Approximate Methods For Analyzing Free Vibration Of Structural Components”, AIAA Journal , 26 (5), 612-618,1987.
  • [9] Du H., Lim M.K., Lin, R.M., “Application Of Generalized Differential Quadrature Method To Structural Problems”. Int. J. Numerical Meth. Engng.,37, 1881-1896,1994.
  • [10] Civalek Ö., “Static, Dynamic And Buckling Analysis Of Elastic Bars Using DQ”, XVI. National Technical Engineering Symposium, Ankara, METU, 2001.
  • [11] Civalek, Ö., Çatal, H.H., Stability And Vibration Analysis Of Plates By Harmonic Differential Quadrature, IMO Technical Journal, 2003; Vol. 14 (1), 2835-2852.
  • [12] Jang S.K., Bert C.W., Striz A.G., “Application Of Differential Quadrature To Static Analysis Of Structural Components”, Inter. J. Num. Meth. Engng., 28, 561- 577,1989.
  • [13] Liew K.M., Teo T.M., and Han J.B., “Comparative Accuracy Of DQ And HDQ Methods For Three- Dimensional Vibration Analysis Of Rectangular Plates”, Int. J. Num. Meth. Engng., 45,1831-1848, 1999.
  • [14] Shu C., Richards B.E., “Application Of Generalized Differential Quadrature To Solve Two- Dimensional Incompressible Navier -Stokes Equations”, Inter. J. Numerical Meth. In Fluids,15,791-798, 1992.
  • [15] Civalek, Ö., Çatal,H.H., Dynamic Analysis Of One And Two Dimensional Structures By The Method Of Generalized Differential Quadrature, Türkiye İnşaat Mühendisleri Odası, Mühendislik Haberleri, Sayı 417, s.39-46,2002.
  • [16] Hamming R.W., “Numerical Methods For Scientists And Engineers”, New York, McGraw-Hill, 1973.
  • [17] Björck A., and Pereyra V., “Solution Of Vandermonde System Of Equations”. Math. comput., 24, 893-903,1970.
  • [18] Striz A.G., Wang X., and Bert C.W., “HDQ Method And Applications To Analysis Of Structural Components”, ACTA Mech., 111,85-94,1995.
  • [19] Shu C., Xue H., “Explicit Computations Of Weighting Coefficients In The Harmonic Differential Quadrature”. J. of Sound and Vib., 204(3), 549-555,1997.
  • [20] Zienkiewicz O.C, “The Finite Element Method In Engineering Science”, 3rd edt.: McGraw- Hill; London, 1977.
  • [21] Berktay I., “Theory Of Plates And Its Applications”, Istanbul, Yıldız University Press, 1992(in Turkish).
  • [22] Bert C.W, Malik M. “The differential quadrature method for irregular domains and application to plate vibration”. Inter. J.of Mechanical Science, 1996; 38(6):589-606.
  • [23] Zienkiewicz O. C, Taylor, R.L., “The Finite Element Method”, Vol. 1.: McGraw- Hill; 1989.
  • [24] Wang C.M, Liew K.M, and Alwis W.A.M, “Buckling of Skew Plates and Corner Conditions For Simply Supported Edges”, J.of Eng. Mechanics, 1991, 118, 651-662.
  • [25] Liew K.M, Han J.B, “A Four-Node Differential Quadrature Method For Straight- Sided Quadrilateral Reissner /Mindlin Plates”, Communications in Numerical Methods in Engineering, 1997,13, 73-81.
  • [26] Kim C.S, Dickinson S.M, “On The Free, Transverse Vibration Of Annular And Circular, Thin Sectorial Plates Subject To Certain Complicating Effects”, Journal of Sound and Vibration, 1989,134, 407-415.
  • [27] Leissa, AW, “Vibration of Plates”, NASA, SP-160, 1969.
There are 27 citations in total.

Details

Subjects Civil Engineering
Journal Section Research Articles
Authors

Ömer Civalek

Hikmet H. Çatal

Publication Date June 30, 2003
Acceptance Date January 1, 2003
Published in Issue Year 2003 Volume: 16 Issue: 1

Cite

APA Civalek, Ö., & Çatal, H. H. (2003). Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, 16(1), 43-71.
AMA Civalek Ö, Çatal HH. Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method. ESOGÜ Müh Mim Fak Derg. June 2003;16(1):43-71.
Chicago Civalek, Ömer, and Hikmet H. Çatal. “Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi 16, no. 1 (June 2003): 43-71.
EndNote Civalek Ö, Çatal HH (June 1, 2003) Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 16 1 43–71.
IEEE Ö. Civalek and H. H. Çatal, “Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method”, ESOGÜ Müh Mim Fak Derg, vol. 16, no. 1, pp. 43–71, 2003.
ISNAD Civalek, Ömer - Çatal, Hikmet H. “Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 16/1 (June 2003), 43-71.
JAMA Civalek Ö, Çatal HH. Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method. ESOGÜ Müh Mim Fak Derg. 2003;16:43–71.
MLA Civalek, Ömer and Hikmet H. Çatal. “Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, vol. 16, no. 1, 2003, pp. 43-71.
Vancouver Civalek Ö, Çatal HH. Linear Static And Vibration Analysis Of Circular And Annular Plates By The Harmonic Differential Quadrature (HDQ) Method. ESOGÜ Müh Mim Fak Derg. 2003;16(1):43-71.
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