Research Article
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Year 2022, Volume 9, Issue 3, 167 - 175, 28.09.2022
https://doi.org/10.17350/HJSE19030000268

Abstract

References

  • Leissa AW, Qatu MS. Vibration of Continuous Systems, US: McGraw-Hill Professional, 2011.
  • Fromme JA, Leissa AW. Free vibration of the rectangular parallelepiped. The Journal of the Acoustical Society of America 48 (1970) 290.
  • Leissa AW. The free vibration of rectangular plates. Journal of Sound and Vibration 31(3) (1973) 257-293.
  • Kirchhoff G. Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die Reine und Angewandte Mathematik 40 (1850) 51–88.
  • Mindlin RD. Influence of rotatory inertia and shear in flexural motions of isotropic, elastic plates. Journal of Applied Mechanics 18(1) (1951) 31-38.
  • Reissner E. The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics 12(2) (1945) 69-77.
  • Reddy JN. A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics 51(4) (1984) 745–752.
  • Touratier M. An efficient standard plate theory. International Journal of Engineering Science 29(8) (1991) 901-916.
  • Soldatos KP. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica 94(3–4) (1992) 195–220.
  • Noor AK, Burton WS. Three-Dimensional Solutions for the Free Vibrations and Buckling of Thermally Stressed Multilayered Angle-Ply Composite Plates. Journal of Applied Mechanics 59(4) (1992) 868-877.
  • Tenek LH, Henneke EG, Gunzburger MD. Vibration of delaminated composite plates and some applications to non-destructive testing. Composite Structures 23(3) (1993) 253-262.
  • Liew KM, Hung KC, Lim MK. A continuum three-dimensional vibration analysis of thick rectangular plates. International Journal of Solids and Structures 30(24) (1993) 3357-3379.
  • Cheung YK, Kong J. Approximate three-dimensional analysis of rectangular thick laminated plates: Bending, vibration and buckling. Computers & Structures 47(2) (1993) 193-199.
  • Chen WQ, Lü CF. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Composite Structures 69(1) (2005) 77-87.
  • Ye JQ. A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges. Computer Methods in Applied Mechanics and Engineering 140(3-4) (1997) 383-392.
  • Malik M, Bert CW. Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method. International Journal of Solids and Structures 35(3-4)(1998) 299-318.
  • So J, Leissa AW. Three-dimensional vibrations of thick circular and annular plates. Journal of Sound and Vibration 209(1) (1998) 15-41.
  • Liew KM, Yang B. Elasticity solutions for free vibrations of annular plates from three-dimensional analysis. International Journal of Solids and Structures 37(52) (2000) 7689-7702.
  • Huang W, Xue K, Li Q. Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions. Materials 14(22) (2021) 7088.
  • Wang Z, Xing Y, Li G. Closed-form solutions for the free vibrations of three-dimensional orthotropic rectangular plates. International Journal of Mechanical Sciences 199 (2021) 106398.
  • Liew KM, Hung KC, Lim MK. Three-dimensional vibration of rectangular plates: Effects of thickness and edge constraints. Journal of Sound and Vibration 182(5) (1995) 709-727.
  • Uzun B, Yaylı MÖ. Nonlocal vibration analysis of Ti-6Al-4V/ZrO2 functionally graded nanobeam on elastic matrix. Arabian Journal of Geosciences 13 (2020) 155.
  • Uzun B, Kafkas U, Yaylı MÖ. Stability analysis of restrained nanotubes placed in electromagnetic field. Microsystem Technologies 26 (2020) 3725-3736.
  • Yaylı MÖ, Uzun B, Deliktaş B. Buckling analysis of restrained nanobeams using strain gradient elasticity. Waves in Random and Complex Media (2021) https://doi.org/10.1080/17455030.2020.1871 112.
  • Alazwari MA, Zenkour AM. A Quasi-3D Refined Theory for the Vibration of Functionally Graded Plates Resting on Visco-Winkler-Pasternak Foundations. Mathematics 10(5) (2022) 716.

Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body

Year 2022, Volume 9, Issue 3, 167 - 175, 28.09.2022
https://doi.org/10.17350/HJSE19030000268

Abstract

In this study, vibration of plates embedded in a rigid enclosure has been investigated analytically for the first time in the literature. It is assumed that the isotropic plate is always in contact with outer enclosure. Therefore, the normal displacement at a boundary surface is constrained but tangential displacement at a surface is allowed. The displacement field is assumed in trigonometric function form. This analytical solution is the only available exact solution of three-dimensional isotropic plate. Numerical results were presented for various geometrical parameters. It is believed that the present formulation and the results can be used as a benchmark for the numerical methods where the exact solution is not possible.

References

  • Leissa AW, Qatu MS. Vibration of Continuous Systems, US: McGraw-Hill Professional, 2011.
  • Fromme JA, Leissa AW. Free vibration of the rectangular parallelepiped. The Journal of the Acoustical Society of America 48 (1970) 290.
  • Leissa AW. The free vibration of rectangular plates. Journal of Sound and Vibration 31(3) (1973) 257-293.
  • Kirchhoff G. Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die Reine und Angewandte Mathematik 40 (1850) 51–88.
  • Mindlin RD. Influence of rotatory inertia and shear in flexural motions of isotropic, elastic plates. Journal of Applied Mechanics 18(1) (1951) 31-38.
  • Reissner E. The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics 12(2) (1945) 69-77.
  • Reddy JN. A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics 51(4) (1984) 745–752.
  • Touratier M. An efficient standard plate theory. International Journal of Engineering Science 29(8) (1991) 901-916.
  • Soldatos KP. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica 94(3–4) (1992) 195–220.
  • Noor AK, Burton WS. Three-Dimensional Solutions for the Free Vibrations and Buckling of Thermally Stressed Multilayered Angle-Ply Composite Plates. Journal of Applied Mechanics 59(4) (1992) 868-877.
  • Tenek LH, Henneke EG, Gunzburger MD. Vibration of delaminated composite plates and some applications to non-destructive testing. Composite Structures 23(3) (1993) 253-262.
  • Liew KM, Hung KC, Lim MK. A continuum three-dimensional vibration analysis of thick rectangular plates. International Journal of Solids and Structures 30(24) (1993) 3357-3379.
  • Cheung YK, Kong J. Approximate three-dimensional analysis of rectangular thick laminated plates: Bending, vibration and buckling. Computers & Structures 47(2) (1993) 193-199.
  • Chen WQ, Lü CF. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Composite Structures 69(1) (2005) 77-87.
  • Ye JQ. A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges. Computer Methods in Applied Mechanics and Engineering 140(3-4) (1997) 383-392.
  • Malik M, Bert CW. Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method. International Journal of Solids and Structures 35(3-4)(1998) 299-318.
  • So J, Leissa AW. Three-dimensional vibrations of thick circular and annular plates. Journal of Sound and Vibration 209(1) (1998) 15-41.
  • Liew KM, Yang B. Elasticity solutions for free vibrations of annular plates from three-dimensional analysis. International Journal of Solids and Structures 37(52) (2000) 7689-7702.
  • Huang W, Xue K, Li Q. Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions. Materials 14(22) (2021) 7088.
  • Wang Z, Xing Y, Li G. Closed-form solutions for the free vibrations of three-dimensional orthotropic rectangular plates. International Journal of Mechanical Sciences 199 (2021) 106398.
  • Liew KM, Hung KC, Lim MK. Three-dimensional vibration of rectangular plates: Effects of thickness and edge constraints. Journal of Sound and Vibration 182(5) (1995) 709-727.
  • Uzun B, Yaylı MÖ. Nonlocal vibration analysis of Ti-6Al-4V/ZrO2 functionally graded nanobeam on elastic matrix. Arabian Journal of Geosciences 13 (2020) 155.
  • Uzun B, Kafkas U, Yaylı MÖ. Stability analysis of restrained nanotubes placed in electromagnetic field. Microsystem Technologies 26 (2020) 3725-3736.
  • Yaylı MÖ, Uzun B, Deliktaş B. Buckling analysis of restrained nanobeams using strain gradient elasticity. Waves in Random and Complex Media (2021) https://doi.org/10.1080/17455030.2020.1871 112.
  • Alazwari MA, Zenkour AM. A Quasi-3D Refined Theory for the Vibration of Functionally Graded Plates Resting on Visco-Winkler-Pasternak Foundations. Mathematics 10(5) (2022) 716.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Ufuk GUL> (Primary Author)
TRAKYA ÜNİVERSİTESİ
0000-0001-9433-6186
Türkiye


Metin AYDOĞDU>
TRAKYA UNIVERSITY
0000-0003-4567-2532
Türkiye

Publication Date September 28, 2022
Application Date May 29, 2022
Acceptance Date July 17, 2022
Published in Issue Year 2022, Volume 9, Issue 3

Cite

Bibtex @research article { hjse1123007, journal = {Hittite Journal of Science and Engineering}, eissn = {2148-4171}, address = {Hitit Üniversitesi Mühendislik Fakültesi Kuzey Kampüsü Çevre Yolu Bulvarı 19030 Çorum / TÜRKİYE}, publisher = {Hitit University}, year = {2022}, volume = {9}, number = {3}, pages = {167 - 175}, doi = {10.17350/HJSE19030000268}, title = {Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body}, key = {cite}, author = {Gul, Ufuk and Aydoğdu, Metin} }
APA Gul, U. & Aydoğdu, M. (2022). Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body . Hittite Journal of Science and Engineering , 9 (3) , 167-175 . DOI: 10.17350/HJSE19030000268
MLA Gul, U. , Aydoğdu, M. "Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body" . Hittite Journal of Science and Engineering 9 (2022 ): 167-175 <https://dergipark.org.tr/en/pub/hjse/issue/72726/1123007>
Chicago Gul, U. , Aydoğdu, M. "Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body". Hittite Journal of Science and Engineering 9 (2022 ): 167-175
RIS TY - JOUR T1 - Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body AU - UfukGul, MetinAydoğdu Y1 - 2022 PY - 2022 N1 - doi: 10.17350/HJSE19030000268 DO - 10.17350/HJSE19030000268 T2 - Hittite Journal of Science and Engineering JF - Journal JO - JOR SP - 167 EP - 175 VL - 9 IS - 3 SN - -2148-4171 M3 - doi: 10.17350/HJSE19030000268 UR - https://doi.org/10.17350/HJSE19030000268 Y2 - 2022 ER -
EndNote %0 Hittite Journal of Science and Engineering Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body %A Ufuk Gul , Metin Aydoğdu %T Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body %D 2022 %J Hittite Journal of Science and Engineering %P -2148-4171 %V 9 %N 3 %R doi: 10.17350/HJSE19030000268 %U 10.17350/HJSE19030000268
ISNAD Gul, Ufuk , Aydoğdu, Metin . "Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body". Hittite Journal of Science and Engineering 9 / 3 (September 2022): 167-175 . https://doi.org/10.17350/HJSE19030000268
AMA Gul U. , Aydoğdu M. Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body. Hittite J Sci Eng. 2022; 9(3): 167-175.
Vancouver Gul U. , Aydoğdu M. Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body. Hittite Journal of Science and Engineering. 2022; 9(3): 167-175.
IEEE U. Gul and M. Aydoğdu , "Three Dimensional Vibration of an Isotropic Plate Enclosed in a Rigid Body", Hittite Journal of Science and Engineering, vol. 9, no. 3, pp. 167-175, Sep. 2022, doi:10.17350/HJSE19030000268