0
Research Papers

Differential Quadrature Free Vibration Analysis of Functionally Graded Thin Annular Sector Plates in Thermal Environments

[+] Author and Article Information
S. H. Mirtalaie

Department of Mechanical Engineering;
Modern Manufacturing Technologies Research
Center,
Najafabad Branch,
Islamic Azad University,
Najafabad, 8514143131, Iran
e-mail: mirtalaie@pmc.iaun.ac.ir

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received July 5, 2017; final manuscript received March 16, 2018; published online May 3, 2018. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 140(10), 101006 (May 03, 2018) (20 pages) Paper No: DS-17-1337; doi: 10.1115/1.4039785 History: Received July 05, 2017; Revised March 16, 2018

In this paper, the free vibration behavior of functionally graded (FG) thin annular sector plates in thermal environment is studied using the differential quadrature method (DQM). The material properties of the FG plate are assumed to be temperature dependent and vary continuously through the thickness, according to the power-law distribution of the volume fraction of the constituents. The nonlinear temperature distribution along the thickness direction of the plate is considered. Based on the classical plate theory, the governing differential equations of motion of the plate are derived and solved numerically using DQM. The natural frequencies of thin FG annular sector plates in thermal environment under various combinations of clamped, free, and simply supported boundary conditions (BCs) are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate where the results are in good agreement. The effects of temperature field, BCs, volume fraction exponent, radius ratio, and the sector angle on the free vibrations of the FG-plate are examined.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Koizumi, M. , 1997, “FGM Activities in Japan,” Compos. Part B, 28(1–2), pp. 1–4. [CrossRef]
Geiger, G. , 1992, “Ceramic Coatings Enhance Material Performance,” Am. Ceram. Soc. Bull., 71(10), pp. 1470–1481. https://www.tib.eu/en/search/id/ceaba%3ACEAB1992413897/Ceramic-coatings-enhance-material-performance/
Mumm, D. R. , and Evans, A. G. , 2000, “On the Role of Imperfections in the Failure of a Thermal Barrier Coating Made by Electron Beam Deposition,” Acta Mater., 48(8), pp. 1815–1827. [CrossRef]
Liew, K. M. , He, X. Q. , and Tapabrata, R. , 2004, “On the Use of Computational Intelligence in the Optimal Shape Control of Functionally Graded Smart Plates,” Comput. Methods Appl. Mech. Eng., 193(42–44), pp. 4475–4492. [CrossRef]
Evans, A. G. , Mumm, D. R. , and Hutchinson, J. W. , 2001, “Mechanisms Controlling the Durability of Thermal Barrier Coatings,” Prog. Mater. Sci., 46(5), pp. 505–553. [CrossRef]
Yang, J. , and Shen, H. S. , 2002, “Vibration Characteristics and Transient Response of Shear-Deformable Functionally Graded Plates in Thermal Environments,” J. Sound Vib., 255(3), pp. 579–602. [CrossRef]
Vel, S. S. , and Batra, R. C. , 2004, “Three-Dimensional Exact Solutions for the Vibration of Functionally Graded Rectangular Plate,” J. Sound Vib., 272(3–5), pp. 703–730. [CrossRef]
Chen, C. S. , 2005, “Non-Linear Vibration of a Shear Deformable Functionally Graded Plate,” Compos. Struct., 68(3), pp. 295–302. [CrossRef]
Abrate, S. , 2006, “Free Vibration, Buckling, and Static Deflections of Functionally Graded Plates,” Compos. Sci. Technol., 66(14), pp. 2383–2394. [CrossRef]
Zhao, X. , Lee, Y. Y. , and Liew, K. M. , 2009, “Free Vibration Analysis of Functionally Graded Plates Using the Element-Free Kρ-Ritz Method,” J. Sound Vib., 319(3–5), pp. 918–939. [CrossRef]
Ramakrishnan, R. , and Kunukkasseril, V. X. , 1973, “Free Vibration of Annular Sector Plates,” J. Sound Vib., 30(1), pp. 127–129. [CrossRef]
Harik, I. E. , 1990, “Vibration of Sector Plates on Elastic Foundations,” J. Sound Vib., 138(3), p. 542–528. [CrossRef]
Xiang, Y. , Liew, K. M. , and Kitipornchai, S. , 1993, “Transverse Vibration of Thick Annular Sector Plates,” J. Eng. Mech., 119(8), pp. 1579–1599. [CrossRef]
Nie, G. J. , and Zhong, Z. , 2008, “Vibration Analysis of Functionally Graded Annular Sectorial Plates With Simply Supported Radial Edges,” Compos. Struct., 84(2), pp. 167–176. [CrossRef]
Jomehzadeh, E. , Saidi, A. R. , and Atashipour, S. R. , 2009, “An Analytical Approach for Stress Analysis of Functionally Graded Annular Sector Plates,” Mater. Des., 30(9), pp. 3679–3685. [CrossRef]
Sahraee, S. , 2009, “Bending Analysis of Functionally Graded Sectorial Plates Using Levinson Plate Theory,” Compos. Struct., 88(4), pp. 548–557. [CrossRef]
Mirtalaie, S. H. , and Hajabasi, M. A. , 2011, “Free Vibration Analysis of Functionally Graded Thin Annular Sector Plates Using the Differential Quadrature Method,” Proc. Inst. Mech. Eng., Part C, 225(3), pp. 568–583. [CrossRef]
Hosseini-Hashemi, S. , Akhavan, H. , Rokni Damavandi Taher, H. , Daemi, N. , and Alibeigloo, A. , 2010, “Differential Quadrature Analysis of Functionally Graded Circular and Annular Sector Plates on Elastic Foundation,” Mater. Des., 31(4), pp. 1871–1880. [CrossRef]
Saidi, A. R. , Hasani Baferani, A. , and Jomehzadeh, E. , 2011, “Benchmark Solution for Free Vibration of Functionally Graded Moderately Thick Annular Sector Plates,” Acta Mech., 219(3–4), pp. 309–335. [CrossRef]
Hasani Baferani, A. , Saidi, A. R. , and Jomehzadeh, E. , 2012, “Exact Analytical Solution for Free Vibration of Functionally Graded Thin Annular Sector Plates Resting on Elastic Foundation,” J. Vib. Control, 18(2), pp. 246–267. [CrossRef]
Asemi, K. , Salehi, M. , and Akhlaghi, M. , 2014, “Three-Dimensional Natural Frequency Analysis of Anisotropic Functionally Graded Annular Sector Plates Resting on Elastic Foundations,” Sci. Eng. Compos. Mater., 22(6), pp. 693–708.
Allahverdizadeh, A. , Naei, M. H. , and Nikkhah Bahrami, M. , 2008, “Vibration Amplitude and Thermal Effects on the Nonlinear Behavior of Thin Circular Functionally Graded Plates,” Int. J. Mech. Sci., 50(3), pp. 445–454. [CrossRef]
Golmakani, M. E. , and Kadkhodayan, M. , 2013, “Large Deflection Thermo Elastic Analysis of Functionally Graded Stiffened Annular Sector Plates,” Int. J. Mech. Sci., 69, pp. 94–106. [CrossRef]
Fallah, F. , and Nosier, A. , 2015, “Thermo-Mechanical Behavior of Functionally Graded Circular Sector Plates,” Acta Mech., 226(1), pp. 37–54. [CrossRef]
Bellman, R. E. , and Casti, J. , 1971, “Differential Quadrature and Long-Term Integration,” J. Math. Anal. App., 34(2), pp. 235–238. [CrossRef]
Bert, C. W. , Jang, S. K. , and Striz, A. G. , 1988, “Two New Approximate Methods for Analyzing Free Vibration of Structural Components,” AIAA J., 26(5), pp. 612–618. [CrossRef]
Bert, C. W. , and Malik, M. , 1996, “Differential Quadrature Method in Computational Mechanics: A Review,” ASME Appl. Mech. Rev., 49(1), pp. 1–27. [CrossRef]
Bert, C. W. , and Malik, M. , 1997, “Differential Quadrature Method: A Powerful New Technique for Analysis of Composite Structures,” Compos. Struct., 39(3–4), pp. 179–189. [CrossRef]
Malekzadeh, P. , 2009, “Two-Dimensional In-Plane Free Vibrations of Functionally Graded Circular Arches With Temperature-Dependent Properties,” Compos. Struct., 91(1), pp. 38–47. [CrossRef]
Malekzadeh, P. , Golbahar Haghighi, M. R. , and Atashi, M. M. , 2010, “Out-of-Plane Free Vibration of Functionally Graded Circular Curved Beams in Thermal Environment,” Compos. Struct., 92(2), pp. 541–552. [CrossRef]
Malekzadeh, P. , Shahpari, S. A. , and Ziaee, H. R. , 2010, “Three-Dimensional Free Vibration of Thick Functionally Graded Annular Plates in Thermal Environment,” J. Sound Vib., 329(4), pp. 425–442. [CrossRef]
Malekzadeh, P. , and Heydarpour, Y. , 2012, “Free Vibration Analysis of Rotating Functionally Graded Cylindrical Shells in Thermal Environment,” Compos. Struct., 94(9), pp. 2971–2981. [CrossRef]
Malekzadeh, P. , and Heydarpour, Y. , 2012, “Response of Functionally Graded Cylindrical Shells Under Moving Thermo Mechanical Loads,” Thin-Walled Struct., 58, pp. 51–66. [CrossRef]
Touloukian, Y. S. , 1967, Thermo Physical Properties of High Temperature Solid Materials, MacMillan, New York.
Javaheri, R. , and Eslami, M. R. , 2002, “Thermal Buckling of Functionally Graded Plates,” AIAA J., 40(1), pp. 162–169. [CrossRef]
Abrate, S. , 2008, “Functionally Graded Plates Behave Like Homogeneous Plates,” Compos. Part B, 39(1), pp. 151–158. [CrossRef]
Brush, D. O. , and Almroth, B. O. , 1975, Buckling of Bars Plates and Shells, McGraw-Hill, New York.
Karami, G. , and Malekzadeh, P. , 2003, “Application of a New Differential Quadrature Methodology for Free Vibration Analysis of Plates,” Int. J. Numer. Methods Eng., 56(6), pp. 847–868. [CrossRef]
Kim, C. S. , and Dickinson, S. M. , 1989, “On the Free, Transverse Vibration of Annular and Circular, Thin, Sectorial Plates Subject to Certain Complicating Effects,” J. Sound Vib., 134(3), pp. 407–421. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Geometry of the plate and coordinate system

Grahic Jump Location
Fig. 2

Order of the boundary numbers

Grahic Jump Location
Fig. 3

Variation of frequency parameter of FGM annular sectorial plates versus the temperature rise (ΔT) for various combinations of BCs

Grahic Jump Location
Fig. 4

Mode shapes of fully simple supported FGM annular sectorial plates

Grahic Jump Location
Fig. 5

Mode shapes of fully clamped FGM annular sectorial plates

Grahic Jump Location
Fig. 6

Mode shapes of FSFS FGM annular sectorial plates

Grahic Jump Location
Fig. 7

Mode shapes of CSCS FGM annular sectorial plates

Grahic Jump Location
Fig. 8

Mode shapes of SCSC FGM annular sectorial plates

Grahic Jump Location
Fig. 9

Mode shapes of FCFC FGM annular sectorial plates

Grahic Jump Location
Fig. 10

Mode shapes of SFSF FGM annular sectorial plates

Grahic Jump Location
Fig. 11

Mode shapes of CFCF FGM annular sectorial plates

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In