Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Meccanica
Published in: Meccanica 6/2012

01-08-2012

Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates on elastic foundations

Authors: M. H. Yas, A. Jodaei, S. Irandoust, M. Nasiri Aghdam

Published in: Meccanica | Issue 6/2012

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Three-dimensional free vibration analysis of functionally graded piezoelectric (FGPM) annular plates resting on Pasternak foundations with different boundary conditions is presented. The material properties are assumed to have an exponent-law variation along the thickness. A semi-analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is utilized to obtain the influences of the Winkler and shearing layer elastic coefficients of the foundations on the non-dimensional natural frequencies of functionally graded piezoelectric annular plates. The analytical solution in the thickness direction can be acquired using the state-space method and approximate solution in the radial direction can be obtained using the one-dimensional differential quadrature method. Numerical results are given to demonstrate the convergency and accuracy of the present method. The influences of the material property graded index, circumferential wave number and thickness of the annular plate on the dynamic behavior are also investigated. Since three-dimensional free vibration analysis of FGPM annular plates on elastic foundations has not been implemented before, the new results can be used as benchmark solutions for future researches.
previous article An investigation into the effect of strain rate on forming limit diagram using ductile fracture criteria
next article MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermophysical properties

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Literature
1.
Gandhi MV, Thompson BS (1992) Smart materials and structures. Chapman & Hall, London
2.
Rao SS, Sunar M (1994) Piezoelectricity and its use in disturbance sensing and control of flexible structures: a survey. Appl Mech Rev 47:113–123 ADSCrossRef
3.
Branco PJC, Dente JA (2004) On the electromechanics of a piezoelectric transducer using a bimorph cantilever undergoing asymmetric sensing and actuation. Smart Mater Struct 13(4):631–642 ADSCrossRef
4.
Kruusing A (2000) Analysis and optimization of loaded cantilever beam microactuators. Smart Mater Struct 9(2):186–196 ADSCrossRef
5.
Zhu XH, Meng ZY (1995) Operational principle fabrication and displacement characteristic of a functionally gradient piezoelectric ceramic actuator. Sens Actuators 48:169–176 CrossRef
6.
Wu CCM, Kahn M, Moy W (1996) Piezoelectric ceramics with functional gradients: a new application in material design. J Am Ceram Soc 79:809–812 CrossRef
7.
Zhong Z, Shang ET (2003) Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate. Int J Solids Struct 40:5335–5352 MATHCrossRef
8.
Lu P, Lee HP, Lu C (2006) Exact solutions for simply supported functionally graded piezoelectric laminates by Stroh-like formalism. Compos Struct 72:352–363 CrossRef
9.
Takagi K, Li JF, Yokoyama S, Watanabe R, Almajid A, Taya M (2002) Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator. Sci Technol Adv Mater 3:217–224 CrossRef
10.
Lee JS, Jiang LZ (1996) Exact electroelastic analysis of piezoelectric laminae via state-space approach. Int J Solids Struct 33(7):977–990 MATHCrossRef
11.
Bert CW, Malik M (1997) Differential quadrature: a powerful new technique for analysis of composite structures. Compos Struct 39(3–4):179–189 CrossRef
12.
Chen WQ, Ding HJ (2000) Bending of functionally graded piezoelectric rectangular plates. Acta Mech Solida Sin 13(4):312–319 MathSciNet
13.
Chen WQ, Ding HJ (2002) On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mech 153:207–216 MATHCrossRef
14.
Lim CW, He LH (2001) Exact solution of a compositionally graded piezoelectric layer under uniform stretch bending and twisting. Int J Mech Sci 43:2479–2492 MATHCrossRef
15.
Reddy JN, Cheng ZQ (2001) Three-dimensional solutions of smart functionally graded plates. J Appl Mech 68:234–241 MATHCrossRef
16.
Lu P, Lee HP, Lu C (2005) An exact solution for simply supported functionally graded piezoelectric laminates in cylindrical bending. Int J Mech Sci 47:437–458 MATHCrossRef
17.
Li XY, Ding HJ, Chen WQ (2008) Three-dimensional analytical solution for a transversely isotropic functionally graded piezoelectric circular plate subject to a uniform electric potential difference. Sci Chin Ser G, Phys Mech Astron 51(8):1116–1125 ADSMATHCrossRef
18.
Xiang HJ, Shi ZF (2009) Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load. Eur J Mech A, Solids 28:338–346 MATHCrossRef
19.
Li Y, Shi ZF (2009) Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature. Compos Struct 87:257–264 CrossRef
20.
Alibeigloo A, Nouri V (2010) Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method. Compos Struct 92:1775–1785 CrossRef
21.
Gupta US, Lal R, Jain SK (1990) Effect of elastic foundation on axisymmetric vibrations of polar orthotropic circular plates of variable thickness. J Sound Vib 139:503–513 ADSCrossRef
22.
Laura PAA, Gutierrez RH (1991) Free vibrations of a solid circular plate of linearly varying thickness and attached to Winkler foundation. J Sound Vib 144:149–161 ADSCrossRef
23.
Xiang Y, Wang CM, Kitipornchai S (1994) Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. Int J Mech Sci 36:311–316 MATHCrossRef
24.
Ju FH, Lee PKH (1995) Free vibration of plates with stepped variations in thickness on non-homogeneous elastic foundations. J Sound Vib 183:533–545 ADSMATHCrossRef
25.
Matsunaga H (2000) Vibration and stability of, thick plates on elastic foundations. J Eng Mech 126:27–34 CrossRef
26.
Gupta US, Ansari AH, Sharma S (2006) Buckling and vibration of polar orthotropic circular plate resting on Winkler foundation. J Sound Vib 297:457–476 ADSCrossRef
27.
Hosseini Hashemi Sh, Rokni Damavandi Taher H, Omidi M (2008) 3-D free vibration analysis of annular plates on Pasternak elastic foundation via p-Ritz method. J Sound Vib 311:1114–1140 ADSCrossRef
28.
Hosseini-Hashemi Sh, Omidi M, Rokni Damavandi Taher H (2009) The validity range of CPT and Mindlin plate theory in comparison with 3-D vibrational analysis of circular plates on the elastic foundation. Eur J Mech A, Solids 28:289–304 MATHCrossRef
29.
Hsu M-H (2010) Vibration analysis of orthotropic rectangular plates on elastic foundations. Compos Struct 92:844–852 CrossRef
30.
Malekzadeh P, Afsari A, Zahedinejad P, Bahadori R (2010) Three-dimensional layerwise-finite element free vibration analysis of thick laminated annular plates on elastic foundation. Appl Math Model 34:776–790 MathSciNetMATHCrossRef
31.
Malekzadeh P (2009) Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations. Compos Struct 89:367–373 CrossRef
32.
Amini MH, Soleimani M, Rastgoo A (2009) Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation. Smart Mater Struct 18:085015, 9 pp ADSCrossRef
33.
Yas MH, Sobhani Aragh B (2010) Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation. Int J Eng Sci 48:1881–1895 MATHCrossRef
34.
Hosseini-Hashemi Sh, Akhavan H, Rokni Damavandi Taher H, Daemi N, Alibeigloo A (2010) Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation. Mater Des 31:1871–1880 CrossRef
35.
Hosseini-Hashemi Sh, Rokni Damavandi Taher H, Akhavan H (2010) Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations. Compos Struct 92:1734–1743 CrossRef
36.
Dumir PC (1988) Large deflection axisymmetric analysis of orthotropic annular plates on elastic foundations. Int J Solids Struct 24:777–787 CrossRef
37.
Nie GJ, Zhong Z (2007) Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Comput Methods Appl Mech Eng 196:4901–4910 ADSMATHCrossRef
38.
Chen WQ, Lv CF, Bian ZG (2003) Elasticity solution for free vibration of laminated beams. Compos Struct 62(1):75–82 CrossRef
39.
Shu C, Richards BE (1992) Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int J Numer Methods Fluids 15:791–798 MATHCrossRef
40.
Bert CW, Malik M (1996) Differential quadrature method in computational mechanics. A review. Appl Mech Rev 49:1–28 ADSCrossRef
41.
Dong CY (2008) Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev–Ritz method. Mater Des 29:1518–1525 CrossRef
42.
Metadata
Title
Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates on elastic foundations
Authors
M. H. Yas
A. Jodaei
S. Irandoust
M. Nasiri Aghdam
Publication date
01-08-2012
Publisher
Springer Netherlands
Published in
Meccanica / Issue 6/2012
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-011-9525-y

Other articles of this Issue 6/2012

Meccanica 6/2012 Go to the issue

OriginalPaper

Effect of the rotation, magnetic field and initial stress on peristaltic motion of micropolar fluid

OriginalPaper

The effects of local thermal nonequilibrium and MFD viscosity on the onset of Brinkman ferroconvection

OriginalPaper

Analytic study on non-Newtonian natural convection boundary layer flow with variable wall temperature on a horizontal plate

OriginalPaper

Effect of rotation on plane waves in generalized thermo-microstretch elastic solid with a relaxation time

OriginalPaper

Oblique stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation

OriginalPaper

MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermophysical properties

Premium Partners

    Image Credits