, Volume 49, Issue 12, pp 2817–2828 | Cite as

Application of the differential quadrature method to free vibration of viscoelastic thin plate with linear thickness variation

  • Yin Feng Zhou
  • Zhong Min Wang


The differential quadrature method has been applied to investigate vibrations of viscoelastic thin plate with variable thickness. Firstly, the governing equations are derived in terms of the thin-plate theory and the two-dimensional viscoelastic differential constitutive relation. Then, the convergence of the method is demonstrated based on the differential equation of uniform thickness elastic square plate, which is reduced from the differential equation of viscoelastic plate with varying thickness. Lastly, the effects of aspect ratio, thickness ratio and dimensionless delay time on the vibrations of the linear thickness viscoelastic plate with different boundary conditions have been studied.


Viscoelastic plate with linear thickness variation Kelvin–Voigt model Differential quadrature (DQ) method Non-periodic creep 


  1. 1.
    Aksu G, Al-Kaabi SA (1987) Free vibration analysis of Mindlin plates with linearly varying thickness. J Sound Vib 119:189–205CrossRefADSGoogle Scholar
  2. 2.
    Mizusawa T (1993) Vibration of rectangular Mindlin plates with tapered thickness by the spline strip method. Comput Struct 46:451–463CrossRefADSGoogle Scholar
  3. 3.
    Sakiyama T, Huang M (1998) Free vibration analysis of rectangular plates with variable thickness. J Sound Vib 216:379–397CrossRefADSGoogle Scholar
  4. 4.
    Mizusawa T, Kondo Y (2001) Application of the spline element method to analyze vibration of skew Mindlin plates with varying thickness in one direction. J Sound Vib 241:485–501CrossRefADSGoogle Scholar
  5. 5.
    Zenkour AM, Mashat DS (2009) Exact solutions for variable-thickness inhomogeneous elastic plates under various boundary conditions. Meccanica 44:433–447MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Zhou YF, Wang ZM (2008) Vibrations of axially moving viscoelastic plate with parabolically varying thickness. J Sound Vib 316:198–210CrossRefADSGoogle Scholar
  7. 7.
    Zhou YF, Wang ZM (2009) Dynamic behaviors of axially moving viscoelastic plate with varying thickness. Chin J Mech Eng 22(2):276–281CrossRefGoogle Scholar
  8. 8.
    Flügge W (1975) Viscoelasticity, 2nd edn. Springer, BerlinCrossRefMATHGoogle Scholar
  9. 9.
    Malekzadeh P, Karami G (2004) Vibration of non-uniform thick plates on elastic foundation by differential quadrature method. Eng Struct 26:1473–1482CrossRefGoogle Scholar
  10. 10.
    Fu YM, Chen Y, Zhang P (2013) Thermal buckling analysis of functionally graded beam with longitudinal crack. Meccanica 48:1227–1237MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Gorman DJ (1982) Free vibration analysis of rectangular plates. Elsevier North Holland Inc, New YorkMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Instrument Science & Opto-electronics EngineeringBeijing University of Aeronautics & AstronauticsBeijingChina
  2. 2.School of Civil Engineering and ArchitectureXi’an University of TechnologyXi’anChina

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