Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Analytical study of dynamic behavior of functionally graded viscoelastic plates subjected to a transverse load with an arbitrary time variations

Authors
-
Abstract
In the present paper, dynamic behavior of a simply supported FGM viscoelastic plate subjected to a transverse load with an arbitrary time variations is investigated analytically. The hierarchical integral model is employed for description of the viscoelastic nature of the materials and a power law is used for description of the transverse variations of the material properties of the viscoelastic FGM plate. Solution of the governing equations of the viscoelastic FGM plate is accomplished through employing a Navier-type spatial solution and a Runge-Kutta solution for the time-dependency using a numerical trapezoidal discretization for the time integrals. Influences of various material properties and geometric parameters on time history of the responses of the plate are investigated comprehensively. Results reveal that due to the damping nature of the viscoelastic material, stiffness of the plate increases at the early time instants and consequently, the maximum dynamic transverse deflection of the plate decreases whereas the natural frequencies increase. 
Keywords

[1]     Praveen, G., and Reddy, J. N., “Nonlinear Transient Thermoelastic Analysis of Functionally Graded Ceramic-metal Plates”, International Journal of Solids and Structures, Vol. 35, No. 33, pp. 4457-4476, (1998).
 
[2]     Cederbaum, G., and Aboudi, J., ”Dynamic Rresponse of Viscoelastic Laminated Plates”, Journal of Sound and Vibration, Vol. 133, No. 2, pp. 225-238, (1989).
 
[3]     Chen, T.M., “The Hybrid Laplace Transform/Finite Element Method Applied to the  Quasi‐static and Dynamic Analysis of Viscoelastic Timoshenko Beams”, International Journal  for Numerical Methods in Engineering, Vol. 38, No. 3, pp. 509-522, (1995).
 
[4]     Ilyasov, M., and Aköz., A., “The Vibration and Dynamic Stability of Viscoelastic Plates”, International Journal of Engineering Science, Vol. 38, No. 6, pp. 695-714, (2000).
 
[5]     Paulino, G.H., and Jin, Z.H., ‘‘Correspondence Principle in Viscoelastic Functionally Graded Materials”, ASME Journal of Applied Mechanics, Vol. 68, pp. 129–132, (2001).
 
[6]     Paulino, G., and Jin, Z.H., “Viscoelastic Functionally Graded Materials Subjected to Antiplane Shear Fracture”, Journal of Applied Mechanics, Vol. 68, No. 2, pp. 284-293, (2001).
 
[7]     Paulino, G. H., and Jin, Z. H.,”A Crack in a Viscoelastic Functionally Graded Material Layer Embedded Between Two Dissimilar Homogeneous Viscoelastic Layers–antiplane  Shear Analysis”,  International Journal of Fracture, Vol. 111, No. 3, pp. 283-303, (2001).
 
[8]     Jin, Z.H., and Paulino, G. H, ‘‘A Viscoelastic Functionally Graded Strip Containing a Crack Subjected to In-plane Loading”, Engineering Fracture Mechanics, Vol. 69, pp. 1769–1790, (2002).
 
[9]     Abdoun, F., Azrar, L., Daya, E.M., and Potier-Ferry, M., ”Forced Harmonic Response of Viscoelastic Structures by an Asymptotic Numerical Method”, Computers & Structures, Vol. 87, No. 1, pp. 91-100, (2009).
 
[10] Assie , A.E., Eltaher, M.A., and Mahmoud, F.F., “The Response of Viscoelastic-frictionless Bodies under Normal Impact”, International Journal of Mechanical Sciences, Vol. 52, No. 3, pp. 446-454, (2010).
 
[11] Assie, A.E., Eltaher, M.A., and Mahmoud, F.F., “Modeling of Viscoelastic Contact-impact Problems”, Applied Mathematical Modeling, Vol. 34, pp. 2336-2352, (2010).
 
[12] Assie, A.E., Eltaher, M.A., and Mahmoud, F.F., “Behavior of a Viscoelastic Composite Plates under Transient Load”, Journal of Mechanical Science and Technology, Vol. 25, No. 5, pp. 1129-1140, (2011).
 
[13] Altenbach, H., and Eremeyev, V.A., “On the Bending of Viscoelastic Plates Made of  Polymer Foams”, Acta Mechanica, Vol. 204, No. 3- 4, pp. 137-154, (2009).
 
[14] Altenbach, H., and Eremeyev, V.A., “Analysis of the Viscoelastic Behavior of Plates Made of Functionally Graded Materials”, ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 88, No. 5, pp. 332-341, (2008).
 
[15] Lakes, R.S., “Viscoelastic Materials”, Cambridge University Press, New York, (2009).
 
[16] Badalov, F.B., Eshmatov, K., and Akbarov, U.I., ”Stability of a Viscoelastic Plate under Dynamic Loading”, International Journal of Applied Mechanics, Vol. 27, No. 9, pp. 892-899, (1991).
 
[17] Ugural, A.C., “Stress in Plates and Shells,” McGraw- Hill, New York, (1999).
 
[18] Gerald, C.F., and Wheatley, P.O., “Applied Numerical Analysis,” 7th Edition, Pearson, California, (2003).  
 
[19] Wang, Y., and Tsai, T., “Static and Dynamic Analysis of a Viscoelastic Plate by the Finite Element Method”, Applied Acoustics, Vol. 25, No. 2, pp. 77-94, (1988).
 
[20] Shariyat, M., and Azadmanesh, M., “Thermal Buckling Analysis of Rectangular Composite Plates Subjected to Large Deflections, Based on a Layerwise Theory and Budiansky's Criterion Modification”, ISME Journal Vol. 9, No. 1, pp. 25-40, (2007).
Volume 15, Issue 3 - Serial Number 32
System Dyanamics and Solid Mechanics
Autumn 2013
Pages 52-72

  • Receive Date 22 November 2013