Abstract
The transient response of sandwich beams, plates, and shells with viscoelastic layers under impulse loading is studied using the finite element method. The viscoelastic material behavior is represented by a complex modulus model. An efficient method using the fast Fourier transform is proposed. This method is based on the trigonometric representation of the input signals and the matrix of the transfer functions. The present approach makes it possible to preserve exactly the frequency dependence of the storage and loss moduli of viscoelastic materials. The logarithmic decrements are determined using the steady state vibrations of sandwich structures to characterize their damping properties. Test problems and numerical examples are given to demonstrate the validity and application of the approach suggested in this paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. D. Johnson and D. A. Kienholz, “Finite element prediction of damping in structures with constrained viscoelastic layers,” AIAA J.,20, 1284–1290 (1982).
T. C. Ramesh and N. Ganesan, “Vibration and damping analysis of conical shells with constrained damping treatment,” Fin. Elem. Analys. Des.,12, 17–29 (1993).
B.-C. Lee and K.-J. Kim, “Effects of normal strain in core material on modal property of sandwich plates,” J. Vibr. Acoust.,119, 493–503 (1997).
J. A. Zapfe and G. A. Lesieutre, “A discrete layer beam finite element for the dynamic analysis of composite sandwich beams with integral damping layers,” Comput. Struct.,70, 647–666 (1999).
D. J. Mead and S. Markus, “The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions,” J. Sound Vibr.,10, No. 2, 163–175 (1969).
T. Kucharski, “Calculation of transient state response of machine members made of composite materials and of sandwich panels,” Comput. Struct.,51, No. 5, 495–501 (1994).
R. L. Bagley and P. J. Torvik, “Fractional calculus in the transient analysis of viscoelastically damped structures,” AIAA J.,23, No. 6, 918–925 (1985).
H.-H. Lee, “Non-linear vibration of a multilayer sandwich beam with viscoelastic layers,” J. Sound Vibr.,216, No. 4, 601–621 (1998).
L. B. Eldred, W. P. Baker, and A. N. Palazotto, “Kelvin-Voigt vs fractional derivative model as constitutive relations for viscoelastic materials,” AIAA J.,33, No. 3, 547–550 (1995).
Y. M. Haddad, Viscoelasticity of Engineering Materials, Chapman & Hall, London (1995).
A. D. Nashif, D. I. G. Johnes, and J. P. Henderson, Vibration Damping, John Wiley & Sons, New York (1985).
K.-J. Bathe and E. L. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall (1976).
E. O. Brigham, The Fast Fourier Transform, Prentice-Hall (1974).
C. Temperton, “Self-sorting mixed-radix fast Fourier transforms,” J. Computat. Phys.,52, 1–23 (1983).
E. O. Brigham, The Fast Fourier Transform and Its Applications, Prentice-Hall (1988).
R. Rikards, A. Chate, and E. Barkanov, “Finite element analysis of damping the vibrations of laminated composites,” Comput. Struct.,47, No. 6, 1005–1015 (1993).
A. Chate, R. Rikards, K. Mäkinen, and K.-A. Olsson, “Free vibration analysis of sandwich plates on flexible supports,” Mech. Compos. Mater. Struct.,2, 1–18 (1995).
E. Barkanov, “Transient response analysis of structures made from viscoelastic materials,” Int. J. Numer. Meth. Eng.,44, 393–403 (1999).
Author information
Authors and Affiliations
Additional information
Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).
Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 367–378, March–April, 2000.
Rights and permissions
About this article
Cite this article
Barkanov, E., Rikards, R., Holste, C. et al. Transient response of sandwich viscoelastic beams, plates, and shells under impulse loading. Mech Compos Mater 36, 215–222 (2000). https://doi.org/10.1007/BF02681873
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02681873