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Transient response analysis of structures made from viscoelastic materials. (English) Zbl 0927.74065
Summary: The response of structures made from viscoelastic materials to transient excitations is studied using the finite element method. The viscoelastic material behaviour is represented by the complex modulus model. We develop an efficient method using fast Fourier transform. This method is based on the trigonometric representation of input signals and matrix of the transfer functions. The implementation preserves exactly the frequency dependence of the storage and loss moduli of materials. Thus this time-domain representation is a mathematically correct way to avoid the non-causal effect. The test problems and numerical examples demonstrate the effectiveness of the approach.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
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[1] Johnson, AIAA J. 20 pp 1284– (1982)
[2] De Wilde, Int. J. Numer. Meth. Engng. 27 pp 429– (1989)
[3] and ?Damping analysis of sandwich structures?, Proc. 4th Int. Conf. on Computer Aided Design in Composite Materials Technology, Southampton, U.K., 1994, pp. 415?422.
[4] Barkanov, Mech. Comp. Mater. 30 pp 484– (1994)
[5] Bagley, AIAA J. 21 pp 741– (1983)
[6] Bagley, AIAA J. 23 pp 918– (1985)
[7] Chen, Int. J. Numer. Meth. Engng. 38 pp 509– (1995)
[8] Lunden, J. Sound Vib. 80 pp 161– (1982)
[9] Karlsson, Int. J. Numer. Meth. Engng. 21 pp 683– (1985)
[10] Kucharski, Comput. Struct. 51 pp 495– (1994)
[11] Inaudi, J. Engng Mech. 121 pp 626– (1995)
[12] Crandall, J. Sound Vib. 11 pp 3– (1970)
[13] and Vibration Damping, Wiley, New York, 1985.
[14] Viscoelasticity of Engineering Materials, Chapman & Hall, London, 1995.
[15] and Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1976”.
[16] The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, N.J., 1974. · Zbl 0375.65052
[17] Temperton, J. Comput. Phys. 52 pp 1– (1983)
[18] The Fast Fourier Transform and Its Applications, Prentice-Hall, Englewood Cliffs, N.J., 1988.
[19] Lin, Proc. Inst. Mech. Engrs., Part C: J. Mech. Engng. Sci. 210 pp 111– (1996)
[20] Rikards, Comput. Struct. 47 pp 1005– (1993)
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