Transient responses of polymers and elastomers deduced from harmonic responses. (English) Zbl 1235.74373

Soula, M.; Vinh, T.; Chevalier, Y.

J. Sound Vib. 205, No. 2, 185-203 (1997).

Summary: The problem of interrelations between viscoelastic time and frequency functions is revisited. The proposed methods do not use the intermediary functions which are extensively used in the rheology of solid materials. Integer linear differential operators or fractional derivatives for constitutive equations relating stress and strain are the two possibilities of choice. From experimental curves of complex moduli versus frequency, obtained over a large range of frequencies, closed form expressions of moduli are obtained. Inverse Fourier transformation gives rise to time exponential series or time hypergeometric series depending on the type of constitutive law adopted.

MSC:

74S30

Other numerical methods in solid mechanics (MSC2010)

Keywords:

viscoelastic time; frequency functions; time exponential series; time hypergeometric series