M. Viktorovitch et al., An integral formulation with random parameters adapted to the study of thevibrational behaviour of structures in the middle- and high-frequency field, J SOUND VIB, 247(3), 2001, pp. 431-452
The fundamentals of a new boundary element formulation applied to the study
of structural dynamics on a wide frequency range is proposed in this paper
. Random geometrical parameters are introduced to the integral representati
ons in order to model the increasing sensitivity of the harmonic vibrationa
l responses to any parameter perturbation when the frequency increases. It
is shown that the significant unknowns of the formulation are the expectati
ons of the square boundary kinematic unknowns. Indeed, these variables are
able to describe accurately the responses of the structures in the low-freq
uency field and deliver a smooth response in the middle- and high-frequency
field, corresponding to the global trend of the structural dynamic respons
e in this frequency domain. The formulation is established for isolated and
assembled one-, two- and three-dimensional structures. Numerical applicati
ons illustrate the effectiveness of the method. (C) 2001 Academic press.