I. Elishakoff and D. Livshits
abstract:
This paper contrasts the exact solutions for the mean-square displacements of a
cantilever under random loading with those delivered by asymptotic method. It is
shown that probabilistic response evaluated by the latter method may lead to
considerable errors: in the case of a beam with viscous damping as much as 100%,
and in that of structural damping 188%. A new, closed-form, solution is proposed
for a cantilever with Voigt damping. In this case asymptotic method exhibits the
maximum error of 312%.
Mathematics Subject Classification: 70L05, 74H50, 82B31
Key words and phrases: Probability, stationary random process, random fields, random vibrations, asymptotic method, dynamic edge effect