FREE DAMPED VIBRATIONS OF VISCOELASTIC MATERYALS

Abstract

Free damper vibrations of viscoelastic rod,beam,plate and shell reducible to the solution of a certain integro-differential equation. Full solution of this equation for the kernel of relaxation in the form of sum of N exponential functions with different negative indexes is constritcted in the present article. lteration processes for calcrrlating frequency and damping

coefficient, which are the real and iinaginaiy parts of two complexconjugated roots of frequency equation, are given.In the case of positive relaxed module, the fact that the frequency equation has N futher real negative poles, in addition to the two complex poles obtained above, is proved. Analysis of obtainetl solutions and their comparisons with results available in literature are performed.

Keywords

• viscoelastic material damped vibrations exponential kernel