A studyof vibrations of a cylinder with a viscoelastic coating

The paper presents the problem of steady-state longitudinal-radial vibrations an elastic hollow cylinder with a viscoelastic coating. properties coating change along radial coordinate only and are described by variable Lame parameters density. ends under sliding interface conditions, outer side surface is subject to periodic loads. Within framework model standard body following principle correspondence, replaced complex functions vibration frequency. solution was obtained using two approaches. first approach, constructed method separation variables reduced solving set boundary value problems for canonical systems first-order differential equations coefficients. each these numerically shooting method. second approach based on finite element implemented in FlexPDE package. We compared solutions given laws variation fixed frequency analyzing graphs real imaginary parts displacement stress components. convergence found shown as function number nodes values measured at three points. amplitude-frequency characteristics plotted different relaxation time. effect estimated. advantages described, areas their practical application revealed.