The investigation of some three-demonsional vibration and stability loss problems of the mechanics of curved composites with employing fem

ABSTRACT In the present thesis the boundary value and eigenvalue problems corresponding to the natural and forced vibrations of the rectangular thick plate fabricated from the composite material with spatially periodically curved structures are investigated. Moreover, the stability loss problem of this plate is also studied within the framework of the Three-Dimensional Linearized Theory of Stability. All problems considered are solved by employing the three dimensional Finite Element Method (FEM). The constitutive relations of the plate material are taken within the framework of the continuum theory by Akbarov and Guz. As the natural and forced vibratons of the plate are investigated by the use of the three-dimensional exact equations of motion of the theory of elasticity, therefore the problems considered in the mathematical sense are the boundary-value or eigenvalue problems for the system partially-differential equations with variable coefficients. The solution of these problems are made for the various type boundary conditions. Under solution procedure, i.e. under FEM modeling of the considered problems it is introduced the corresponding functionals the validity of which is proven. The numerical results are obtained for each considered problem and the discussion of these results are given. Keywords : Composite, fundamental frequency, forced vibration, spatial periodical curving, stability. IX