Nonlinear parametric oscillations of a viscoelastic shallow shell of variable thickness

Abstract

The problem of parametric oscillations of an isotropic viscoelastic shallow shell of variable thickness under periodic load is considered. It is believed that under the influence of specified load, the shallow shell allows displacements (in particular, deflections), commensurate with its thickness. In a geometrically nonlinear statement, taking into account the viscoelastic properties of material, a mathematical model of the problem has been developed using the classical Kirchhoff-Love hypothesis. Using the Bubnov-Galerkin method based on the polynomial approximation of the deflections, the problem is reduced to the study of the system of integro-differential equations, where time is the independent variable. The solution of the system of integrodifferential equations is determined by the proposed numerical method. Based on this method, a numerical solution algorithm is described. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. At the same time, the effect of geometric nonlinearity, viscoelastic properties of material, as well as other physicomechanical and geometric parameters and factors (rheological parameters, thickness, initial shape imperfections, aspect ratios, boundary conditions, excitation coefficient) on the area of dynamic instability is taken into account. The results obtained in this study are in good agreement with the results and data obtained by other authors.

Improving the manufacturability of floor slabs by pre-installing elements that partially replace reinforced concrete and formwork

“…As can be seen from the presented results, the proposed innovative design of precastmonolithic floor slab provides significant savings in material resources: steel -by 26% and concrete mix by 47%. The results obtained do not go beyond the limits noted by other researchers and designers [9,10]. In value terms, the savings on materials are 387 thousand rubles per floor slab.…”

“…Another possible and practical way of reducing own weight of flat floor slabs in a precast-monolithic building frame is also the replacement of a part of concrete with plastic inserts of various shapes: balls and similar bodies of revolution (Bubble Deck technology), rectangular parallelepipeds (NAUTILUS technology), etc. In their projects, the developers show up to 35%, and even up to 50% savings in reinforced concrete with the resulting other improved technical and economic indicators (cost, timing) [9,10]. Analytical studies of comparative strength and deformation properties of such systems in comparison with a solid reinforced concrete slab were also carried out [11].…”