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Mathematical model and method of determination of amplitude-frequency characteristics of corrugated cylindrical shells for geometrically nonlinear vibrations

Marchuk Mykhailo, Goriachko Taras, Kindratskyy Bohdan, Pakosh Vira

Vibrations in Physical Systems

2020

Vol. 31, nr 3

art. no. 2020316

On the basis of spatial geometrically nonlinear theory of elasticity by using quadratic approximations for components of the vector of displacements along the normal coordinate to the median surface is developed a new mathematical model of nonlinear dynamics of cylindrical shells with corrugated configuration for median surface. The perturbation method for the solution of systems of nonlinear differential equations for problems of determination of amplitude-frequency characteristics is generalized. In a combination of finite element and generalized perturbations methods, a new methodology for solving problems of free geometrically nonlinear vibrations of shells with complex guide geometry was developed and verified. With its help the influence of geometrical parameters of corrugating at circular coordinate on the main frequency of the elongated cylindrical panel is investigated.

Corrugated shell displacements during the passage of a vehicle along a soil-steel structure

Machelski C., Mumot M.

Studia Geotechnica et Mechanica

2016

Vol. 38, nr 4

25--32

Corrugated steel plates are highly rigid and as the constructions can be immersed in soil, they can be used as soil-steel structures. With an increase of cover depth, the effectiveness of operating loads decreases. A substantial reduction of the impacts of vehicles takes place as a road or rail surface with its substructure is crucial. The scope of load’s impact greatly exceeds the span L of a shell. This article presents the analysis of deformations of the upper part of a shell caused by a live load. One of the assumptions used in calculations performed in Plaxis software was the circle-shaped shell and the circumferential segment of the building structure in the 2D model. The influence lines of the components of vertical and horizontal displacements of points located at the highest place on the shell were used as a basis of analysis. These results are helpful in assessing the results of measurements carried out for the railway structure during the passage of two locomotives along the track. This type of load is characterized by a steady pressure onto wheels with a regular wheel base. The results of measurements confirmed the regularity of displacement changes during the passage of this load.