Вип. 101

Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in nonsmooth dynamical systems is of the special scientists’ interest. In this paper we apply relatively young mathematical tool – continuous wavelet transform CWT – for investigating the chaotic behavior and intermittency in particular in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate route to chaos via intermittency, to distinguish and analyze the laminar and turbulent phases.

The article is devoted to a further analysis of the natural vibrations of inhomogeneous shells under the action of static loads. The method of investigation is based on a unified methodology that combines the problems of static stability and the vibrations of elastic shells. The problems of natural vibrations take into account the presence of a prestressed state of the shell structure from the action of static loads. The presence of a static load significantly affects the spectrum of the natural frequencies of the shell. This approach allows us to determine the critical load by the dynamic criterion. The method of investigating of inhomogeneous shells is based on the uniform methodological positions of the 3-d geometrically nonlinear theory of thermoelasticity and the finite-element method in the form of the moment finite-element scheme. So, a thin shell is considered by this method as a three-dimensional body which is modeled throughout the thickness by one isoparametric solid finite element with multilinear shape functions. Two nonclassical hypotheses are used to describe the stress–strain state of a thin inhomogeneous shell. The kinematic hypothesis of deformed straight line in the thickness direction: though stretched or shortened during deformation, a straight segment along the thickness remains straight. This segment is not necessarily normal to the mid-surface of the shell. The displacements are assumed distributed linearly along the thickness, which is conventional in the theory of thin shells. The static hypothesis compressive assumes that the stresses in the fibers are constant throughout the thickness of the shell. Modal analysis of a shallow ribbed panel demonstrates the effectiveness of the developed method. The natural frequencies and mode shapes are determined at each increment of static loading.

Вип. 101

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