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Year 2001, Volume 28 / Issue 3

Pages: 150

Article price - $35.00

Nonstationary Contact Problems for a Cylinder in Liquid Layer on a Solid Half-Space

V. M. Seimov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv

Nonstationary problem for the cylinder interacting with thew layer of compressible liquid and elastic halfspace under dynamic or kinematic loadings is considered. The system of differential equations is solved, which describes the wave processes in liquid layer and elastic halfspace, and the bending vibration of the cylinder. Method of integral transforms (Laplace on time, and Hankel on radial coordinate), method of orthogonal polynomials, method of coordinate functions, and method of collocations are used. In the domain of the Laplace images the problem is reduced to a system of algebraic equations. The Laplace transform inversion is made numerically by means of the Fourier integral. The solutions are obtained for harmonic and nonstationary problems on horizontal and angular vibration of rigid cylinder, and on bending vibration of elastic cylinder. Numerical analysis is made for the case of horizontal vibration of rigid cylinder undergoing the action of horizontal force. The time dependencies of reaction of foundation, displacement and hydrodynamic pressure on the cylinder at nonstationary loading are detected. The dependence of desired functions from the height of liquid layer and mass of the cylinder is established. The considered problems are of interest at studying and calculation of oscillations of a gravitational offshore platforms undergoing the wave, ice, and seismic loading.

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