Non-stationary contact problems for the cylinder in fluid layer on a solid half-space

Acoustic bulletin, Vol. 2 4, (1999) p.58-68
Nonstationary problem for the cylinder interacting with layer of compressible liquid and elastic halfspace under dynamic or kinematic loadings is considered. The system of differential equation is solved that 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 nonstationary problems on horizontal and angular vibration of rigid cylinder, and on bending vibration elastic cylinder. Numerical analysis is made for case of horizontal vibration of rigid cylinder undergoing the action of horizontal force. There are detected the time dependences of reaction of foundation, displacement and hydrodynamic pressure on the cylinder at nonstationary loading. The dependence of desired functions from the height of liguid layer and mass of the cylinder is established. The considered problems are of interest at studying and calculation of oscillations of the offshore platforms undergoing the wave, ice, and seismic loading.
contact problem, nonstationary load, oscillations of the offshore platforms