Abstract
The problems of longitudinal oscillations of high vertical rods with orientation to the application of results in the problems of seismic calculations are considered. Mathematical models of free, forced harmonic and forced random oscillations caused by kinematic disturbances of the lower end are obtained. Application of methods of separation of variables and finite differences in combination with visualization of calculations in Matlab environment gave own values and own functions, and then amplitudes and mean square deviations of oscillations. It is shown how the preliminary consideration of harmonic oscillations significantly simplified the solution of the stochastic problem. Influence of characteristic frequency and broadband parameter of input random process on the form and standard deviation of longitudinal oscillations is studied.
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