Oscillations of the variable cross beams under seismic and technogenic influences (part II)

Abstract

The forced transverse oscillations of the variable cross section compressed beams under seismic and technogenic impacts are considered. The source of oscillations is the kinematic perturbations of the beam ends in the form of a harmonic or random vector process. The mathematical model of oscillations is presented as a boundary value problem from the basic partial differential equation of the fourth order hyperbolic type in spatial coordinate and the second order in time, which is supplemented by the boundary conditions. The beam fluctuations are interpreted as the spatiotemporal random fields inhomogeneous in space and stationery in time. In the deterministic case, the amplitudes of the forced oscillations are determined, the influence of the kinematic disturbances’ frequency and the beam oscillations’ shift of their phases is studied. In the stochastic problem, the standard deviations for the deflections are calculated, the influence of the characteristic frequency and correlation of the components of the vector perturbation process on the deflections’ output function is studied. The problem is solved by the methods of the variables’ separation, finite differences and the theory of random processes. The examples are considered, the conclusions are drawn from the calculations results in the Matlab computing complex environment.