The Analysis of Influence of High-Frequency Vibrations on the Nonlinear Model of a Construction

The authors analyze the effect of high-frequency additive and multiplicative non-stationary or stationary vibrations on a nonlinear mechanical system with a finite number of degrees of freedom. The influences are defined within the correlation theory. It is considered that only the «slow motion» determined by mathematical expectation is of interest.  High-frequency vibrations of phase coordinates are small and may be omitted in the calculations. For example, this is done when false readings («walks») of the pendulum accelerometer are analyzed at fast vibrations. First, the initial equation of motion is statistically linearized. To find the solution, the phase coordinate vector is represented as an integro-power series by the matrix containing the aligned random vibrations, and members up to quadratic ones are considered, inclusively. As a result, a convenient explicit dependence of the expectation vector on the elements of the correlation matrix is obtained. Using this equation, it is possible to establish a hierarchy with regards to their contribution to the «error» (vibration component of the solution). The fundamental matrix of the linearized system for the organization of the computing procedure is represented in the form of a multiplicative integral.

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