Statistical Characteristics of the Damped Vibrations of a String Excited by Stochastic Forces

Abstract

Our theoretical study aims at finding some statistic parameters characterizing the damped vibrations of a string excited by stochastic impulses. We derive the dependence of these parameters on the parameters of the string as well as on the stochastic distributions of the impulse magnitude, and on the place of the action. We also carry out a numerical simulation verifying the derived mathematical model and interpret the differences between the results obtained in simulation and the mathematical calculations. This study is the fourth stage of a research aimed at designing a probe that facilitates the process of measuring of the parameters, determining the quality of a technological process.