Numerical Solution of Stochastic Differential Equations Used in Random Vibration

Abdelmadjid Chabani; Francisco Javier Cara Cañas; Abdelmadjid Berga

doi:10.15866/ireme.v11i1.9800

Numerical Solution of Stochastic Differential Equations Used in Random Vibration

Abdelmadjid Chabani^(1*), Francisco Javier Cara Cañas⁽²⁾, Abdelmadjid Berga⁽³⁾

^(*) Corresponding author

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DOI: https://doi.org/10.15866/ireme.v11i1.9800

Abstract

The vibratory environment found in the majority of cases consists of random vibrations. Therefore, each recording of the same phenomena results in a signal different from the previous ones. Such vibrations can be only analyzed in a stochastic manner. In this paper, we present applications of the stochastic differential equations in random vibrations of Mass-Spring-Damper System. The motivation behind stochastic calculus is to define a calculus for situations in which ordinary methods of calculus do not apply due to randomness concerned with the system or the input. In this work, we will construct and implement methods for solving the stochastic differential equation modeling the Mass-Spring-Damper System with disturbances at the source (stochastic input) and stochastic differential equations with random coefficients.
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Keywords

Stochastic Calculus; Wiener Process; Stochastic Differential Equations; Mass-Spring-Damper System; Numerical Solution

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