Response of a slender structure subject to stochastic ground motion and body force

The stochastic analysis of the deflection behaviour of an idealised slender structure subject to stochastic disturbance is studied. In a previous work by the authors, the response of an Euler-Bernoulli beam subject to stochastic disturbance was studied. The current work extends the same techniques to a modified Euler-Bernoulli beam with both flexural beam and shear properties. The beam is subjected to a stochastic ground motion in the form of periodic motion with disturbance in the amplitude of the motion. The disturbance is in the form of Gaussian white noise. This results in a Stochastic Partial Differential Equation (SPDE) version of the modified Euler-Bernoulli beam equation. The stochastic analysis was then conducted by numerical methods using a combination of a finite difference scheme and Monte-Carlo Simulation. Given that the input force is Gaussian, it is also observed that the response of the system is a Gaussian process.