Fig 9 - uploaded by Tao Gao
Content may be subject to copyright.
Download
View publication
3D colour-map representation of the temporal covariance matrix from y = 0 to y = 1 (colour online).

3D colour-map representation of the temporal covariance matrix from y = 0 to y = 1 (colour online).

Source publication
Fig. 1 Schematic of the two-dimensional problem. The solid line depicts...
Fig. 2 Fourier spectrum of the response to the load (24) on the top of...
Fig. 4 (a) Various distribution fitted to the deflection data recorded...
Fig. 5 Colour-map image representation of the covariance matrix at time...
+4 Fig. 6 3D colour-map representation of the covariance matrix at...
Response of an Euler-Bernoulli beam subject to a stochastic disturbance
Preprint
Full-text available
  • Sep 2022
This work concerns the bending of a slender cantilever beam subject to an external force with the inclusion of a stochastic effect characterised by white noise. The beam deflection is governed by the classic dynamic Euler-Bernoulli equation. Its response to the stochastic external load is investigated by learning pattern from the simulation data wh...
Cite
Download full-text

Context in source publication

Context 1
... image in Fig. 8. It can be clearly seen that the temporal covariance converges to a limit with oscillations in long term. This calculation has been repeated for different positions along the beam. By using the same visualisation technique of stacking up the colour-map images, a three-dimensional colour-map representation is formed and plotted in Fig. 9 that provides a clear view on the overall evolution of the temporal covariance. On the other hand, the temporal correlation matrix is again found to be of a unit matrix, showing that the beam deflection is (perfectly) positively temporally correlated at a fixed position. 4. Combining the results obtained from the previous three steps, ...