The modal data measured on the global structure are disassembled to obtain the independent substructural dynamic flexibility matrices under force and displacement compatibility conditions.
Secondly, based on this condition, an algorithm for determining the required control gain matrices of acceleration and displacement feedback, which assign the desired eigenstructure, is developed.
Similar to ANCF, Eq. (15) establishes the relationship between the stiffness matrix and the nodal displacement.
This can modify the capillary forces in the oil/rock matrix and the oil displacement mobility and the sweep efficiency.
The device, in combination with SIMS imaging, was used to measure matrix crystal size, analyte incorporation to the matrix, and the chemical displacement of the analyte after matrix deposition.
Once the panel is adjusted by three adjustors, the facet displacement in this panel can be written as [28, 29] Delta {varvec r}_{i} '{varvec S}_{ni} {varvec a}_{n}, (11 where a n —Panel adjustment vector, S ni —Transform matrix between adjustment vector and displacement of the ith facet.
And then by taking into account the nodal spectral forces, we are able to obtain the dynamic stiffness in a matrix form as: F a F b = F r A 1 r B 1 r A 2 r B 2 r = F r T r - 1 q 1 r 0 0 q 2 r ⇒ K dyn = F r T r - 1 (18)where F r and T r as the spectral force and displacement matrix for the rod spectral element, respectively are given in "Appendix".
The theory employs Fourier series representations for fiber, coating and matrix displacement fields in the cylindrical coordinate system that satisfy exactly equilibrium equations and continuity conditions in the interior of the unit cell.
The theory employs Fourier series representations for hollow fiber and matrix displacement fields in the cylindrical coordinate system which satisfy exactly the equilibrium equations and continuity conditions in the interior of the unit cell.
The frame impedance matrix relating forces and displacements at terminations is then applied at junctions of ring segments corresponding to these terminations.
