The egenvalue spectum of simply supported beam with magnetorheological fluid damper is analyzed by iterative perturbation method.

Using the resolvent technique, we established the equivalence between the generalized set-valued variational inclusions and the fixed point problems, and some perturbed iterative algorithms, proved that its proximate solution converge to its exact solution in real Hilbert space.

Based on the fundamental theory of the cable-prestressed steel truss established in paper [1], the inversive iterative perturbation equations which can be used to determine the stiffeness of elements of the prestressed steel truss with elastic supports are put forward by using the principle of matrix perturbation and introducing the concepts of the combined elements and stiffeness factors.

Since the model parameters could not be measured directly,an inverse problem of determining model parameters was put forward,and numerical inversions for a real life example of multi-component solutes transport under different conditions were carried out by applying an optimal perturbation iteration algorithm.

Furthermore,numerical simulations for the unknown parameters inversion were carried out by applying an optimal perturbation iteration algorithm.