Plates on elastic foundations have attracted the attention of many researchers. Some elementary models have been introduced to consider interactions between the plate and its foundation.Other improved models have been proposed to develop basic models. In this work, a model based on the Winkler-foundation theory is proposed, while the constant parameter of Winkler is assumed to be Variable, such as non-uniform springs with the functionality of the domain position, along with the plate and beam span in order to consider the non-uniform behavior of the foundation. The governing equation on the system is solved by using the Galerkin method and effects such as the presence of rigid points in the foundation are considered.

The influence of surface roughness magnitude and direction on dry static Friction Coefficient between two similar steel samples has been studied through an experiment. A testing apparatus has been designed and fabricated to measure the Friction Coefficient for a few forms of surface asperity. The average, maximum and minimum values of static Friction Coefficients among steel samples have been measured and numerically proposed in terms of some discrete values of the surface roughness, base and counter body angles. Correction Coefficient defined as the ratio of maximum to minimum Friction Coefficient has been found on the result basis. According to the results of the experiments, dry static Friction Coefficient between two similar steel samples is affected by both magnitude and direction of surface roughness. Under the condition of static equilibrium, the Colomb - Amonton formula has been used to determine Friction Coefficient between samples. The flexibility and mass of the string have been neglected, and the reservoir pendulum-like swinging and the water movement therein have been avoided within the experiments.

An increase in the flow velocity in flow through large porous media and deflection of flow regime from Darcy law causes a nonlinear relationship between hydraulic gradient and pore velocity of media. One of the most important subjects in flow through large porous media is relationship between Friction Coefficient and flow characteristics which was previously focused by some investigators but it is needed to extract general and more accurate relationships for all of their data series. Also, in most of previous studies the Friction Coefficient was presented in Darcy-Weisbach form which is not so common in the open channel flow between hydraulic engineers like Manning Coefficient. In this study, the required data were collected from four different sources. Three series of them were operated in the sediment contained flow through mode and another one was operated in sediment free flow through mode. Using some basic equations about pore velocity and Frictional Coefficient, the new relationships were developed and calibrated for estimation of manning Coefficient in open channel flow through porous media. It was found that modified Wilkins equation had a better estimation for manning Coefficient in both sediment free and sediment contained flow rather than Ergun and Sedghi's one. Also, it was found that general trend of Moody diagram for pipe flow is established in flow through large porous media such that by increase in the media Reynolds number, the Manning Coefficient limits to a constant value and become dependent to the media characteristics.

The seismic response of 20-story benchmark building with semi-active Variable Friction dampers (SAVFD) is investigated under various earthquake ground motions. A recently proposed predictive control algorithm is employed. A parametric study is carried out to arrive at optimum value of gain multiplier so as to have maximum response reduction. The numerical study is carried out for the benchmark building installed with SAVFD and compared with passive and uncontrolled case. The effectiveness of dampers is studied in terms of the reduction in structural responses and performance criteria. To reduce the cost of dampers study is carried out with lesser number of dampers at appropriate locations. Results show that SAVFD reduces earthquake responses effectively with better performance in respect of acceleration response reduction as compared with passive dampers. In addition, it is observed that the lesser number of dampers at appropriate locations results similar response reduction which reduces cost of the dampers.

In the present study, the influence of the Coefficient of Friction on the seismic response of sliding base isolated structures is investigated. The building is modeled as a simplified single-story structure resting on a group of sliding supports. The Frictional forces mobilized at the sliding supports are assumed to have a hysteretic plasticity behavior. Bilateral interaction between the stiffness of the two horizontal orthogonal directions of the isolators has been taken into consideration. The results show that the variations of the Coefficient of Friction influence the response of a sliding base isolated building. Effects of vertical excitation on the normal and Frictional forces are considered too. The influence of the bi-directional interaction of Frictional forces and vertical excitation on the response is investigated by comparing the response of the system to mono-directional (excluding vertical component and no interaction between the two horizontal orthogonal directions), bi-directional (excluding vertical component) and tridirectional earthquake excitations. It is demonstrated that the response of the sliding isolated structures is influenced significantly by the bi-directional interaction of Frictional forces and by incorporation of the vertical component. Further, the base shear response may be underestimated if the effects of the vertical component are neglected and the sliding structures are designed merely on the basis of single-component or two-component excitation.