This paper presents delay-dependent stability analysis for some types of nonlinear Time-delay systems. Motivated by Lyapunov-Krasovskii functionals and the related theorems on stability of Time-delay systems, we introduce a new procedure for generating such functionals. The main reason for considering Lyapunov-Krasovskii functionals is the less conservatism of this method. The obtained conditions are sufficient and local. Applying the introduced procedure on a typical system with Time-invariant parameters derives more results and a numerical example presents the capability of the method.

A Time-dependent periodic coefficients (TDPC) model was proposed to analyze the Global Positioning System (GPS) Time series. Due to the variations of the amplitude and phase-lag of the GPS signals over Time, we propose a TDPC to analyze the daily Time series. A new solution approach, where the serial correlations of the disturbances are eliminated by sequentially differencing the measurements, was used to estimate the model parameters using weighted least squares. As a numerical performance of the proposed method, the Time series of 19 permanent stations in the United States via the Website of Scripps Orbit and Permanent Array Center (SOPAC) between the 2000 and 2010 year was selected. The results show a decrease in the RMS values of the residuals, especially for the height components. Moreover, using the 90 simulated GPS data analysis, in which their noises were different combinations of white noise and flicker noise, we demonstrate that the proposed model can extract amplitude varying periodic variabilities from GPS coordinate Time series.

Time-dependent reliability analysis of mechanical structures is concerned by the use of an outcrossing approach. In this approach the so-called outcrossing rate plays a critical role and thus it is important to estimate it as straight ward as possible. Despite the availability of a variety of methods to estimate this rate in the literature, still more general and at the same Time less sophisticated approaches are desired. In this paper, an analytical method is proposed to evaluate the required outcrossing rate in which the basics of "Parallel System Reliability Formulation" in the framework of directional simulation are used. To indicate the accuracy and efficiency of the method, it is applied to carry out the reliability analysis of a hydrokinetic turbine blade. Since the random variables/processes involved in this analysis possess a set of extremely different variances (and thus make a so-called "non-proportional space); it is shown that the proposed method is also capable to satisfactorily employ a technique of directional importance sampling in order to prohibit massive computations, normally required in such spaces. The results of the analysis show that the proposed method could be successfully applied for the circumstances whose involving processes may be non-stationary and whose space of random variables/processes is extremely non-proportional.

This paper is concerned with the problem of delay-dependent passive analysis and control for interval stochastic Time-delay systems. The system matrices are assumed to be uncertain within given intervals, the Time delay is a Time-varying continuous function belonging to a given range, and the stochastic perturbation is in the form of a Brownian motion. By using ItO's differential formula and the Lyapunov stability theory, delay-dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the Time delay. Based on the criteria obtained, a delay-dependent passive controller that ensures the stochastic passivity of the closed-loop system is presented. Then, the controller gain is characterized in terms of LMIs, which can be easily checked by resorting to available software packages. Numerical examples are given to demonstrate the effectiveness of the method.

Natural gas consumption fluctuates due to seasonal demand, extraction limitations, price changes, and political conflicts. These fluctuations necessitate the storage of natural gas. Among various storage methods, salt caverns have several advantages for storing hydrocarbons compared to other methods. These advantages include the low permeability of rock salt and the low cost of construction. However, salt caverns may be affected by weak layers such as marl or mudstone within the formation’s layering sequence. This research aimed to numerically study the long-term behavior of a salt cavern excavated in interbedded salt rock with weak interlayers. The effects of placement angle (0°, 30°, 45° and 60°), layer thickness (10, 15 and 20 meters), number of (1 or 2 or 3) and three different levels on operational Time were analyzed. FLAC3D finite difference software was selected because of its Cpower creep behavior model. A total of twenty-two numerical models were executed. The results emphasize the importance of level, placement angle, thickness and interlayers numbers on displacement, stability and safety of a salt cavern over its operational Time. The Ratigan dilatancy safety factor is not suitable for assessing the effects of geometric parameters of interlayers on salt cavern stability. Generally, constructing a cavern in salt layers containing weak interlayers is not recommended.

An analysis of the unsteady-state thermo-mechanical problem of functionally graded thick-walled spheres is presented in this paper. The material properties, except Poisson's ratio, are assumed to be an arbitrary function of radial direction. Considering linearly increasing boundary temperature and employing Laplace transform techniques, the Time-dependent temperature is obtained. In a special case, by assuming the material properties to follow a power-law function, the Navier equation is solved for an arbitrary Time. This led to radial displacement, radial stress, and hoop stress as a function of radial direction. In the numerical results calculated by FEM software, ABAQUS is compared to the analytical results. The present results agree well with existing analytical results.

In this paper, a new approach for constructing quadratic Lyapunov-Krasovskii functionals for a class of nonlinear Time-delay systems is developed. The functionals are then used to derive delay dependent stability conditions. These conditions are sufficient and local. Numerical example shows that the results obtained using the proposed method is less conservative than those obtained by the existing methods.