In this paper, the vibration characteristics of the cantilever rectangular plate with side crack are studied in the way of analysis, which including natural frequency and mode shape. The influences of different parameters of crack, such as the locations and lengths of crack, to the vibration characteristics of the cantilever rectangular plate are investigated. The modal function of the crack plate consists two parts, which are (1) the modal function of intact cantilever rectangular plate from beam functions combination method and (2) corner functions presenting the discontinuity of displacement and slope along the crack. The natural frequencies and modal shapes can be obtained when taking the modal function into the method of Ritz. At last, the effects of the crack location and crack length on the vibration characteristics are investigated, and it could provide the theoretical basis for engineering application and the relevant study.

Ferrous micro-beads from fly-ash were used as starting material to prepare CoZn-Z type barium ferrite. As the main impurity in the beads, SiO2plays an important role on the electromagnetic properties of the ferrites. To investigate the effect of SiO2content, a series of CoZn-Z type ferrites with various contents of SiO2(1 wt%, 2 wt% and 5 wt%) were prepared with analytical pure Fe2O3and SiO2. The density, phase composition, microstructure and electromagnetic properties of the sintered samples were investigated. The results show that the permeability of samples alters little at a low content of SiO2about 1 wt%, but deteriorates dramatically when the addition of SiO2is above 2 wt%. The ferrous micro-beads were then treated by alkali cleaning to reduce the content of SiO2to about 1 wt%, and the samples prepared with these treated beads show a similar performance on the electromagnetic properties with pure CoZn-Z type ferrite.

Many practical problems emphasize the importance of not only knowing whether an element is selected but also deciding to what extent it is selected, which imposes a challenge on submodule optimization. In this study, we consider the monotone, nondecreasing, and non-submodular maximization on the integer lattice with a cardinality constraint. We first design a two-pass streaming algorithm by refining the estimation interval of the optimal value. For each element, the algorithm not only decides whether to save the element but also gives the number of reservations.Then, we introduce the binary search as a subroutine to reduce the time complexity. Next, we obtain a one-pass streaming algorithm by dynamically updating the estimation interval of optimal value. Finally, we improve the memory complexity of this algorithm.

In this paper, the physical model of the cantilever beam with a surface crack is established to study the free vibration of the cracked beam from three aspects that are theoretical analysis, FEM analysis, and experiment. At the same time, the relation between the crack parameter and the vibration characteristics, which are natural frequencies and the modes of each order, is obtained through analysis. The theoretical analysis is on the basis of the mode analysis theory and applied mechanics. The crack is regarded as a flexible hinge. Utilizing the external boundary conditions and internal boundary conditions at the crack, the free vibration characteristics are obtained combining with the vibration mechanics. With the ANSYS software, a finite element model of the cracked beam is established by the beam element. During the process of calculation, it calculates the natural frequencies and the modes of cracked beam with different parameters of crack. The results obtained from the experiment are in agreement with the results obtained from the theoretical and the FEM analysis. So the accuracy of the theoretical analysis and the numerical simulation is verified by the experiment. At last, the effects of the crack location and depth on the natural frequencies and modes of each order are shown, and it could provide the theoretical, numerical and experimental basis for the identification of cracked materials and the relevant study.

Team formation problem is a very important problem in the labor market, and it is proved to be NP-hard. In this paper, we design an efficient bicriteria streaming algorithms to construct a balance between gain and cost in a team formation problem with cardinality constraint on the integer lattice. To solve this problem, we establish a model for maximizing the difference between a nonnegative normalized monotone submodule function and a nonnegative linear function. Further, we discuss the case where the first function is α-weakly submodular. Combining the lattice binary search with the threshold method, we present an online algorithm called bicriteria streaming algorithms. Meanwhile, we give detailed analysis for both of these models.