The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors. To achieve this end, by taking cubic-type elements into account, isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness. The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation. For the simply supported microsized uniform porous functionally graded material (U-PFGM) plate having the oscillation amplitude equal to the plate thickness, it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%, the dilatation gradient tensor causes to reduce it about 1.93%, and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%. On the other hand, for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness, these percentages are equal to 0.62%, 1.64%, and 4.40%, respectively. Accordingly, it is found that by changing the boundary conditions from clamped to simply supported, the effect of microsize on the reduction of frequency ratio decreases a bit.
Let Mn denote the partial maximum of a strictly stationary sequence (Xn). Suppose that some of the random variables of (Xn) can be observed and let [(M)\tilde]n\tilde M_n
stand for the maximum of observed random variables from the set {X1, ..., Xn}. In this paper, the almost sure limit theorems related to random vector ([(M)\tilde]n\tilde M_n
, Mn) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies
some regular conditions. 相似文献
A chiral secondary amine phosphoramide was developed and identified as a powerful catalyst for the Mukaiyama–Michael addition of fluorinated enol silyl ethers to tetrasubstituted olefins. The resulting products are obtained with high enantioselectivities and contain a quaternary carbon stereocenter bearing either a difluoroalkyl or monofluoroalkyl group. 相似文献
A series of (Fe57Co24Ni4Nb2B13)x-(SiO2)1−x nano-granular thin films were fabricated by magnetron sputtering with different oblique incidence angle θ and excellent soft magnetic properties are achieved. Based on the results of magnetic field anneal at different temperature Ta, it is evidenced that orientation of atomic pairs contributes to the annealing treatment, and could manipulate magnetic anisotropy. The damping coefficient α decreases with increasing angle θ and this is ascribed to the anisotropy dissipation. 相似文献
In this paper, a deteriorating simple repairable system with k + 1 states, including k failure states and one working state, is studied. The system after repair is not ‘as good as new’ and the deterioration of the system is stochastic. Under these assumptions, we study a replacement policy, called policy N, based on the failure number of the system. The objective is to maximize the long-run expected profit per unit time. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal solution may be determined analytically or numerically. Furthermore, we prove that the model for the multistate system in this paper forms a general monotone process model which includes the geometric process repair model as a special case. A numerical example is given to illustrate the theoretical results. 相似文献