Optimal Design of Large Circular Vibrating Screen Based on MultipleFrequencies Constraints and Analytical Sensitivity Methods
Multiple frequencies constraints and analytical sensitivity methods were used in structural optimization design of the side plate of 4YK1860 vibrating screen to lower the damage of side plate caused by high dynamic stress. The mass of side plate of the vibrating screen was taken as object function, mode frequencies were regarded as state parameters, size of plate were used as constraint parameters and an optimization criterion which is applicable to solve this kind of problem was given. Meanwhile, sensitivity characteristics of variable parameters were considered during the process of optimization. The results show that the optimization program with embedded analytical sensitivity calculation methods is of a higher solving precision and with a more stable calculating process. After structure optimization, the thickness of side plate to withstand large impact is increased, the thickness of stiffener and peripheral angle are decreased, the mass of side plate is reduced by 7.75% and a better optimization effect is achieved. The analysis of the optimal vibrating screen presents that the mass of vibrating screen decreases by 3.5%, elastic deformation frequency which is close to the working frequency increases by 8.8% and the dynamic stress decreases by 48%. The natural frequencies of vibrating screen are improved and modal frequency is far from the working frequency of the exciting motor, stress concentration of vibrating screen is weakened and thus the structural stiffness and reliability of vibrating screen is enhanced.
A unified approach for shape sensitivity analysis of elastic shells
A shape sensitivity analysis is presented of a shell loaded along its boundary, within the framework of a linear elastic approach that takes into account the effect of transverse shear deformation. By making an analogy with continuum mechanics and taking advantage of the concept of the total (time) derivative in its spatial description, an explicit general expression for the shape derivative of the total potential energy is obtained in terms of the strain–stress state and the shell shape change velocity field. For this purpose, a suitable velocity distribution over the middle surface of the shell, decomposed on a local basis given by the unit normal and the tangent plane of the shell, is adopted. This approach and the direct method of shape sensitivity analysis leads to a very useful expression for the shape sensitivity of the total potential energy. This expression is an explicit function of the tangent and normal components of the known velocity field that characterizes the shape change of the shell.
Growth from Solutions
Growth from solutions is the crystallization of a compound whose chemical composition differs markedly from that of the initial liquid phase. Commonly used solvents are water, multicomponent aqueous or nonaqueous solutions, and melts of some chemical compounds. Differentiations are made based on growth temperatures and on the chemical nature of the solvent. In growth from low-temperature aqueous solutions, the temperatures generally do not exceed 80–90°C; in growth from superheated aqueous solutions (hydrothermal method), they reach 800°C, and in growth from salt melts (molten-salt, flux, or fluxed melt growth), they usually do not exceed 1200–1300°C, but sometimes reach 1500°C.