Nonlinear forced vibrations of curved microbeam resting on nonlinear foundation using the modified strain gradient theory

The nonlinear forced vibrations of a curved micro- beam resting on the nonlinear foundation are examined. The equations of motion are derived using the Hamilton's principle and the modified strain gradient theory which is capable to examine the size effects in the microstructures. The nonlinear partial differential equations of motion are reduced to a time-dependent ordinary differential equation containing quadratic and cubic nonlinear terms. A frequency response of the curved microbeam for the primary resonance is determined using multiple time scales perturbation method. From the application point of view, the frequency response curves may be useful to select the optimum values of design parameters. The effects of geometry parameters and foundation moduli on the vibration behavior of the curved microbeam are illustrated.Розглянуто нелінійні змушені коливання викривленої мікробалки, яка лежить на нелінійній основі.Рівняння руху отримані на основі принципу Гамільтона і модифікованої теорії градієнтів деформації. що дає змогу вивчити ефекти розміру в мікроструктурі. Нелінійні рівняння руху з частинними похідними зведено до залежного від часу рівняння, яке містить квадратично і кубічно нелінійні члени. Визначено частотну характеристику викривленої балки для першого резонансу, для чого використано метод багатомасштабних у часі збурень. З прикладної точки зору, криві частотної характеристики можуть бути корисними для вибору оптимальних значень параметрів при проектуванні. Проілюстровано вплив геометричних параметрів модулів основи на коливання викривленої мікробалки

A new approach in separation process evaluation. Efficiency ratio and upgrading curves

In mineral processing separation efficiency (SE), operation efficiency (OE), selectivity index (SI) and other indices have been used to evaluate the separation process. Up to now, no study has been conducted on the relationship between the SE, OE and SI indices. In this research, two upgrading curves are proposed based on the above indices for process and selectivity evaluation. The first upgrading curve is based on recovery R, SE, and OE as a function of concentrate grade. This curve has three background lines, including no upgrading line, ideal upgrading line and the ideal mixing line. The proposed upgrading curve is applicable not only for process evaluation by specification of OE and SE, but also for selectivity evaluation with the lowest difference between SE and OE. The curve showed that the recovery value is always greater than the SE and OE values. The parameters of OE, SE and R were used for plotting the upgrading curve as a function of concentrate grade taking into consideration all of them at a time. A new selectivity indicator, namely Efficiency Ratio (ER) as the selectivity parameter, is proposed as the ratio of OE to SE. The ER values fluctuate between 1 and . It can be presented as a function of concentrate and tailing grades (ER = [c(1-t)]/[1(c-t)]). The results showed that ER is insensitive to the feed grade and has the inverse relationship with SI. To measure the separation selectivity, another upgrading curve is proposed based on ER and SI parameters. This curve is divided into seven separation classes for evaluation the class of a separation process from ideal class to no separation one. The results of this research can be useful for separation process evaluation

Pulsed laser deposition of bismuth telluride thin film and annealing effects

Pulsed laser deposition method was used to prepare Bi2Te3 thermoelectric thin films on a soda lime glass substrate at room temperature. Surface morphology of Bi2Te3 thin films was studied by AFM (atomic force microscopy) images. The influence of thermal annealing in vacuum condition on microstructure and surface morphology of films was investigated in wide range of temperature. The results demonstrate that annealing induces a transition from amorphous to polycrystalline structures and increases electrical conductivity. X-ray diffraction analysis proves that the film annealed at 300 °C for 120 min appears in large grain size polycrystalline structure but film annealed at 400 °C in the same condition has a preformed crystal growth texture in (006) direction