In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating Rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

Packing Rectangular shapes into a Rectangular space is one of the most important discussions on Cutting & Packing problems (C&P); such as: cutting problem, bin-packing problem and distributors pallet loading problem, etc. Assume a set of Rectangular pieces with specific lengths, widths and utility values. Also assume a Rectangular packing space with specific width and length. The objective function is, to pack the pieces into the space in Order to get the maximum sum of utility value of the packed pieces. To generate the related packing pattern this paper proposes a new formulation metl10dbased on the column generation, approach. In this method one each cycle of the algorithm; a one-dimensional pattern is generated based on the shadow prices 'Of the Simplex method. The set of generated one-dimensional patterns are used: to construct the two-dimensional packing pattern. Also, the proposed model and the present models in the.state-of-1beart have been compared.

We first prove that there always exists a maximal Rectangularly dualizable graph for a given Rectangularly dualizable graph and present an algorithm for its construction. Further, we show that a maximal Rectangularly dualizable graph can always be transformed to an edge-irreducible Rectangularly dualizable graph and present an algorithm that transforms a maximal Rectangularly dualizable graph to an edge-irreducible Rectangularly dualizable graph.

Due to the energy concerns, it is always desired to run the mechanical elements under optimized operating conditions. Many lubricated mechanical elements such as gears, rolling element bearings, cam and followers etc. usually operate under mixed-lubrication regime. In this regime, both the lubricant film as well as the asperities contribute in carrying the load. The life span of these elements is divided into two regimes: running-in and steady-state. In this research an efficient model has been presented to predict the variation in asperities height during running-in. The predicted results are verified with experimentally-obtained published data. A parametric study on the effect of operating conditions such as load and speed as well as initial surface roughness and material hardness on the roughness variation during running-in has been conducted.

Introduction: Labyrinth weirs compare with straight weirs had required less freeboard in upstream so they are more appropriate for the irrigation networks. So they could maked more space to sotrage water and restrained foold with higher discharge. Labyrinths weirs have three generally form triangles, trapezoidal and Rectangular that Tullis et al. (15) presented formula (3) for discharge coefficient of labyrinth weirs (triangles and Rectangular) and a few studiescarried out on Rectangular shape and its hydraulic characteristics are not specified.Therefore main aim of this paper study and characterized hydraulic characteristics of Rectangular labyrinth weirs by using laboratory data.Materials and Methods: In this study Rectangular labyrinth weir discharge and coefficient discharge relationships used dimensional analysis and experiment on hydraulic modeling, constant coefficient was defined.Laboratory flume is shown in Figure 2 (0.5 m wide x 12 m long x 0.8 m deep). Models was made from clear plexiglass plate with 10 cm thickness thatcuted using leaser device and the crest manualy shaped quadrant with radius 10 cm, all models using silicon glue install in the flume. The upstream depth readership by point gauge that installed in upstream of models. Discharge calcutaed byupsterm depth of triangular weir that installed in down stream of flume. Data were analyzed by SPSS software and to compare relationships with each other used two parameter root mean square error and correlation coefficient and charts darw in Excel Results and Discussion: discharge coefficient formula (11) carried out by using SPSS software that compared with formula (3). Results showed (Tables 2 and 3) that the correlation coefficient of formula (11) was more than a formula (3) and formula (11) RSME was less than formula (3) RSME except in first and fifth hydraulic model (rectengular1 and 5) that they were almost equal. So the formula (11) was more accurate than a formula (3) to peredict discharge of flow in flume. In previous step we used all data, we saw flourmloa (11) had more accurate then we diceded data divided in to three groups: high change, length change and all that calculated correlation coefficient and RSME for formula (11) to figure out which group have more accurate, results was brought in table 4. The result showed that constant coefficient of formula (11) yields from all data was useful for the design proposed. Plotted discharge changes against H/P for Rectangular labyrinth and straight weirs in Figs.3 and 4. In constant discharge and high with raising length weir, decreased depth of flow over the weir because the effective weir length was raised and the ratio of distributed length to apex length (b) was decreased. As well as in constant H/P and high weir with raising apex length, discharge was increased that similarity of the results of Tullis et al. (15) and Khode et al. (8). In length, and the ratio H / P constant with increasing height in the discharge coefficient due to submergence reduce local side Jt Hay reduce interference, but increases with increasing height from 0.20 to 0.25m m discharge coefficient decreases as flow rate and Weber number decreased as a result of the effect of surface tension and increased resistance to flow. In length, and the ratio H / P fixed amount of overflow discharge increases with increasing height as the ratio H / P value of the denominator increases and therefore increases the total height of the water upstream. For design overflow Rectangular labyrinth weirs recommends0.20£H/P£0.40that maximum aeration and discharge coefficient in this range is the result of Hay and Taylor (7) and Darvas (4) is consistent. In discharge and fixed weir height and maximum height of the water upstream directly at least equal to 1.8 of the overflow stright weirs. So for the areas where there is a height restriction of water upstream, the water level upstream of Rectangular labyrinth weirs less direct overflow weirs requires the use of this is recommended.Conclusion: The results showed the relationship (11) that uses most of effective parameters has more accurate results and proposed for design aim. In constant water head upstream discharge of labyrinth weir maximum 2.6 times more than straight weir discharge and in constant discharge water head upstream of straight weir 1.8 times more than upstream labyrinth weir water head so use a labyrinth weir appropriate for areas that have head and discharge restrictions. Best range of ratio H/P for of design was 0.20 to 0.40 and maxim coefficient discharge happened in this range.

Submerged Rectangular orifice is among discharge measuring device which is suitable in small canal especially when the amount of fallis not adequat for application of weir, during the past decade many study have been conducted for evaluation of discharge coefficient of orifice. For free the case of submerged orifice only an average value of 0.61 has been mentiond in the literature. Since this coefficient depends to the flow characteristics and the orifice dimensions, an equation for determination of discharge coefficient is needed. The development of such formula is the main goal of this study. To do so an experimental program was conducted and applying the dimensional analysis and data obtained from these tests, one relation was developed. This relation can be used where an accurate value of the discharge coefficient and consequently the flow discharge is needed.

A topological index is a real number related to a graph, which is considered as a structural invariant. Some examples are Sombor index, Randi´c index, Zagreb indices, and Harmonic index. In the present paper, we consider the function Ind from the set of all Rectangular grids to the set of real numbers, which assigns to each Rectangular grid, one of its above indices. Then we show that the only non-degenerate indices over retangular grids, are Sombor index and Randi´c index, while Zagreb indices and the Harmonic index are degenerate. In the following, we determine Rectangular grids with fixed diameter d, where maximum and minimum of the above indices occures on them, in the case m ≥ 3, n ≥ 3. Finally, we find the amounts of these indices.