In this paper, an analytical solution describing the deflection of a cracked beam repaired with piezoelectric patch is introduced. The solution is derived using perturbation method. A novel analytical model to calculate the proper dimensions of piezoelectric patches used to repair cracked beams is also introduced. This model shows that the thickness of the piezoelectric patch depends mainly on the thickness of the cracked beam, the electro-mechanical properties of the patch material, the applied load and the crack location. Furthermore, the model shows that the length of the piezoelectric patches depends on the thickness of the patch as well as it depends on the length of the cracked beam and the crack depth. The additio

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Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is

In this work, the effects of size, and temperature on the linear and nonlinear optical properties in InGaN/GaN inverse parabolic and triangular quantum wells (IPQW and ITQW) for different concentrations at the well center were theoretically investigated. The indium concentrations at the barriers were fixed to be always x_max = 0.2. The energy levels and their associated wave functions are computed within the effective mass approximation. The expressions of optical properties are obtained analytically by using the compact density-matrix approach. The linear, nonlinear, and total absorption coefficients depending on the In concentrations at the well center are investigated as a function of the incident photon energy for different