In this investigation, Rayleigh–Ritz method is used to calculate the natural frequencies of rectangular isotropic and laminated symmetric and anti-symmetric cross and angle ply composite plate with general elastic supports along its edges. Each of the admissible functions here is composed of a trigonometric function and an arbitrary continuous function that is introduced to ensure the sufficient smoothness of the so-called residual displacement function at the edges. Perhaps more importantly, this study has developed a general approach for deriving a complete set of admissible functions that can be applied to various boundary conditions. Several numerical examples are studied to demonstrate the accuracy and convergence of the current s

In this study, the modified Rayleigh-Ritz method and Fourier series are used to determine the thermal buckling behavior of laminated composite thin plates with a general elastic boundary condition applied to in-plane uniform temperature distribution depending upon classical laminated plate theory(CLPT). A generalized procedure solution is developed for the Rayleigh-Ritz method combined with the synthetic spring technique. The transverse displacement of the orthotropic rectangular plates is not a different term as a new shape expansion of trigonometric series. In this solution approach, the plate transverse deflection and rotation due to bending are developed into principle Fourier series with a sufficient smoothness auxi

This study investigates the influence of asymmetric involute teeth profiles for helical gears on the bending stress. Theoretically, bending stress has been estimated in spur involute gears which have symmetric teeth profile by based on the Lewis, 1892 equation. Later, this equation is developed by, Abdullah, 2012. to determine the effect of an asymmetric tooth profile for the spur gear on the bending stress. And then these equations are applied with stress concentration factor once for symmetric and once other for asymmetric teeth profile. In this paper, the bending stresses for various types of helical gear with various types of asymmetric teeth profile are calculated numerically for defined the stress concentration fac

Previously, many empirical models have been used to predict corrosion rates under different CO₂ corrosion parameters conditions. Most of these models did not predict the corrosion rate exactly, besides it determined effects of variables by holding some variables constant and changing the values of other variables to obtain the regression model. As a result the experiments will be large and cost too much. In this paper response surface methodology (RSM) was proposed to optimize the experiments and reduce the experimental running. The experiments studied effects of temperature (40 – 60 °C), pH (3-5), acetic acid (HAc) concentration (1000-3000 ppm) and rotation speed (1000-1500 rpm) on CO₂ corrosion performance of t

In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

Phenylthiourea  (PHTU),was  tested  as  inhibitor for  the  corrosion  of  low  carbon  steel  in different  HCI  acid concentration by mass loss ,and polarization measurements .it was found that (PHTU) is a good inhibitor for the corrosion of low carbon steel in 1,3,and 5N HCI solution ,and its inhibition efficiency (0) increases with its concentration and attains approximately 97% at l g/I .polarization curves indicate that (PHTU) acts as an anodic type inhibitor .the inhibitor was adsorbed on the low carbon steel surface according to the Langmuir adsorption isotherm model. Results show that the rate of corrosion of low carbon steel increased with increasing temperature o

The inhibitor property of curcuma longa L. extract in different concentrations of simulated refinery wastewater (0.05% - 2% wt) and at various temperatures (30, 35 and 40 ˚C) was investigated using weight loss method. The results showed that the presence of about 1.2 % (v/v) of curcuma extract gave about 84% inhibition indicating its effectiveness on mild steel corrosion in simulated refinery wastewater, besides the adsorption process on the mild steal surface obeyed the Langmuir adsorption isotherm.