Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

In the literature, several correlations have been proposed for bubble size prediction in bubble columns. However these correlations fail to predict bubble diameter over a wide range of conditions. Based on a data bank of around 230 measurements collected from the open literature, a correlation for bubble sizes in the homogenous region in bubble columns was derived using Artificial Neural Network (ANN) modeling. The bubble diameter was found to be a function of six parameters: gas velocity, column diameter, diameter of orifice, liquid density, liquid viscosity and liquid surface tension. Statistical analysis showed that the proposed correlation has an Average Absolute Relative Error (AARE) of 7.3 % and correlation coefficient of 92.2%. A

This paper demonstrates an experimental and numerical study on the behavior of reinforced concrete (RC) columns with longitudinal steel embedded tubes positioned at the center of the column cross-section. A total of 12 pin-ended square sectional columns of 150 × 150 mm having a total height of 1400 mm were investigated. The considered variables were the steel tube diameters of 29, 58, and 76 mm and the load eccentricity (0, 50, and 150) mm. Accordingly, these columns were divided into three groups (four columns in each group) depending on the load eccentricity (e) to column depth (h) ratio (e/h = 0, 1/3, and 1). For each group, one column was solid (reference), and the other three columns contained steel tubes with hollow rat

Glass Fiber Reinforced Polymer (GFRP) beams have gained attention due to their promising mechanical properties and potential for structural applications. Combining GFRP core and encasing materials creates a composite beam with superior mechanical properties. This paper describes the testing encased GFRP beams as composite Reinforced Concrete (RC) beams under low-velocity impact load. Theoretical analysis was used with practical results to simulate the tested beams' behavior and predict the generated energies during the impact loading. The impact response was investigated using repeated drops of 42.5 kg falling mass from various heights. An analysis was performed using accelerometer readings to calculate the generalized inertial load. The in

The provision of openings in serviceable reinforced concrete beams may result in a substantial decline in the beam's capacity and integrity, indicating the necessity of opening strengthening. The present study investigates the experimental response of reinforced concrete T-beams with multiple web-strengthened openings disposed in shear span to static and impact loads. Fourteen RC T-beams were tested in two groups, each of seven beams. The first group was tested under static loading up to failure, while the second group was tested under repeated impact loading until the width of shear cracks reached 0.3 mm. The residual static strengths of the beams subjected to impact loading were then determined. The test variables considered were

The provision of openings in serviceable reinforced concrete beams may result in a substantial decline in the beam's capacity and integrity, indicating the necessity of opening strengthening. The present study investigates the experimental response of reinforced concrete T-beams with multiple web-strengthened openings disposed in shear span to static and impact loads. Fourteen RC T-beams were tested in two groups, each of seven beams. The first group was tested under static loading up to failure, while the second group was tested under repeated impact loading until the width of shear cracks reached 0.3 mm. The residual static strengths of the beams subjected to impact loading were then determined. The test variables considered were

Glass Fiber Reinforced Polymer (GFRP) beams have gained attention due to their promising mechanical properties and potential for structural applications. Combining GFRP core and encasing materials creates a composite beam with superior mechanical properties. This paper describes the testing encased GFRP beams as composite Reinforced Concrete (RC) beams under low-velocity impact load. Theoretical analysis was used with practical results to simulate the tested beams' behavior and predict the generated energies during the impact loading. The impact response was investigated using repeated drops of 42.5 kg falling mass from various heights. An analysis was performed using accelerometer readings to calculate the generalized inertial load