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

Background: Titanium implant is widely used in dentistry because of its extraordinary biocompatibility and mechanical properties. To increase bone–implant connection and provide early loading after placement, implant is stored in different storage medium and treated with UV light. Both of them are applicable methods to increase the bioactivity of titanium and overcome the biological aging. This study was designed to assess the effect of vacuum storage method and air storage with and without UV light treated of Cp Ti implant mechanically and histologically. Materials and methods: Titanium screws were acid etched and prepared in four different modes using different storage methods (air or vacuum and, with or without UV treatment. The implan

Buckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g

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

Critical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge

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

In this research the behavior of reinforced concrete columns with large side openings under impact loads was studied. The overall cross sectional dimensions of the column specimens used in this research were (500*1400) mm with total height of (14000) mm. The dimensions of side openings were (600*2000) mm. The column was reinforced with (20) mm diameter in longitudinal direction, while (12) mm ties were used in the transverse direction. The effect of eccentric impact loads on the horizontal and vertical displacement for this column was studied.                              &