Abstract:Integral transforms have wide applications in the various disciplines of engineering and science to solve the problems of heat transfer, springs, mixing problems, electrical networks, bending of beams, carbon dating problems, Newton's second law of motion, signal processing, exponential growth and decay problems. In this paper, authors discussed the duality relations of Kamal transform with Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms. Tabular presentation of Laplace transform, L… Show more
“…After conducting experiments with moving loads on the beams, as in Refs. 54,55 we will get the beam's deflection signals corresponding to different excitation conditions, as shown in Figure 7. The beam's deflection graph is shown in Figure 7, with the moving speed of load V 1 performing the experiments at many different speeds from V 1 to V 6 .…”
Section: Results and Commentsmentioning
confidence: 99%
“…After conducting experiments with moving loads on the beams, as in Refs. 54,55 we will get the beam’s deflection signals corresponding to different excitation conditions, as shown in Figure 7.Figure 7.The signal received from the translocation sensor corresponding to the levels of velocity V 1 .…”
A defective structure has been evaluated and identified in beam models’ deflection measurement signals in much research. However, many results have not been optimally exploited and evaluated to find new parameters for data excavation. This manuscript proposes a cumulative welding model and a cumulative circle of deflection signals for a defective beam under the impact of a moving force. Based on this evaluation model, the manuscript recognizes that the speed of the moving force will determine the regression speed of the received datasets, which is considered the basis for showing the working ability of a beam structure with defects. Moreover, the structure’s cumulative regression circle also shows its resilience in that structure after the impact of the load. The development of defects in the structure will depend on both the structure’s level and resilience after each bearing-load cycle. Our research has shown us that the method of evaluation and use of both the cumulative model and cumulative circle from the deflection’s measured value have yielded more results compared to the previous method. This research can evaluate many defects in different situations while simultaneously evaluating many types of structures.
“…After conducting experiments with moving loads on the beams, as in Refs. 54,55 we will get the beam's deflection signals corresponding to different excitation conditions, as shown in Figure 7. The beam's deflection graph is shown in Figure 7, with the moving speed of load V 1 performing the experiments at many different speeds from V 1 to V 6 .…”
Section: Results and Commentsmentioning
confidence: 99%
“…After conducting experiments with moving loads on the beams, as in Refs. 54,55 we will get the beam’s deflection signals corresponding to different excitation conditions, as shown in Figure 7.Figure 7.The signal received from the translocation sensor corresponding to the levels of velocity V 1 .…”
A defective structure has been evaluated and identified in beam models’ deflection measurement signals in much research. However, many results have not been optimally exploited and evaluated to find new parameters for data excavation. This manuscript proposes a cumulative welding model and a cumulative circle of deflection signals for a defective beam under the impact of a moving force. Based on this evaluation model, the manuscript recognizes that the speed of the moving force will determine the regression speed of the received datasets, which is considered the basis for showing the working ability of a beam structure with defects. Moreover, the structure’s cumulative regression circle also shows its resilience in that structure after the impact of the load. The development of defects in the structure will depend on both the structure’s level and resilience after each bearing-load cycle. Our research has shown us that the method of evaluation and use of both the cumulative model and cumulative circle from the deflection’s measured value have yielded more results compared to the previous method. This research can evaluate many defects in different situations while simultaneously evaluating many types of structures.
“…When handling non-infinite signals or signals with restricted frequency, M.T. performs better [5,6,8]. A wide range of problems involving differential equations, partial differential equations, integral equations, and population development and decay are among the many uses of M.T.…”
In recent years, Mohanad transform, a mathematical approach, has drawn a lot of interest from researchers. It is useful for solving many engineering and scientific problems, such as those involving electric circuits, population growth, vibrational beams, and heat conduction. The Mohanad transform is defined and introduced in this study, along with its fundamental qualities,including linearity and convolution. It is also discussed in connection with other integral transforms and how it is used in derivatives. Additionally, we use the Mohanad transform to solve a few systems of ordinary differential equations (ODEs) and review its properties in this paper. Determining the concentration of a chemical reactant (material) in a series is a physical chemistry problem that we use in the application part. We achieve this by developing a model based on ordinary differential equations (ODEs) and then solving them using the Mohanad transform. This research proves that, with little computational effort, we can get the exact solutions of ordinary differential equations (ODEs) via the Mohanad transform. We used graphs and tables to show our answer.
“…Higazy et al [47] introduced a new decomposition method "Sawi decomposition method" to determine the solution of Volterra integral equation. Aggarwal with other scholars [48][49][50][51][52][53][54][55] introduced the relations of duality among the established integral transformations. Ali et al [56] determined the solution of fractional Volterra-Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method.…”
The solution of various problems of engineering and science can easily determined by representing these problems in integral equations. There are numerous analytical and numerical methods which can be used for solving different kinds of integral equations. In this paper, authors used recently developed integral transform “Rishi Transform” for obtaining the analytical solution of linear Volterra integral equation of second kind (LVIESK). For this, the kernel of LVIESK has assumed a convolution type kernel. Five numerical examples are considered for demonstrating the complete procedure of determining the solution. Results of these problems suggest that Rishi transform provides the exact analytical solution of LVIESK without doing complicated calculation work.
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