| dc.description.abstract |
Mathematical modeling skills are essential in both engineering and engineering education. These skills enable a deeper understanding of the phenomena being studied and help bridge the gap between theoretical and experimental communities. The objective of this research is to progress towards a theoretical analysis of nonlinear physical structures in vibrating systems, utilizing the homotopy perturbation method (HPM). Specifically, the physical structures being studied are the vibration of a vehicle passing over a speed bump and bungee jumping problems. Speed bumps are critical traffic safety features found in urban roads and expressways, which play a vital role in preventing traffic accidents, but their impact on vehicle vibrations and passenger comfort, are a significant concern. On the other hand, bungee jumping is an increasingly popular and adventure sport worldwide. Many sporting organizations and government agencies have developed codes of practice for bungee jumping. The speed bump model is modified to nonlinear damped equation and extended to external force and bungee jumping system is modified to nonlinear damped equation, which make the problems more realistic. We have chosen the HPM and He’s Frequency amplitude method (HFAM) as effective mathematical tools to solve these problems. The results derived by the proposed techniques agree harmoniously with the obtained numerical solutions through the fourth-order Runge-Kutta method (RK4) nicely, which proves the validity and accuracy of them. The dynamic behaviors of the solution and phase diagram are discussed; some plots of the solution of the nonlinear system are drawn graphically to show the impact of the distinct parameters. |
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