Research Article
Modelling and Simulation of Engineering Design,
A Second-Order Differential Equations in Mechanical and Electrical Systems
Issue:
Volume 15, Issue 3, June 2026
Pages:
53-63
Received:
4 April 2026
Accepted:
20 April 2026
Published:
22 September 2026
Abstract: This paper presents a rigorous and systematic investigation into the fundamental role of second-order ordinary differential equations (ODEs) in the modelling, analysis, and design of engineering systems. The study is anchored on two canonical and cross-disciplinary case studies: the quarter-car suspension system and the series RLC circuit. For each system, the governing differential equations are derived from first principles using Newtonian and Kirchhoffian formulations, respectively, followed by complete analytical solutions obtained via the characteristic (auxiliary) equation framework.The classical dynamic response includes underdamped, critically damped, and overdamped are comprehensively analyzed, with explicit linkage to practical engineering design criteria. In particular, damping ratio targets are contextualized within industry standards, where passenger vehicle suspensions typically operate within ζ ≈ 0.3–0.4 to ensure ride comfort, while high-performance systems adopt ζ ≈ 0.65–0.70 to achieve improved transient response characteristics. The forced harmonic response is further examined, with emphasis on resonance behavior, amplitude amplification, and stability considerations, highlighting its critical implications for structural integrity and failure prevention, as exemplified by the Tacoma Narrows Bridge collapse. A unified cross-domain analytical framework is established, demonstrating that mechanically and electrically distinct systems are governed by mathematically analogous second-order ODEs. This analogy enables the transfer of insights and design strategies across engineering domains. Furthermore, numerical solutions obtained using the Euler method and the fourth-order Runge–Kutta (RK4) algorithm are systematically benchmarked against exact analytical solutions. Convergence and error analyses confirm the superior accuracy of RK4 with global truncation error of order O(h⁴), compared to the first-order accuracy O(h) of the Euler method. The paper concludes by highlighting key design implications and emphasizing the transformative role of simulation-driven engineering in accelerating system development, optimizing performance, and reducing reliance on costly experimental prototyping.
Abstract: This paper presents a rigorous and systematic investigation into the fundamental role of second-order ordinary differential equations (ODEs) in the modelling, analysis, and design of engineering systems. The study is anchored on two canonical and cross-disciplinary case studies: the quarter-car suspension system and the series RLC circuit. For each...
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Research Article
AI-Enabled Adaptive Process Control and Decision-Making Framework for Advanced Metal 3D Printing Systems
Fasil Kebede Tesfaye*
,
Abraham Debebe Woldeyohannes
Issue:
Volume 15, Issue 3, June 2026
Pages:
64-73
Received:
29 August 2026
Accepted:
8 September 2026
Published:
9 October 2026
Abstract: Metal 3D Printing, Laser Powder Bed Fusion and Directed Energy Deposition is a deal for making complex metal parts. We can make these parts with a lot of design freedom and material efficiency. Even with a lot of progress it is not widely used in industries. This is because of some problems like process instability, defects and stress buildup. Most research looks at process modeling, control and optimization. This means we do not have a system that can support autonomous manufacturing. This study proposes a framework that uses intelligence to control and make decisions for advanced metal 3D printing systems. This framework combines physics-based modeling, real-time monitoring, adaptive control and digital twin technology to make a manufacturing system. We use math to understand how heat, material and process interact during metal 3D Printing. We also use intelligence and optimization algorithms to improve accuracy, energy efficiency, surface quality and reliability of metal 3D Printing. The digital twin environment helps us predict quality detect defects and correct the process in time for metal 3D Printing. We tested our framework using metal 3D Printing machines and common engineering alloys like Ti-6Al-4V, Inconel 718 and SS316L. Our framework showed high accuracy improved surface quality, reduced energy consumption and robust process stability for metal 3D Printing. The digital twin was very accurate which means we can make decisions and optimize the process in time, for metal 3D Printing. Our results show that using intelligence, adaptive control, digital twins and data-driven optimization can greatly improve the performance and reliability of metal 3D Printing. Our framework provides a foundation for generation intelligent metal 3D printing systems that can control themselves predict quality and improve process management. This can help accelerate the use of manufacturing technologies, in aerospace, biomedical and high-performance engineering applications.
Abstract: Metal 3D Printing, Laser Powder Bed Fusion and Directed Energy Deposition is a deal for making complex metal parts. We can make these parts with a lot of design freedom and material efficiency. Even with a lot of progress it is not widely used in industries. This is because of some problems like process instability, defects and stress buildup. Most...
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