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Electromechanical Analogies: Representation of mechanical systems as electrical circuits

Koulouridakis Matthaios

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Summary

In the environment around us and in nature more broadly, we encounter various types of physical systems that are analyzed and described according to the fundamental principles and physical laws governing them. These systems include all those that represent and are based on physical phenomena, such as a mass-spring mechanical system that relies on the motion of an object connected to a spring, or a simple electrical circuit where the phenomenon of electricity is related to the movement of charged particles.But what happens when we want to use one physical system to represent and approach another? The answer to this question is particularly intriguing because by utilizing knowledge and fundamental laws from one system, we can apply a simple transformation to address and solve more complex problems. The tools and methods developed in one area can be transferred to solve problems in another.This paper demonstrates how mechanical elements can be represented by their electrical counterparts, allowing engineers to apply well-established techniques from electrical circuit analysis to solve problems in mechanical systems. This approach not only simplifies the analysis of complex mechanical systems but also facilitates the use of well-developed tools from electrical circuit theory and simulation, ultimately aiding in the design and optimization of mechanical systems.The paper begins by establishing the correspondence between mechanical and electrical components. For example, mass is analogous to inductance, damping corresponds to resistance, and stiffness relates to capacitance. The paper also illustrates the analogy in quantities between mechanical and electrical systems, such as force and voltage, velocity and current, as well as displacement and charge. By understanding these fundamental relationships, engineers can leverage their knowledge of electrical circuit theory to tackle challenges in mechanical systems.One of the main advantages of using electromechanical analogies is the ability to simplify the analysis of complex mechanical systems. By representing mechanical elements as their electrical equivalents, engineers can apply well-established electrical circuit analysis techniques, such as Kirchhoff's laws and network analysis, to solve problems in mechanical systems. This approach not only saves time and effort but also allows for a more intuitive understanding of the system's behavior.Therefore, the primary goal of this thesis is to consolidate knowledge regarding the analogy between mechanical and electrical problems for one-dimensional elements while simultaneously studying the fundamental theory and concepts of electrical circuits and mechanical systems to enhance understanding of these analogies.

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