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Lumping parameters (mass, stiffness and damping) for a continuous mechanical system is one of the early topics of discussion in courses like System Dynamics and Vibrations. When the system includes multiple continuous elements such as beams, bars or rods along with spring elements, determining the equivalent lumped stiffness can be difficult, especially with respect to how each stiffness element is arranged (in parallel or series) with respect to other elements. In this paper, the spring connectivity diagram (SCD) approach is introduced as a simple way to analyze such problems. In this method, the effective stiffness of all continuous elements is first determined, the nodes at the ends of all stiffness elements are identified and the SCD is obtained by connecting each stiffness element to the proper nodes. The stiffnesses in the resulting diagram may then be combined to determine the equivalent lumped stiffness of the entire system. Three examples are provided to show the application of this intuitive approach to different types of problems that involve continuous and spring stiffness elements. An assessment of the effectiveness of this technique is provided based on a System Dynamics exam question.
Yazdi, A. (2022, August), Spring Connectivity Diagram: An Intuitive Approach to Determining the Equivalent Lumped Stiffness of a System of Springs and Simple Continuous Elements Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. https://peer.asee.org/40371
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