Lumped element modeling of operational structures by inverting the mobility models

• We visualize the operational structural dynamics of a structure.
• The impedance model is obtained by mathematically inverting a mobility model.
• It gives the lumped element system in a unique and exact manner.
• It facilitates identification of modal parameters.
• It shows that an operational structure is a coupled system between a base system and an appendage system.

This paper is concerned with what a source precisely sees when it drives a receiver such as a continuous structural object. An equivalent lumped element system consisting of masses, springs and dampers is developed to visually represent the operational structural dynamics of a single-input structure at the driving point. The development is solely based on the mobility model of the driving point response. The mobility model is mathematically inverted to give the impedance model that is suitable for lumped element modeling. The two types of structures studied are unconstrained inertial objects and constrained resilient objects. The lumped element systems presented suggest a new view to dynamics that a single-input flexible structure in operation can be decomposed into the two subsystems: a base system of single degree of freedom (or of a mass for an inertial object) whose mass is in contact with the source and an appendage system consisting of a series of oscillators each of which is attached to the base mass. The driving point response is a result of the coupling between the two subsystems.

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