3.  Elements of Lumped Parameter Models

In modeling systems for dynamic analysis, the modeler’s goal is to determine a differential equation that adequately describes the system behavior without introducing unnecessary complication. A successful modeler identifies the critical elements of a system and then incorporates them into a lumped parameter model. For a mechanical example, consider an automobile chassis/body and its interactions with the road through its suspension. Figure 3.1a shows the front suspension for a 1924 Ford Model T. Although all elements of the dynamic system can deform elastically, have mass, and offer the potential to dissipate mechanical energy as heat, we recognize that certain elements are inherently more flexible while others have significantly more mass. We therefore lump the elements together into ideal masses/inertias, springs, and energy loss elements (dampers) so that we can realistically analyze the system using a simplified model. Through analysis of this model, we identify the most important system dynamics.