Dynamic Modeling and Updating of a Stacked Plate Dynamic System

The dynamic control of stacked-plate mechanical systems such as circuit board assemblies is a common technical problem that often requires a complete description of the open loop system dynamics prior to controller development. Often, a preliminary finite element model (FEM) of the test article is developed to understand the dynamics of the system to perform a modal test. The results of this modal test must then be used to update the stiffness, mass and damping matrices to yield correct FEM frequencies mode shapes and damping. This work describes the mathematical development of a finite element model of a multi-plate test article and proceeds with a model update using differentiated velocity data collected at discrete points on the structure with a laser Doppler vibrometer (LDV) and drive point measurements collected at the excitation location with an impedance head. Using these data, accelerance FRFs were computed and the first three flexible mode shapes were estimated and these shapes were compared to the corresponding FEM shapes using both percent frequency difference and modal assurance criterion (MAC). Several parameters of the system model were modified yielding improved correlation with the experimental results.