Predicting Changes in Vibration Behavior With Respect to Multiple Variables Using Empirical Sensitivity Functions

Engineers must routinely predict how structural systems will vibrate after design modifications are made to the mass, damping, or stiffness properties of the components. To reduce the cost of product development, sensitivity prediction methods are desired that can be applied using only empirical data from an initial prototype. Embedded sensitivity functions derived solely from empirical data have previously been applied (a) to identify optimal design modifications for reducing linear vibration resonance problems and (b) to predict the change in frequency response. In this previous work, predictive methods were developed that assumed that only one design parameter in the system was modified. In many applications, it is necessary to extend this approach to all major parameters for a more accurate prediction of the structural dynamic response. This paper utilizes a multivariable Taylor series to take into account multiple parameter changes that affect a broadband frequency range. The method is applied to a single degree of freedom analytical model to determine the accuracy of the predictions. Finite element analyses are then conducted on a three-story structure and an automotive vehicle component with modifications to the stiffness and mass distributions to demonstrate the feasibility of these predictions in applications to more complicated structural systems.