Predicting changes in vibration behavior using first- and second-order iterative embedded sensitivity functions

In product manufacturing and test environments, engineers must predict how mechanical components will vibrate when design modifications are made to the mass, damping, or stiffness properties of the components. If component models are not available, then engineers must rely on test data from the initial component to conduct their design sensitivity analysis. Embedded sensitivity functions derived solely from test data have previously been applied to identify optimal design modifications for reducing linear vibration resonance problems in certain frequency ranges. However, forced response predictions were not accurate due to the nonlinear nature of the frequency response function variation for large design modifications. This paper develops two techniques for predicting the forced response of mechanical components for local changes in properties based on (a) first-order multi-step iterative prediction and (b) second-order iterative sensitivity functions. The methods are applied to a single degree of freedom analytical model to determine the accuracy of the predictions. Some tests and finite element analyses are conducted on a cantilever beam, a sub-system of an automotive vehicle, a structural component of a truck dumping system, and a lever arm with a modification to the mass distribution to demonstrate the feasibility of these predictions in experimental and analytical applications.