Sensitivity Analysis of Complex Eigensolutions for Brake Noise

When structures may have dynamic instability complex eigenvalue analysis is a useful tool to predict it. Although the accurate prediction itself is significant, it is also crucial to obtain sensitivity of unstable eigensolutions in order to eliminate instability efficiently. Since the mathematical relationship between stiffness matrix and design variables may seldom be found in reality, finite difference method has been typically used to approximate the sensitivity. The novel way to accurately calculate the sensitivity is developed without implementing finite difference method. This paper shows the advantages of analytical sensitivity analysis compared to other methods for choosing the most important components' eigenvalues. It also provides necessary amount of frequency shift for each chosen components' eigenvalue to eliminate unstable eigenvalues.