A discrete inverse vibration problem with parameter uncertainty

摘要

Inverse vibration problems consider the use of eigenvalue data to calculate the properties of a linear dynamic system. The present study examines the effects of uncertainty in such problems. The type of problem studied is limited to simple spring-mass systems, that is, undamped discrete systems. A procedure is available for finding the values of these spring constants and masses from two sets of eigenvalues, one from the system with one free end, and one from the same system with a more restrictive boundary condition. Expressions are derived for estimating the statistics of these system parameters using the statistics of the eigenvalues. These expressions are based on first-order and second-order perturbation expansions and require the evaluation of partial derivatives of the stiffnesses and masses in terms of the eigenvalues. Results are obtained for several systems which differ in amount of uncertainty, boundary conditions, and number of degrees of freedom. These results are compared to those given by Monte Carlo simulation. The results show excellent agreement for sufficiently small degrees of randomness, as would be expected from using a perturbation method.