Perturbation Method of Structural Design Relevant to Holographic Vibration Analysis

Abstract

Holographic vibration analysis provides a rapid way of obtaining accurate data on the shapes of normal vibration modes. At present, these data can be used to change the design of a structure only if a theoretical solution for the structure's vibration modes is known, either in closed form or by finite element analysis. A method is presented here to bypass formal solutions for the normal modes of a structure in predicting the results of small changes to a prototype, when normal-mode data, such as that obtained by hologram interfere me try, can be used as a starting point. From the known mode shapes and frequencies of a structure, it is possible to calculate new mode shapes and frequencies by first-order perturbation, given small changes in mass distribution and stiffness moduli. An optimum design could be obtained by repeating the process a number of times with successively smaller changes being made to the structure.