This paper presents a method for obtaining structural matrices from experimental frequency response function (FRF) data and using these structural matrices to predict the response of the structure to modifications at various locations. The approach taken is designed for subsequent use in optimizing structural modifications to efficiently reduce radiated acoustic power. A series of programs were written for identifying the structural matrices (mass matrices, stiffness matrices and damping matrices) from the measured FRF data. These matrices are used to obtain the modified response of the structure resulting from adding linear springs at different locations on the structure. Experimental results from a beam are presented to verify these programs. Work is in progress on extending this method to incorporate modifications to the structure produced by constrained-layer damping materials.
The programs for obtaining the structural matrices and the structural response are composed of approaches used by several prior authors. Potter and Richardson’s [1,2] method is used for obtaining the relative modal parameters (modal mass, modal stiffness and modal damping). Luk and Mitchell’s [3,4] pseudo-inverse method is employed to obtain the structural matrices for cases when the number of modes measured is much less than the number of test points. A method for deriving the absolute value of modal parameters from the measured FRF data is also developed using modal analysis theory. Linear springs are added at various positions to modify the structure. The structural matrices are used to predict the modified structural responses scaled to displacement per unit force. A series of linear spring modifications are modeled and implemented experimentally to verify these programs.