A dimensionless mobility formulation for evaluation of force and moment excitation of structures

The problem addressed is the simultaneous excitation of a structure by a force and moment. These two forms of excitation are dimensionally incompatible, and so their relative importance is normally difficult to assess. Here, a dimensionless form of the mobility matrix is developed thereby allowing proper comparison. The off-diagonal elements of the matrix quantify the coupling between two excitations of whatever dimensions, in other words the extent to which an applied force or moment affects the power input by another force or moment. It is shown that off-diagonals of unit magnitude indicate the maximum possible extent of coupling between the corresponding excitations. A precise definition of weak and strong coupling is therefore possible. Illustrative examples of dimensionless mobilities for infinite, semi-infinite, and finite plates are given. It is also shown that the eigenvalues of the dimensionless mobility matrix relate the actual delivered power to the "point-by-point" power input. The results are shown to have wider relevance than originally intended; specifically, the dimensionless mobilities provide a measure of the suitability for active vibration control of different points on a structure, or mixed excitations.