Simplified Characterisation of Multiple Point Excited Structures Using Mobility Matrix Eigenvalues and Eigenvectors

A significant difficulty in characterising structure-borne sound sources is that the structural dynamic properties of the source and receiver are represented by matrices containing many elements. The concept of 'equivalent mobility' is proposed here to provide a simplified characterisation of such structures. It is shown that multiple point excitation of any structure can be modelled as excitation by a single equivalent force at a single equivalent point. The mobility matrix can then be viewed as an ordinary point mobility whose real and imaginary parts, and magnitude are defined over a range rather than being single valued. Because it is effectively a single figure representation, comparisons between structures become possible which cannot be achieved with a matrix representation. The cost of the simplification is that the exact description of the structure is traded for an upper and lower bound, but importantly no restricting assumptions are introduced and there is no loss of rigour or physical meaning. Equivalent mobilities for several practical structures are presented.