The influence of cross-order terms in interface mobilities for structure-borne sound source characterization: Plate-like structures

With the introduction of the concept of interface mobilities, substantial simplifications can be obtained for vibrational source characterization and the description of the associated transmission process involving multi-point or continuous interfaces. The applicability of interface mobilities, however, depends on the admissibility of neglecting the so-called cross-order terms. Under the assumption of a uniform force-order distribution, the cross-order terms reduce to the cross-order interface mobilities. It is demonstrated that the cross-order interface mobilities represent the dependence of point and transfer mobilities on the location relative to boundaries and discontinuities. From theoretical and experimental analyses of circular interfaces located on plate-like structures, it is found that the influence of the cross-order terms features three distinct frequency regions. Provided that the structure can vibrate freely along the interface, the cross-order terms are significant only at intermediate Helmholtz numbers. For engineering practice, however, the omission of the cross-order interface mobilities appears to result in an acceptable estimate throughout the entire frequency range.