Lateral moment and axial force excitation of deep beams; point and point-cross mobilities

Abstract

The cross-coupling at an excited interface between, on the one hand, a lateral moment and an axial translational velocity and, on the other, an axial force and a lateral rotational velocity is studied for an arbitrarily deep beam. Complete descriptions are developed for the two associated point-cross mobility elements. In addition, the point mobility is established relating to an axial force excitation at an edge of the beam. From the theoretical results it can be concluded that reciprocity with respect to the point-cross mobility elements is strictly, only valid in the hypothetical case of point excitation. The numerical results demonstrate, however, that reciprocity can be invoked in an approximate sense also for realistic excitation conditions. Moreover, it is shown that a reduction of an axial force excitation, remote from the neutral layer, to a combined force and moment excitation at the neutral layer is not applicable except for very small Helmholtz numbers. Finally, it can be concluded that the shear-tensional nearfield affects the point-cross mobilities in the case of two-dimensional beam-like structures. A similar influence is established for the axial point force mobility but an unambiguous description has not been found.