A Further Discussion on the Singularity of Driving-Point Receptance in Structural Dynamics

Abstract Driving-point receptance of a structure, defined as the displacement amplitude of the structure at the same point and in the same direction as a unit point harmonic force causing the displacement, is a well-established and widely applied quantity in structural dynamics. However, as noted and discussed by the correspondence author in 2018, because of the use of point force, driving-point receptance is essentially singular (i.e., infinite) by its definition, except when the structure is modeled as a beam, plate, or shell. Nevertheless, with the evolvement of structural dynamics, various methods have been developed to calculate the above-defined driving-point receptance, but without considering the singularity issue, giving rise to concerns about the validity of the various structural dynamic analyses based on the calculated driving-point receptance. This article, as a continuation of the previous study, aims to further raise awareness of the singularity issue in numerical models, explore how the singularity causes nonconvergence in several typical driving-point receptance calculation methods, and propose ways to address the issue.