Length of Mode Shapes in Numerical and Experimental Models

A new concept of length of a continuous mode shape has been recently defined by the authors, which depends on the mode shape and how the volume is distributed in the structure. This concept was then extended to discrete systems by introducing the concept of a volume matrix. However, finite element programs do not provide the lengths of the mode shapes according to this new definition. Moreover, the volume matrices cannot be exported from the finite element programs. In this paper, an approximate approach is proposed to calculate the length of numerical mode shapes from the nodal components. It has been demonstrated that the length can be estimated with a reasonable accuracy if small finite elements are used. These new techniques are illustrated by several numerical models assembled in ABAQUS. The length of numerical mode shapes can be used to estimate the length of experimental mode shapes using the structural dynamic modification, which is valuable information to validate the modal masses estimated with the existing techniques to determine the modal masses in operational modal analysis.