Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 1: Theory

Abstract

This paper presents a new method to calculate the so-called Craig-Bampton component mode synthesis (CMS) matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered. Experimental implementation of the method requires estimating the modal parameters corresponding to the measured free boundary modes and the Maclaurin series expansion coefficients corresponding to the omitted modes. Theoretical developments are presented in the present paper, Part 1. The performance of the new method is then demonstrated in Part 2 (Morgan et al., 1998) by comparison of experiment and analysis for a simple two-beam system.

Forced Response of Coupled Substructures Using Experimentally Based Component Mode Synthesis

“…12 The CMS matrices were calculated using the residual¯exibility method, and then were transformed to Craig±Bampton form. 1 The translationalDOF at points 1±3 on the plate were selected as active, with the remaining DOF selected as omitted. The translationalDOF at points4 and 6 on the beam were selectedas active,with the remaining DOF selected as omitted.…”

“…1,2 The details are not presented here; however, the resulting CMS matrices are in exactly the same form as in the constraint-modes CMS method of Craig and Bampton. 7 There are four matrices that represent the CMS model of a substructure: transformation, reduced stiffness, mass, and damping matrices.…”

“…However, rigid-body modes are included as inertia-relief modes. 1 For the forced-response method, a further partitioning of the active DOF with respect to coupling c and noncoupling n DOF is useful, because all active DOF are not necessarily coupling DOF:…”

“…For the coupling-forces load case, they include the coupling DOF and any additional noncoupling DOF selected to be included as active DOF. 1 These are the same DOF required for the calculation of the CMS models, so no additional measurement locations need be included for the calculation of the forced response. Second, the new method theoretically is highly accurate.…”

Formulation of an experimental substructure model using a Craig–Bampton based transmission simulator

“…Urgueira [4] considered the need for the inclusion of residual compliances when free interface substructure modes are used, and the difficulty associated with measuring rotations. Morgan et al [5,6] developed a modified residual flexibility approach based on frequency response measured at the substructure interface. A Craig-Bampton [7] substructure representation was then recovered from the measured experimental results.…”