Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

Abstract

This paper demonstrates how to calculate Craig-Bampton component mode synthesis 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, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

Baseband Methods of Component Mode Synthesis for Non-Proportionally Damped Systems

“…This additional restriction prevents the direct recovery of the constraint modes matrices in equations (20) and (21). Instead, the two-stage transformation procedure, shown in reference [1], is used to recover a formulation that is equivalent to the Craig-Bampton method. The first transformation is from the reduced dof in Equation (28): in which K , and M , are defined as shown in equations (40) and (41).…”

“…The matrices R F and R I have the same dimension as K, have ranks of dimension x, and are real valued (provided complex conjugate modes are included in pairs). The constraint relation between the active and omitted displacement dof is determined from the partitioned residual flexibility matrix in the same manner as for the proportionally damped case [1], giving…”

“…Any method can be used to estimate the coefficients in the Maclaurin series expansion. A proposed method using approximate residual functions corresponding to three-and four-dof representations is described in reference [1]. Once the coefficient matrices are estimated, the computational modes are determined by equating the Maclaurin series expansion coefficients to that corresponding to the computational modes in the residual flexibility formulation:…”

“…This procedure follows the same line of development as used for the proportionally damped case in reference [1]. This paper is organised as follows.…”

“…For the undamped rigid body modes, inertia relief modes are calculated in the same manner as for the proportionally damped case [1]:…”