SENSORS, DEGREES OF FREEDOM, AND GENERALIZED MODESHAPE EXPANSION METHODS

Abstract

Modeshape expansion techniques deal with the spatial incom- patibility linked to the measurement of modeshapes through a limited set of physical sensors and their analytical predic- tion at a (larger) number of finite element degrees of free- dom. Expansion methods are formulated here with the mini- mal assumption that sensor measurements be linearly related to finite element DOFs. This allows the localization of experi- mental points independently from the FE mesh, the measure- ment of translations in arbitrary directions, as well as the com- bined use of translation and strain sensors. Various methods to interpolate sensor motion from DOF motion are discussed. Generalized static, dynamic, and minimum residual expansion methods are introduced and it is shown how reduction meth- ods traditionally used in Component Mode Synthesis applica- tions allow the use of the proposed methods for industrial size finite element models.