Estimation of Rotational Degrees of Freedom by EMA and FEM Mode Shapes

In this paper a new technique is presented to estimate the rotational degrees of freeedom of a flexural structure, using only a limited number of sensors that measure the translational DoFs of the system. A set of flexural mode shapes in a limited number of nodes is obtained by modal testing, while a different set of approximated mode is calculated by a Finite Element Model (FEM) at all the nodes and degrees of freedom of the structure. The technique is based on the classical assumption that the response can be determined by a linear combination of the structure's mode shapes. The structure's mode shapes are approximated by using the local correspondence principle for mode shapes, i.e. by using an optimally selected set of finite element mode shapes as Ritz vectors for the true mode shapes. This allows to obtain the rotational response at unmeasured DoFs. The technique is validated by comparing predicted and experimental results.