Dynamic Properties of the Rigid Body and Supports from Vibration Measurements

Abstract

A novel method is presented to determine the dynamic characteristics of a multi-DOF rigid body structure from vibration measurements and coordinates of the transducers. These characteristics include the center of gravity, moment of inertia, and mass; stiffness, center of stiffness and moment of stiffness; damping, center of damping and moment of damping; and corresponding principal values and axes. The method is capable of handling complicated structures with various DOFs, from 2 up to maximum 6. The mass modified matrices M−1K and M−1C (or mass M, stiffness K, and damping C matrices) are first obtained based on measured vibration data and estimated rigid-body modes by Data Dependent Systems (DDS) methodology, which is accurate even for highly damped structures. Relationships between the physical characteristics and the mass modified matrices have been derived to solve the dynamic properties. The properties of up to 5 individual spring and dashpot supports can be determined by solving linear simultaneous equations. New concepts about the center of stiffness, moment of stiffness, center of damping, and moment of damping and the estimation method are presented. An example, using a simple structure, demonstrated the capability of the proposed method.

Experimental Determination of Rigid Body Properties: An Evaluation on the Use of Piezoelectric or MEMS Tri-Axial Accelerometers

“…These rigid body properties are mass, position of the centre of mass and inertial moments and they may be estimated using numerical or analytical approaches or using experimental driven procedures. The latter have been addressed by several authors [1][2][3][4][5][6][7][8][9][10], considering different methods that can be divided into two main categories: Frequency domain methods [1][2][3][4][5] and Time domain methods [6,7]. The Time domain methods [6,7] present advantages mainly due to the fact that there is no need to transform the acquired data into the frequency domain, although care should be taken whenever the structure does not behave like a rigid body in the frequency range of interest.…”