Selection of an Adequate Model of a Piezo-Elastic Support for Structural Control in a Beam Truss Structure

Axial and lateral loads of lightweight beam truss structures e.g. used in automotive engineering may lead to undesired structural vibration that can be reduced near a structural resonance frequency via resonant piezoelectric shunt-damping. In order to tune the electrical circuits to the desired structural resonance frequency within a model-based approach, an adequate mathematical model of the beam truss structure is required. Piezo-elastic truss supports with integrated piezoelectric stack transducers can transfer the axial and lateral forces and may be used for vibration attenuation of single beams or whole beam truss structures. For usage in a single beam test setup, the piezo-elastic support’s casing is clamped rigidly and is connected to the beam via a membrane-like spring element that allows for rotation as well as axial and lateral displacements of the beam. In this contribution, the piezo-elastic support is integrated into a two-dimensional beam truss structure comprising seven beams, where its casing is no longer clamped rigidly but is subject to axial, lateral and rotational displacements. Based on the previously verified and validated model of the single beam test setup, two different complex mathematical models of the piezo-elastic support integrated in the two-dimensional beam truss structure are derived in this contribution. The two mathematical models differ in their number of degrees of freedom for the piezo-elastic support as well as in the assumption of rigid or compliant casing. By comparing numerically and experimentally determined structural resonance frequencies and vibration amplitudes, the model that more adequately predicts the truss structure’s vibration behavior is selected on basis of the normalized root mean squared error. For future works, the more adequate model will be used to tune electrical circuits for resonant piezoelectric shunt-damping in a three-dimensional truss structure.