Performance of the Expanded Virtual Point Transformation on a Complex Test Structure
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APPLICATIONS PAPER
Performance of the Expanded Virtual Point Transformation on a Complex Test Structure 2 · D. J. Rixen3 · M. Bolteˇzar2 ˇ T. Bregar1 · A. El Mahmoudi3 · G. Cepon
Received: 3 December 2019 / Accepted: 24 August 2020 © The Society for Experimental Mechanics, Inc 2020
Abstract The Virtual Point Transformation (VPT) makes it possible to experimentally identify the full DoF FRF matrix by projecting the measured displacements onto the Interface Deformation Modes (IDMs). The VP FRFs were already successfully used in Frequency-Based Substructuring (FBS); however, the VPT is susceptible to deviations in the impact location and orientation, as well as to deviations in the sensor’s sensitivity and positioning. Uncertainties associated with the sensors can be decreased by using the expanded VPT. This expanded VPT allows the projection of a directly measured rotational response onto the Interface Deformation Modes (IDMs). The consistency of the transformation is achieved by using a rotational weighting matrix, which is formulated to minimize the norm of the overall displacements due to the rotational residual at the VP for each rotational sensor. The rotational response is measured using a direct piezoelectric rotational accelerometer. In this paper the application of the expanded virtual point transformation and the possible advantages are explored on a complex and engineering-like test structure. Both transformations, standard and expanded, are performed for each VP to enable a side-by-side comparison. Keywords Frequency-based substructuring · Expanded virtual point transformation · Rotational accelerometer · Interface rotation
Introduction The Dynamic Substructuring (DS) framework makes it possible to dynamically characterize a complex product by subdividing it into smaller subsystems [1]. Each subsystem can then be analyzed independently and virtually assembled to predict the overall dynamics of the final product. This component-wise approach has proven to be advantageous, especially during the early design stage, when a full prototype might not be available. The dynamic characterization of each subsystem can be in different domains, such as the physical, modal, frequency, time or state-space domain [2]. Even with distinct differences ˇ G. Cepon [email protected] 1
Gorenje d.d., Partizanska 12, 3503 Velenje, Slovenia
2
Faculty of Mechanical Engineering, University of Ljubljana, Aˇskerˇceva 6, 1000 Ljubljana, Slovenia
3
Institute of Applied Mechanics, Technical University of Munich, reetBoltzmannstr. 15, 85748 Garching, Germany
between each representation, there are two conditions that must be satisfied at the interface between the substructures and are mathematically equivalent throughout the different domains. The first condition is displacement compatibility and the second is force equilibrium. One of the frameworks where the numerical and experimental models can be coupled interchangeably is Frequency-Based Substructuring (FBS). The idea of frequency-based assembly was already conside
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