15 A Tutorial on an Open-Source Python Package for Frequency-Based Substructuring and Transfer Path Analysis 111 Engine mount Source Transmission mount Rollmount Receiver structure Fig. 15.6 Schematic representation of the automotive laboratory test structure [12] Source Characterization with the In-Situ TPA With the in-situ transfer path analysis, the equivalent forces can be determined directly from the assembled configuration. The equivalent forces are a sole property of the source [11], which makes them indispensable in the design process, since various modifications of the passive side can be evaluated, without the need to repeat the source characterization [16, 17]. It is a common industry practice that the active components are outsourced to external suppliers. By utilizing the property of equivalent forces, the target settings can be specified on a component level and thus outsourcing the task of source characterization. Here an application of in-situ TPA is shown on an automotive laboratory test structure (Fig. 15.6). The test structure is designed to mimic the dynamics in a real car of an engine transmission unit flexibly mounted on a chassis. Rubber mounts from the automotive industry are used to suspend a steel plate holding the excitation source, which is an electrodynamic shaker. The structure is intended as a laboratory test bench for an application of different concepts of dynamic substructuring and transfer path analysis [12]. Additional Features of pyFBS The pyFBS introduces an object-oriented approach for dynamic substructuring in frequency domain. The current state-ofthe-art FBS methodologies are implemented within the package. Each method can be used interchangeably with others or as a standalone unit. In the next sections, the key features of the pyFBS are outlined. Singular Vector Transformation Singular vector transformation (SVT) consists in projecting the acquired data into subspaces composed by dominant singular vectors, which are extracted directly from the available FRF datasets. No geometrical and/or analytical model is required. If some basic requirements are met, the reduced orthonormal frequency-dependent basis would be able to control and observe most of the rigid and flexible vibration modes of interest over a broad frequency range. The SVT can tackle challenging scenarios with flexible behaving interfaces and lightly damped systems. The method combines reduction with filtering and regularization. It shows an overall low sensitivity to measurement error and significantly reduces the condition number of the interface problem [3].
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