PSI - Issue 64

Ge-Wei Chen et al. / Procedia Structural Integrity 64 (2024) 724–731 Ge-Wei Chen, Xinghua Chen, Piotr Omenzetter / Structural Integrity Procedia 00 (2019) 000–000

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3. Hybrid vibration testing Two light-weight APS Dynamics Model 400 ELECTRO-SEIS® long stroke shakers with APS 0412 Reaction Mass Assembly (Fig. 2a) worked in tandem with environmental sources to excite the bridge in the vertical and lateral direction. Because for most practical systems, the maximum modal displacements of individual modes do not coincide, trade-off optimal locations for the exciters were selected as the points with the largest sum of absolute values of the mode shapes of interest. At the same time, we avoided placing exciters too close to a node of any mode of interest. Based on additional practical considerations, the shaker locations were determined to be on the longest span as shown in Fig. 1b. For lateral excitation, the two shakers were positioned at the mid-span and at the deck centreline, and for the vertical excitation at 1/3 of the span length and 3.5 m off the centreline to also provide torsional forcing. Two synchronised electro-dynamic shakers can provide a combined sine excitation force of 0.89 kN in the frequency range 0-12 Hz. Chirp sweeps of constant amplitude and 10-minutes duration were performed during actual testing with the instantaneous frequency varying linearly from 2.5 Hz for the vertical direction and from 0 Hz for the lateral direction, respectively, and up to 10 Hz. The electro-dynamic shakers provided a relatively weak excitation with the additional response of a similar magnitude to that by ambient sources, which is demonstrated later. Micro Electro-Mechanical Systems (MEMS) accelerometers Model X6-1A and Model X6-2 from Gulf Coast Data Concepts (Figs. 2b and c) are battery-powered and record data locally and therefore avoid the need for troublesome cabling needed on large structures. A total of 62 of these tri-axial accelerometers were deployed to measure the vibrations of the bridge deck. The sensors incorporate over-sampling, anti-aliasing and real-time data digital streaming via an I2C bus. An 8-bit Silicon Labs 8051 microprocessor collects the data, processes the stream and logs it to a micro SD card. Although they cannot be controlled remotely or transmit data wirelessly, they offer a cost-effective alternative to wireless platforms with good quality and reliability of data (Chen et al., 2013). The real-time clocks of the accelerometers were synchronised to the same computer clock before the tests; this took only 10 minutes. The acceleration range of the sensors is ±2.0 g with 16-bit resolution, i.e., the sensitivity is 16,384 counts/g. Before performing the HVT, on the previous day AVT data were collected for comparison under excitations from ground vibrations generated by traffic on the motorway passing underneath the bridge and nearby motorway on- and off ramps, weak winds and possible micro tremors; see (Chen et al., 2017) for more details. For vertical tests, the 62 accelerometers were arranged along both curbs of the bridge deck generally at the 1/4, 1/2 and 3/4 of the span-length, whereas during the lateral tests, they were placed along the centreline of the bridge. Using the large number of sensors, only a single setup for each vibrations direction was enough to map the full mode shapes.

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Fig. 2. Experimental equipment: (a) electro-dynamic shakers configured for vertical forcing; (b) close-up of tri-axial MEMS accelerometers; (c) accelerometers with D-cell batteries arranged along bridge curb. 4. System identification theory 4.1. Autio-regressive method AR models use parametric stochastic difference equations for describing time series (Maia and Silva, 1997). A multivariate AR model of order q for acceleration response ̈( ) subject to Gaussian white noise ( ) at discrete time k can be written as follows: