Nonlinear behavior of additively manufactured steel beams with trapped-powder dampers: Supplementary Files

Table of contents Supplementary data for the paper: "Nonlinear Behavior of Additively Manufactured Steel Beams with Trapped-Powder Dampers" Jonathan K. Black, 2025-08-07 Contents Filename Description raw_data.zip Raw time histories, FRFs, and beam measurements processed.zip Results of linear and nonlinear processing graphs.zip Full set of graphs referenced in the paper Abbreviations •B[x]: These are the labels for the beam samples. The number [x] is the thickness of the powder pocket in microns. •Mode name abbreviations •Drive point abbreviations, e.g. Z039B: see Fig. 2 in the paper. •Test procedure phases: see Table 1 in the paper. •P1_lin: Phase 1, Linear testing •P4_nl: Phase 4, Final nonlinear testing Abbreviation in paper Abbreviation in data Type of mode Mode Z[#] bn[#] Soft [ non-stiff] direction bending mode [#] Mode Y[#] bs[#] Stiff direction bending mode [#] Mode T[#] t[#] Torsion mode [#] Folder structure Each zip folder has the following folder structure: ↳Level 1: Beam label (e.g. B500, B3000) ↳Level 2: Phase of test procedure (P1_lin or P4_nl) For example, /raw_data/B500/P4_nl/ contains the nonlinear test ringdown data for the beam with a 500µm powder pocket. The results of processing that data are contained in /processed/B500/P4_nl/, and the graphs made from that processed data are contained in /graphs/B500/P4_nl/. The exception to this pattern is that the summary plots, which combine data from multiple beams, are contained in /graphs/summary/. Raw data: FRFs, time histories, and beam measurements raw_data.zip Frequency Response Functions (FRFs) Example: /raw_data/B500/P1_lin/FRF_Z073B.mat •The FRFs from linear testing are stored as .mat files, as exported from TestLab •The provided example MATLAB script /raw_data/plt_FRF.m shows how to read in and plot one of these files. Note that some of the Phase 1 data were collected with an exponential window applied to the response signal, as noted in the readme files. This means that some of the FRFs have artificially higher damping. However, the purpose of Phase 1 was not to get accurate damping values. Time histories Example: /raw_data/B500/P4_nl/meas0_Z090M_med.mat •The hammer force and accelerometer ring-down signals are stored as .mat files, as exported from TestLab. •The reference force and the acceleration measurement from the relevant* accelerometer are stored as two Signal structs in the same file. Determine which is which by looking at the units in Signal[#].y_values.quantity.label. •The provided example MATLAB script /raw_data/plt_Sig.m shows how to read in and plot one of these files. •For B000 and B100, when Phase 4 was simplified, each Signal file contains multiple hits. For B3000, a different method was used to export data from TestLab, so the format is slightly different. The script plt_Sig.m works with all of these. * For hits in the Z-direction, the Z-accelerometer signal is saved. For Y-direction hits, the Y-accelerometer signal is saved. Beam measurements /raw_data/density_measurements.xlsx •This Microsoft Excel spreadsheet contains the mass and dimensions measurements of the beams, including many that were not included in this study. •See Figure B.1 for the definitions of the dimensions in this sheet. •The Sheet titled "raw_data" contains the measured values for mass and the three external dimensions. •The Sheet titled "corrections" contains the formulas used to adjust the measurements as explained in Appendix B. •The Sheet titled "density_20250506" contains the data and the plot used to estimate the bulk densities of the fused and unfused powder regions. Results of linear and nonlinear processing processed.zip Summary boxplots Example: /graphs/summary/boxplot_bn1.fig •These boxplots summarize all the data for a given mode. •Each beam has three boxplots: one for each of three amplitude ranges. See the example below. Model variance bar graphs Example: /graphs/summary/barsd_add_mdlnrm_bn1.fig •The bar graphs compare the relative uncertainty of several models for the data. See Section 3.4 in the paper for an explanation. •The uncertainty of each model is normalized by dividing by the uncertainty of the linear model. Here is an example of how to interpret these graphs. This example bar graph is for B1000, bn1; it is taken from the figure barsd_add_mdlnrm_bn1.fig. •The model A has 30% of the linear model uncertainty, meaning accounting for nonlinearity decreases uncertainty by 70% in this case. •The model A, PS has significantly lower uncertainty than the model A, meaning that knowing powder state decreases the uncertainty considerably. •The model A, DP has almost the same uncertainty as the model A. Therefore, accounting for nonlinearity and the drive point does not decrease the uncertainty relative to only considering nonlinearity. •The model A, PS, DP, HT has 13% of the uncertainty of the linear model. Therefore, the uncertainty can be reduced by 87% by accounting for all four of the factors in the experiment.