A Variable-Impulse Hammer Impact Test (VIHIT) Method for Improved Mode Shape Identification

The impact hammer, equipped with a force transducer, is a portable and practical tool for inducing measurable excitations in structural health monitoring (SHM). However, its reliability is often limited by uncontrolled factors such as swing power, angle, impact location, and operator consistency, particularly in nonlinear structures operating at low frequencies. While many researchers have avoided hammer testing by instead using better controlled drop mass systems or operational modal analysis (OMA) techniques, this study presents a new experimental modal analysis (EMA) approach that improves the accuracy of impact hammer testing: variable impulse hammer impact testing (VIHIT) using a single-input single-output (SISO) roving hammer and single fixed accelerometer. For a mode of interest, the imaginary component of the frequency response function (FRF) is evaluated at each test location using multiple impulses of varying magnitude. This output quantity exhibits an inverse power relationship with the input autopower spectral density (APSD) at the modal frequency. Evaluating the trend at a reference input APSD from sufficiently excited tests produces a very accurate mode shape for that input. For a given structure, nonlinear damping ratios vary with excitation and can be extracted using inverse FRF analysis. This method addresses variability in impact hammer testing by establishing reproducible trends for different impulse levels and test locations. Application to degraded timber beams demonstrated reductions in mode shape variability relative to conventional averaging and revealed impulse-dependent damping ratios ranging from approximately 0.02 to 0.04, highlighting the method's ability to characterize nonlinear dynamic behavior. The result is a more accurate approach for extracting modal properties and mode shapes and characterizing nonlinear dynamic behavior using a SISO roving impact hammer system.