Investigation on the relationship between wave propagation speed and vibration frequency in concrete floors using nonlinear regression model

While dealing with structures equipped with operating mechanical devices, keeping the machinery-induced vibrations below the acceptable limits is of enormous importance. The fundamental step to controlling undesirable vibrations in such structures is to localize the vibration source. The accuracy of locating the source of vibration using different methods, e.g., Time Difference of Arrival (TDOA) or Steered Response Power (SRP) method, depends on accurate estimation of the propagation speed. The propagation speed is a function of vibration frequency. The objective of this study is to investigate a nonlinear regression model to obtain the relationship between Wave Propagation Speed (WPS) and the vibration frequency on a concrete floor. The development of this relationship is based on a series of experiments on a concrete floor in a building using a shaker as a vibration exciter, and four accelerometers to record vertical vibration. First, the shaker generates sinusoid forces with a specific frequency and the accelerometers, configured collinearly, record acceleration measurements. Then, the WPS is estimated using cross-correlation to measure the time difference of arrival between pairs of accelerometers. This process is repeated for a range of frequencies resulting in a dataset that includes the vibration frequency as independent and the WPS as dependent variables. The relationship between speed and frequency is then optimally estimated using a nonlinear regression model.