A Generalised Multiple-Mass Based Method for the Determination of the Live Mass of a Force Transducer
Many applications in Experimental Modal Analysis (EMA) require that the sensors’ masses are known. This is because the added mass from sensors will affect the structural mode shapes, and in particular its natural frequencies. EMA requires the measurement of the exciting forces at given coordinates, which is often made using piezoelectric force transducers. In such a case, the live mass of the force transducer, i.e. the mass as ‘seen’ by the structure in perpendicular directions must be measured somehow, so that compensation methods like mass cancelation can be performed. This however presents a problem on how to obtain an accurate measurement for the live mass. If the system is perfectly calibrated, then a reasonably accurate estimate can be made using a straightforward method available in most classical textbooks based on Newton’s second law. However, this is often not the case (for example when the transducer’s sensitivity changed over time, when it is unknown or when the connection influences the transmission of the force). In a self-calibrating iterative method, both the live mass and calibration factor are determined, but this paper shows that the problem may be ill-conditioned, producing misleading results if certain conditions are not met. Therefore, a more robust method is presented and discussed in this paper, reducing the ill-conditioning problems and the need to know the calibration factors beforehand. The three methods will be compared and discussed through numerical and experimental examples, showing that classical EMA still is a field of research that deserves the attention from scientists and engineers.