Force limited random vibration testing: the computation of the semi-empirical constant C2 for a real test article and unknown supporting structure

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the test article (load), C2 is a very important parameter for FLVT. A number of computational methods to estimate C2 are described in the literature, i.e. the simple and the complex two degree of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of C2 to perform a representative random vibration test based on force limitation, when the description of the supporting structure (source) is more or less unknown. Marchand discussed the formal description of obtaining C2 , using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between test article and supporting structure. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected. The asparagus patch model consists of modal effective masses and spring stiffnesses associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter C2 . When no mathematical model of the source can be made available, estimations of the value C2 can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value C2 can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature has been analyzed and discussed to get more knowledge about the applicability of the probabilistic metho