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

To prevent over-testing of the load during the random vibration test an adaptation of the random base acceleration can be applied (notching). Besides that the random force limits at the base of the load can be defined by the force limited vibration test (FLVT). To define the random force limits by the semi-empirical method (SEM) the random acceleration vibration specification, the total mass, the turnover (natural) frequency of the load, and the semi-empirical constant C2 are key parameters. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and supporting structure (source) are connected. The asparagus patch model consists of parallel placed single degree of freedom (SDOF) elements. When the random acceleration vibration specification is given the CSMA method is suitable to reconstruct interface random accelerations and associated forces between load and source to compute the value of the parameter C2. In this study the Hybrid Mathematical Dynamic Modelling (HMDM) has been developed. The asparagus patch model of the load is coupled with a multi degree of freedom (MDOF) system of the source, consisting of a number in series placed SDOF elements and a very large mass to simulate a fixation, which is not the case with the CSMA method. The selected primary probabilistic design variables of the source have prescribed intervals and uniform distributions and are discussed in detail to justify the choice against current design rules in spacecraft structures design. The computation of the value C2 can be performed in conjunction with the CSMA and HMDM methods, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source respectively. To perform the probabilistic analyses the Rosenblueth Point estimates for probability moments (PEM) and the Monte Carlo Simulation (MCS) are both applied. Data of three deterministic cases available from literature have been analysed in detail and discussed to get more knowledge about the applicability of the probabilistic approach. To compute the interface random accelerations and forces and subsequently the semi-empirical constant C2, the CSMA method is preferred slightly for modelling the load and probabilistic source.