ESDU 19006
Force limited random vibration testing  The computation of the semiempirical constant C^{2} for test article and supporting structure
Abstract:
Within the framework of the qualification process, the design requirements are verified by analyses and vibration tests i.e. a random vibration test with prescribed random enforced acceleration at the base of the test article (load). To prevent overtesting 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 semiempirical method (SEM) the random acceleration vibration specification, the total mass, the turnover (natural) frequency of the load, and the semiempirical constant C^{2} are key parameters. A number of computational methods of estimating C^{2} are described in the literature, i.e. the simple and the complex two degree of freedom system (STDFS and CTDFS). The SEM, several notching approaches, the calculation of C^{2} are reviewed and discussed in the Item.
Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (paralleloscillator representation) of load and supporting structure (source) are connected. The asparagus patch model consists of parallel placed single degree of freedom (SDOF) elements. The mass of the SDOF element represents the modal effective masses and the spring stiffnesses are associated with the natural frequency of the fixed load. The supporting structure of the load (source) will be modelled by the asparagus patch model too. 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 C^{2}.
When no mathematical model of the source can be made available, estimations of the value C^{2} can be found in the literature. A number of examples of the values of C^{2} were assessed from the literature.
During the FLVT both the applied random acceleration and specified force limits are monitored. When interface force grows beyond the force limit specification, the enforced random acceleration at the base of load will be adapted (notched).
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Data Item ESDU 19006  

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