Force limited vibration testing: an evaluation of the computation of C² for real load and probabilistic source

Abstract

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 load(test item), C 2 is a very important parameter for FLVT. A number of computational methods to estimate C 2 are described in the literature, i.e. the simple and the complex two degrees of freedom system, STDFS and CTDFS, respectively. Both the STDFS and the CTDFS describe in a very reduced (simplified) manner the load and the source (adjacent structure to test item transferring the excitation forces, i.e. spacecraft supporting an instrument). The motivation of this work is to evaluate the method for the computation of a realistic value of C 2 to perform a representative random vibration test based on force limitation, when the adjacent structure (source) description is more or less unknown. Marchand discussed the formal description of getting C 2 , using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between load and source, in combination with the apparent mass and total mass of the the load. This method is very convenient to compute the factor C 2 . However, finite element models are needed to compute the spectra of the PSD of both the acceleration and force at the interface between load and source. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected, consisting of modal effective masses and the spring stiffnesses associated with the natural frequencies. When the random acceleration vibration specification is given the CMSA method is suitable 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 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 C 2 can be done in conjunction with the CMSA 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 method keywords: Random vibration, Force limited vibration testing (FLVT), Coupled systems modal approach (CSMA), Probabilistic system.

Force limited random vibration testing: the computation of the semi-empirical constant $$C^2$$ C 2 for a real test article and unknown supporting structure

“…This range may be confirmed by the calculation of the modal effective mass of simple structures [31]. The residual mass is the sum of the modal effective masses excited outside the frequency range of interest and the residual mass m rs will be assumed to be 5 % of the total mass of the source, such that…”

“…The fuzzy design parameters are discussed in detail in [31] and are common to the modal data of the load. The fuzzy design parameters of the source are described in the following section.…”

“…The design parameters of the source are related to the mass and modal properties of the load and are discussed in [31].…”