Dynamic Modeling and Experimental Validation of a Cable-Loaded Panel

Abstract

Power and signal cable harnesses on spacecraft are often at 10% of the total mass and can be as much as 30%. These cable harnesses can impact the structural dynamics of spacecraft significantly, specifically by damping the response. Past efforts have looked at how to calculate cable properties and the validation of these cable models on onedimensional beam structures with uniform cable lengths. This paper looks at how to extend that process to twodimensional spacecraftlike panels with nonuniform cable lengths. A shear beam model is used for cable properties. Two methods of calculating the tiedown stiffness are compared. Of particular interest is whether or not handbooks of cable properties can be created ahead of time and applied with confidence. There are three frequency bands in which cable effects can be described. Before any cables become resonant, the cable effects are dominated by mass and static stiffness. After all the cables become resonant, the effect is dominated by increased damping in the structure. In between these two frequency cutoff points, there is a transition zone. The dynamic cable modeling method is validated as a distinct improvement over the lumped-mass characterization of cables commonly used today. NomenclatureA = cross-sectional area, mm 2 d C = cable diameter, mm E = Young's modulus, MPa E = accumulated root-mean-square response average error, m=s 2 f = frequency, Hz F min , F max = frequency limits for root-mean-square response, Hz f A = axial force per unit length, N=m f T = transverse force per unit length, N=m Gf = frequency response function, m=s 2 =N h B = beam thickness, mm h TC = connector height, mm I, I Eff = area moment of inertia, mm 4 kG = shape factor shear modulus product, MPa k tie = tiedown axial stiffness, N=m k X = axial spring stiffness, N=m k y , k z = transverse spring stiffness, N=m k = rotational spring stiffness, N m=rad L = cable length, mm L RBE2= RBE2 element length, mm t = time, s u = axial deflection, mm v, w = transverse deflection, mm V component = strain energy ratio of component at a given mode x = position, 0 < x < L, mm x 0 = boundary condition position, mm = cross-section angle of rotation, rad f = accumulated root-mean-square response, mm=s , e = structural damping factors , cu = mass density, kg=mm 3

Experimental Techniques and Structural Parameter Estimation Studies of Spacecraft Cables

“…Results from these tests are presented, which verify the cable parameter estimation algorithm and boundary condition assumption. Further analyses, results, and conclusions regarding the structural dynamic behavior of cable-loaded structures can be found in [15,16]. Babuška et al [15] discuss validation of a modeling methodology using cable parameters identified in this work on a beam with simulated free boundary conditions.…”

A stochastic methodology for predictions of the environment created by multiple microvibration sources

“…In order to obtain the modal perturbation prediction, a flat randomisation of 50% has been applied to the values in Eq. (15). 100 different computations have been performed and the final prediction is given by:…”

“…In this case, besides the typical issues related to predicting responses in the mid-frequency, the low amplitude of the inputs can produce further uncertainties which can manifest themselves as nonlin-earities. A typical example is the behaviour of cables secured onto panels [13,14,15] when very low forces are applied: the presence of the cables can influence the characteristics of the panel in terms of stiffness and damping values. The cables themselves become paths for vibration transmission and modelling them with simple non-structural mass (as it is often done for structural analyses) does not give accurate results.…”

Modelling the effect of electrical harness on microvibration response of structures

“…In particular, Goodding, Babuska et al developed a method to study the behaviour of space structures supporting cables where the finite element model of the structure is updated with the addition of a model of the cable [20,21]. The model updates required to represent the cable are calculated from a combination of: direct measurements, dynamic tests, static tension tests and wire handbook data (all this data is then fed into different tests to retrieve modulus of elasticity, shear modulus and damping) [22]; the cable attachments are also modelled. This work provided a good estimation of the effect the harness has on spacecraft structures and also gives excellent results for spacecraft panels with cables [22], however extending it to whole spacecraft structures would require a substantial modelling effort which is difficult to justify in the context of a commercial spacecraft project development.…”

“…The model updates required to represent the cable are calculated from a combination of: direct measurements, dynamic tests, static tension tests and wire handbook data (all this data is then fed into different tests to retrieve modulus of elasticity, shear modulus and damping) [22]; the cable attachments are also modelled. This work provided a good estimation of the effect the harness has on spacecraft structures and also gives excellent results for spacecraft panels with cables [22], however extending it to whole spacecraft structures would require a substantial modelling effort which is difficult to justify in the context of a commercial spacecraft project development. In addition, even when these relatively complicated modelling techniques were applied, it would still be necessary to extend them to reproduce the nonlinearities observed in the microvibration response and which are the studied in this article.…”