Inclusion of Shear Effects, Tension, and Damping in a DTF Beam Model for Cable Modeling

Abstract

The distributed transfer function method is applied to equations of motion for a space flight cable in an ongoing effort to characterize the effects of adding cabling to space structures. A cable model is presented in which the cable is modeled as a shear beam with multiple boundary constraints. Tension in the cable is included and a variety of damping mechanisms are incorporated. Comparison of the model results to experimental data is included, showing that the distributed transfer function cable model with equivalent cable property inputs can bound the range of cable responses and that hysteretic and connection stiffness damping improve the comparison between the model and experimental data. NomenclatureA = area of cable cross-section c v = damping coefficient for motion-based viscous damping c s = transverse damping coefficient for spring connection = rotational damping coefficient for spring connection E = composite elastic modulus of the cable EI = bending stiffness of the cable F(s) = transfer function matrix G = shear modulus G(s) = Laplace transform of the GHM damping expression as a function of s I = area moment of inertia k = connection spring stiffness = connection spring rotational stiffness l i = cable section length M = left side boundary condition matrix N = right side boundary condition matrix q = applied external force s = Laplace transform variable T = axial tension of the cable T m = transition matrix w = cable displacement W(x,s) = Laplace transform of the lateral cable displacement = GHM damping parameter, numerator = shear angle 2 = GHM damping parameter, denominator = GHM damping parameter, numerator = GHM damping parameter, denominator η(x,s) = solution vector for the distributed transfer function method = shear factor ρ = cable density = total rotation angle ψ = Laplace transform of the cable rotation

Experimental and Theoretical Analysis of Cabled Beams

“…The cabled beam model combines the cable model presented in [3] with constraint matrices to model the attachment points and time hysteretic damping in the cable. The cables for this study have an overwrap that keeps the individual wires in the same basic configuration and maintains radial compression on the cable.…”

“…where ( ) is the Laplace transform of the solution vector, F(s) is the fundamental matrix for the system in which system properties are incorporated, and ( ) represents any applied forces. Full details of the developed cable model can be found in [3], so this paper focuses on the cabled beam model. To use the DTFM, a fundamental matrix is determined based on the equation of motion.…”