No abstract

Helmholtz resonators are used in a variety of applications to reduce the transmission of unwanted sound. This work demonstrates that mechanically coupled resonators can be used to design a particular transmission loss response, provide a wider bandwidth of attenuation, and adapt the transmission loss characteristics of a structure to attenuate disturbances of varying frequency. An analytical model is developed for a single, coupled resonator system mounted on a one-dimensional duct. Experiments are conducted on a similar system that uses a thin membrane to couple the resonator volumes. A simplistic model of the membrane is presented to estimate equivalent “piston” properties from measured physical properties. Experiments confirm that the coupled resonator system behaves as predicted by the model simulations, and that the transmission loss can be shaped by adjusting the mass or stiffness of the coupling member. The experimental results also illustrate the structural-acoustic coupling effects between the resonators and the membrane, and indicate that a more inclusive model of the membrane and acoustic dynamics is required in order to accurately predict the resonator transmission loss.

No 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

Signal and electrical power cables pose unique challenges to spacecraft structural design and are often poorly modeled or even neglected. The objective of this research was to develop test methods and analysis techniques to accurately model cable-loaded spacecraft, using linear finite element models. Test methods were developed to characterize cable extensional and bending properties when subjected to low-level lateral dynamic loads. Timoshenko beam theory, including shear and bending, was used to model cable lateral dynamics, and the model formulation applicability was validated through experiment. An algorithm was developed to estimate cable area moment of inertia and shear area factor, shear modulus product, from a single driving point mobility function. Test methods and the parameter estimation algorithm were validated, using metallic rod test specimens. Experiments were performed on cables of differing constructions and spans, to develop a database for finite element modeling validation experiments. Nomenclature A= specimen cross-sectional area, mm 2 a n = nth mode shear beam wave number b n = nth mode shear beam wave number c k = rational fraction polynomial numerator coefficient d eff = effective shear beam diameter, mm d k = rational fraction polynomial numerator coefficient E = Young's modulus, Pa f = external force, N f meas = measured force, N f trans = force transmitted to the cable specimen, N G = shear modulus, Pa H = mass-corrected driving point accelerance, m s 2 N 1 H meas = measured driving point accelerance, m s 2 N 1 I = cross-sectional area moment of inertia, mm 4 j = 1 p k = beam area shape factor kG = shear modulus product with shear area shape factor L = beam span, mm M = suspended mass, kg m = beam linear density, kg=m m dp = added mass at the driving point, kg R g = nondimensional radius of gyration S = beam slenderness ratio s = Laplace variable, 1=s t = temporal variable, s v = beam lateral deflection, mm x = position along the beam span, mm x dp = driving point acceleration, m=s 2 = beam cross-sectional rotation angle, rad = nondimensional modulus ratio n = nth mode frequency parameter = mass density, kg=m 3 ! = circular frequency, rad=s ! n = nth mode circular frequency, rad=s