Abstract: The mathematical model of the transmission syst. em takes into account the dependence of the line and earth parameters on the frequency. The solution of the propagation matrix equations for a polyphase lossy power line, is obtained by applying modal analysis. In order to define the effects of parameter variations on modal quantities, a new sensitivity model is presented. The al gorithm for the calculation of the modal sensitivity functions is suitable for easy computer implementation. The sensitivity analysis of the modal attenuation constants is carried out for horizontal lines with ground wires: the normalized sensitivity functions presented are of general validity. The computation of the niodal attenuation constants, carried out with the "exact" and the "approximate" method, leads to values whichprove to be in closer agreement with experimental results already known.

Abstract: It is noted that reduced models and reduced controllers for flexible space structures are obtained by retaining those modes which make the greatest contribution to quadratic control objectives. Attention is given to the relative importance of damping, frequency and mode shapes in the mode truncation decisions for the following control objectives: attitude control, vibration suppression and figure control. It is also shown that using Modal Cost Analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop coordinates which are most critical to the quadratic control performance criterion. In this manner, the modes which need to be controlled are deduced from truncations of the optimal controller.

Abstract: The role of damping in the prediction of spacecraft structural responses and loads, and in the structural design of spacecrafts is discussed. The methods used to incorporate damping in the structural analysis are summarized and some experiences and procedures relating to damping in recent spacecraft design are discussed. Methods for modal testing and the experimental determination of damping, the use of discrete dampers, and the estimation of payload response are studied. A collection of damping data for recent spacecraft and related hardware is provided in the appendix.

Abstract: This paper presents results of an experimental program conducted to obtain data which can be used for correlations of rotor blade dynamic analyses. Measurements were made of the rotating frequencies and mode shapes of a representative full-scale, two-bladed helicopter rotor in a vacuum. The blades were cantilevered to the hub. Mode shape data were obtained optically using a system of cameras developed specifically for this purpose. Excitation of the rotor was provided by vertical oscillatory motion of the hub. To compare experimental and analytical results, correlations of some experimental measurements with calculations from an existing blade modes computer program based on a Holzer-Myklestad procedure are presented, and the differences between the results are discussed. The experimental and analytical natural frequencies were generally in good agreement as were the principal components of the modal deflections for the flap and lag modes. The torsion mode shape indicated disagreement between the measured and calculated results in regard to the amount of flap and lag motions present in this mode, while the spanwise variations of the measured and calculated torsional components were in agreement.

Abstract: An unusual application of the method proposed by Asher (1958) for structural dynamic and modal testing is discussed. Asher's method has the capability, using the admittance matrix and multiple-shaker sinusoidal excitation, of separating structural modes having indefinitely close natural frequencies. The present application uses Asher's method in conjunction with a modern Fourier analyzer system but eliminates the necessity of exciting the test structure simultaneously with several shakers. Evaluation of this approach with numerically simulated data demonstrated its effectiveness; the parameters of two modes having almost identical natural frequencies were accurately identified. Laboratory evaluation of this approach was inconclusive because of poor experimental input data.

Abstract: Modal estimation of wave-front phase from phase derivatives is discussed. It is shown that it is desirable to minimize the number of modes estimated and the number of measurements used to maintain the quality of the estimates of low-order modes. It is also shown that mode cross coupling occurs when one tries to estimate modes higher than astigmatism.