In the recommended study, generalized coordinates such as components of wave functions would be considered as a substitute for higher order modes. Various sets of functions would be investigated, and the accuracy of the solutions obtained would be compared by substitution into the equations of motion. The study would proceed as follows: • Treat simple structures, such as beams and plates, • Assess accuracy and compare with modal approach, • Based on the above results, develop methods to generate the desired functions for complex lumped mass structures such as the power station, and • Evaluate accuracy and compare with modal approach. The end-product would be a computer program which would automatically generate the required expansion functions. b. Time-History Program with Accurate Evaluation of Gravity- Gradient Excitation To study, in detail, the control of a flexible structure in a gravity-gradient field, it is necessary to determine accurately the difference between the gravity force and the orbital centrifugal force at each mass point. In many existing computer programs these effects are computed and then subtracted; however, the effects are nearly equal, and it is the small difference which is of consequence. This procedure is, therefore, considered too inaccurate to be of value. To improve the procedure significantly, the gravity and orbital centrifugal effects should be expanded in a series, analytically subtracted, and the result should be programmed in a general time-history structural program. This computer program should be sufficiently general so that structures of any shape and mass distribution may be treated. In addition, to include gravity effects properly, it should have the capability of including a large variety of control systems as well as a general set of externally applied loads. It should not rely on orthogonal functions such as modes for the reduction of coordinates, so that the above described expansion functions may be used. The resulting program would be a powerful tool for predicting the dynamic behavior of a flexible structure in space. c. Dynamic Response to Thermal Excitation When the SSPS enters and leaves the Earth's shadow, it undergoes severe temperature changes. The thermally induced deformations during this alternate cooling and heating may result in significant vibration of the SSPS, and an investigation of this effect is recommended.
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