ACTIVE DYNAMIC ANALYSIS AND CONTROL OF SPACE BASED ADAPTIVE MEMBRANE STRUCTURES

Abstract

Today's space technology is intended to enable operations of satellites in higher orbits to improve their coverage. On the other hand, higher altitude operation requires larger focal lengths to provide high ground resolutions. Larger apertures can provide higher ground resolutions at the price of significantly higher system’s costs. In this regard, inflatable membrane structures are greatly attracting the interests of scientists as a scientific platform in outer space exploration missions due to their outstanding performance in weight and stowage volume. The inflatable membrane structures are extremely lightweight and high structural efficiency. Due to its structural form, it becomes easily collapsible and transported around. But, the large and flexible membrane structures possess terrible dynamic properties and minimal effective bandwidth. Hence, all possible failure modes must be fully analyzed before launching them to space. The next level of research will require active dynamic analysis, wrinkling analysis, vibration control, and shape morphing control to identify the failure modes of these inflatable structures. Hence, this research work presents the numerical and experimental analyses of wrinkling, vibration and shape control at various loading and boundary conditions. First part of the present work discusses the wrinkling analysis of the membrane structures. Formation of wrinkles takes place when membrane is subjected to non-positive minor principal stresses and at the same time, large deformation occurs. A better understanding of the effects of wrinkles on the structural performance and stability of these structures is essential and desirable. Tension field theory is used to carry out the analytical analysis of the different prescribed conditions. As a precondition for wrinkling, development of compressive stresses in the transverse direction is found and it is dependent on shape, the length-to-width aspect ratio (β) & thickness of the membrane structures. Shape and size of wrinkles also depend on the applied tensile strain, shear strain, transverse loading and torsional loading. Various prescribed models are analyzed numerically and experimentally to observe the behavior of membrane structures for various conditions. First condition describes the wrinkling analysis of membrane structure with edge tensile load. The effect of tension load, length-to-width aspect ratio (β) and Poisson's ratio (ν) have been studied to observe the membrane behavior. Second condition discusses the wrinkling analysis of membrane with corner tensile loads. The effect of symmetric and asymmetric loading on RMS error, wrinkle’s amplitude and wavelength of wrinkles are studied. ii Also, the thermal wrinkling analyses are discussed using different representative conditions. The third condition investigates the effect of thickness and load variation on wrinkling behavior of membrane under the shear loading. Fourth condition discusses the effect of transverse loading on membrane wrinkles. Wrinkling analysis of annular circular membrane structure has been performed under shear loading as fifth condition. The second part of this study covers the vibration analysis of a thin membrane with prescribed boundary conditions under wrinkled and non-wrinkled state. The wrinkled membrane vibrates along equilibrium position of wrinkle configuration. Based on the Lagrange equation, the differential equation of vibration has been established for wrinkled membrane. The vibration modes of wrinkled membrane are strongly correlated with wrinkle configurations. Local stiffness of wrinkle wave peaks is larger because of large stress. Vibration frequency apparently increases with wave peak vibration. With the wrinkle out-of-plane deformation, the natural frequency of vibration changes in oscillation. The active vibration control analysis has been carried out using linear quadratic regulator (LQR) and the control mechanism is analyzed. The optimal placements of the piezoelectric actuators have been also discussed. The last part of the analysis is focused on shape analysis and control of the membrane structures. Here, the major discussion includes the shape analyses and wrinkling control of the membrane reflector. The shape analyses of the planar and parabolic membrane structures are discussed. The procedure of making actual (fabricated) parabolic membrane with ideal parabolic shape with flat pieces of the membrane is described. This covers the cutting pattern analysis and optimization of number of gores in the membrane with respect to seaming and central cap size. The effect of pressure variation in shape error and sensitivity of the reflector are also discussed. Shape selection of planar polygon membrane depends upon two factors, surface error and maximum principal stress present in the structures. It is found that the surface error decreases with the increase in number of polygon size. Various methods like edge trimming, punching, anchor points, multilayer, layup composite and mix- method are used to control the wrinkling formation and RMS error of the membrane structures. It is found that optimum edge trimming shows promising results with optimum number of anchor loadings