Analytical studies for buckling and the quasistatic thermal-structural response of an asymmetrical rolled-up solar array of the type used on the Hubble Space Telescope are presented. A buckling analysis assuming asymmetric loading because of geometric asymmetry establishes critical buckling forces and buckling modes. Quasistatic thermal-structural responses of the solar array subjected to the sudden radiation heating typical of a night-day orbital transition are also developed. Computations conducted for the Hubble Space Telescope show that the solar arrays were deployed with a solar blanket prestress that would induce global torsional buckling. Numerical computations for the quasistatic response show that thermally induced bending-torsional deformations would cause bending moments in the solar array's booms consistent with the local buckling failure observed by the astronauts. NomenclatureEqs. (24) and (28) c = BiSTEM speci c heat, J/(kg ¢ K) d = solar blanket xed end offset, m EI = BiSTEM bending stiffness, N ¢ m 2 EC = BiSTEM warping stiffness, N ¢ m 4 F x = solar blanket tension, N/m GJ = BiSTEM torsional stiffness, N ¢ m 2 g 1 , g 2 = nonhomogeneous term due to thermal effects; see Eq. (46) h = BiSTEM wall thickness, m I E = BiSTEM polar moment of inertia, m 4 k = BiSTEM thermal conductivity, W/(m ¢ K) L = solar array length, m M T = thermal bending moment, N ¢ m M x1 , M x2 = BiSTEM torque, N ¢ m M 1 , M 2 = BiSTEM bending moment, N ¢ m P = BiSTEM average axial force, N P cr = critical buckling force, N P f 1 , P f 2 = ratios of P 1 and P 2 to P P 1 , P 2 = BiSTEM axial force, N R = BiSTEM radius, m s 0 = solar heat ux, W/m 2 T = temperature, K N T = average temperature, K T m = perturbation temperature, K N T ss = steady-state average temperature, K T ¤ = steady-state perturbation temperature, K t = time, s V 1 , V 2 = BiSTEM shear force, N w m = solar blanket de ection, m w s = spreader bar de ection, m w s0 , h s 0 = center of spreader bar de ection and rotation w 1 , w 2 = BiSTEM de ection, m x, y, z = solar array coordinates, m x m = maximum bending moment position, m a = BiSTEM coef cient of thermal expansion, 1/K a s = BiSTEM thermal absorptivity a 1 , a 2 = magnitude of BiSTEM de ection, m b i , b 0 i (i D 1, 2) = torsional buckling eigenvalue [see Eq. (12)], 1/m c 1 , c 2 = magnitude of BiSTEM angle of twist, rad d = Kronecker delta function e s = BiSTEM thermal emissivity h x 1 , h x2 = BiSTEM angle of twist, rad k 1 , k 2 = bending buckling eigenvalue [see Eq. (8)], 1/m q = BiSTEM density, kg/m 3 r = Stefan-Boltzmann constant, W/(m 2 ¢ K 4 ) t = thermal response time, s v = BiSTEM angular coordinate, rad

Digital vibration control of a flexible cantilever beam using a thermal bending mo ment caused by the temperature gradient across the section of the beam is attained both by experi ments and simulations. Foil strain gauges bonded on the surfaces of the beam are used as an actuator which is capable of producing a thermal gradient. Thermal bending moments are applied in the proper sense to a flexible cantilever beam having very low natural frequency so that active control of the first mode bending vibration is realized. Experimental results show that the damping ratio is increased by about ten times. Simulations are based on the theoretical analysis in which the equation of state is derived from the equation of bending vibration for the beam, considering the heat flow on both upper and lower surfaces. A linear control law is determined based on the digital optimal regulator theory. A minimal order state observer is used to estimate a state variable which is not available in the measurements. Experimental results are consistent with the simulated ones.

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Analytical studies of the natural vibration characteristics and dynamic response for a simple model of an asymmetric flexible rolled-up solar array are presented. A natural vibration analysis of the solar array model including bendingtorsion coupling due to geometric asymmetry provides natural frequencies and mode shapes. Unusual features of the lower mode frequencies and mode shapes are discussed. The dynamic response of the solar array induced by sudden radiation heating for a typical night-day orbital transition is formulated. Additionally, numerical calculations are conducted for the solar array of the Hubble Space Telescope (HST). Variations of the dynamic response with the axial preload forces of the solar array booms are examined, and the vibration response due to the radiation heating of the HST solar array is discussed.

We have developed a tailless, two-winged flapping drone with a full span length of 180 mm and a total weight of 20.5 g. The developed flapping drone is characterized by three biomimetic techniques: an anisotropic vein pattern reinforcing the wing surfaces, an elastic flapping mechanism, and gravity center position control in the abdomen. On the basis of experimental and numerical results, the flapping wings are reinforced by a vein pattern made of an anisotropic carbon fiber-reinforced plastic (CFRP) laminate to passively provide appropriate aeroelastic deformation and positively utilize snap-though buckling on the wing surface at stroke reversals to provide a fast feathering rotation. The flapping wing kinematics are provided by a novel flapping mechanism with an energy recovery system using the elasticity of the mechanical system. Unlike other previously developed flapping robots, feedback control to stabilize the pitch and roll angles of the drone's body is conducted using a technique of gravity center position control, where the tail angles of the body are changed similarly to the abdominal movements of insects in flight. The developed flapping drone has succeeded in an autonomous hovering flight for more than 30 s and a vertical takeoff under a wireless condition with the gravity center position control.