This paper examines the well-posedness and adaptive stabilization of a satellite vibration caused by internal disturbances. The structure of the satellite is made up of two flexible, symmetrical wings that are connected to a central body. The wings are modeled as transmission Euler-Bernoulli beams with dynamic boundary conditions. We design high-gain adaptive regulators by measuring velocity feedback at the central body to quickly dampen vibrations. We demonstrate an exponential decay result for the system employing the multiplier method. The theoretical results are supported by a numerical simulation.