Articulated aerial robots, which comprise multiple link units connected by joints, can change their shapes during flight to perform advanced aerial manipulation. The more links indicate a higher ability to handle larger objects. The critical challenge with the increase in the number of link units is the elastic vibration of the chain-like structure, which significantly hampers stable flight. Thus, the number of links is limited to four in most of our previous multilinked model. However, the redundancy in the control input (thrust force) for a model with more than four propellers (four links) can help to address the elastic vibration. Therefore, in this study, we first present the elastic vibration model due to the torsional motion of the link rod in chain-like structure, based on multi-rigid body dynamics. Subsequently, we develop a control method with an optimization-based control gain design to suppress this elastic vibration via the redundancy of a control input. Finally, we demonstrate the feasibility of the proposed methods in vibration suppression by experiments with an eight-link multilinked model that is difficult to fly with conventional control methods.