The elastic oscillation structure based on central pattern generators (CPGs), which can produce rhythmic motions, is discussed. First, Hopf CPG, the typical CPG model, being a signal generator for the elastic oscillation structure, is analysed via the theory of differential equations. Next, the well-posedness results of a coupling system composed by the CPG and an elastic beam are proved by means of the linear operator semi-group theory. Then, the numerical results using the finite difference method indicate that the coupled system can obtain a variety of periodic motion behaviours by choosing the internal parameters of the CPG network. Finally, the dynamic simulation of complex system motion is investigated using COMSOL Multiphysics. Song Chen and Yubiao Liu contributed equally to this work. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

In this paper, we investigate the well-posedness and the asymptotic stability of a two dimensional Mindlin-Timoshenko plate imposed the so-called acoustic control by a part of the boundary and a Dirichlet boundary condition on the remainder. We first establish the well-posedness results of our model based on the theory of linear operator semigroup and then prove that the system is not exponentially stable by using the frequency domain approach. Finally, we show that the system is polynomially stable with the aid of the exponential or polynomial stability of a system with standard damping acting on a part of the boundary.