In this thesis, a cell of an active metamaterial, which does not obey the principle of dynamic reciprocity has been designed. Aided by computer tools, a rectangular cross-section tube was constructed, which is periodically intermitted by double membranes. It is suitable for 3D printing so that the measuring and driving members of the active vibration isolation system can be attached to it. Between the membranes, in rectangular acoustic cavities, there are two electromagnetic actuators that can exert a force perpendicular to the surface of the membranes. Sensors, four accelerometers, capable of measuring the vibration velocity, are attached to the terminals of the force actuator. The setup is designed in such a way that the dynamic response of the membranes and the acoustic cavities is predominantly determined by their first mode of vibration, allowing for a good approximation with a mathematical model for a classical linear vibrational system with four degrees of freedom and concentrated parameters. The equations of motion have been derived together with a total of 16 transfer functions between the forces and vibration velocities of each of the four membranes in the system. The vibration velocity signal is used to close feedback loops, so that the force generated by the actuator is proportional to the vibration velocity of the membrane. In this setup, the measuring and driving members of the feedback loops are not colocated. If only one of the two sensors per actuator is use, it is possible to achieve active damping through the feedback loop, resulting in an asymmetric damping matrix of the system. This results in a loss of acoustic reciprocity when the sound passes through the cell of the active metamaterial. the parameters of the passive system were determined. By analyzing the stability of such a system using the generalized Nyquist criterion. The mathematical model has been numerically verified using a coupled structural-acoustic model of the active metamaterial cell using tools for a finite element analysis of free vibration of mechanical systems with distributed parameters. Furthermore, the loss of acoustic reciprocity has been demonstrated and quantified across a wide frequency spectrum by comparing the mathematical lumped parameter model and numerical distibuted parameter model.