In this paper a new approach for designing mechatronic vibrating branched structures has been presented. Mechatronic structures have been built from mechanical discrete systems connected to piezoelectric actuator and externalLxRxCx network, with different configurations. Modeling simplification has been performed by use of non dimensional transformations and retransformations. In each case reverse task has been solved by distribution into partial fraction method in respect to required dynamic properties in form of frequency spectrum: resonant and anti resonant frequencies. Furthermore, different configurations of final LxRxCx network have been presented. These considerations have been supported by calculation examples, and all results have been presented in the graphical form. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

This work presents methods of reduction of the vibration of mechanical systems by means of active elements as well as examples of implementation of active reduction of vibration by means of electrical elements [1], [2]. This work also describes a structural and parametric synthesis, which can be defined as the design of systems meeting specific requirements. These requirements refer to the frequency values of the systems’ vibration. The presented approach i.e. a non-classical synthetic method applied in designing mechanical systems with elements reducing unwanted vibrations. As a result of the synthesis, one can obtain the structure and parameters of the system of required properties. The synthesis may also be applied to modify the already existing systems in order to achieve a desired result [1–3].

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In the paper, the problem of designing of mechatronic discrete systems for vibration control has been investigated and generalized. As the design method, the synthesis has been used. Main focus of the paper is given to formalization of the mechatronic structures that contains elements with negative values on different stages of the synthesis process. The study is done based on different distributions methods of dynamical characteristics, dimensionless transformation and retransformation algorithm, simultaneously with verification of possible configurations of connections of piezostack actuators with external electric networks. As the result, various classifications of mechatronic discrete systems and general design constrains have been presented and discussed.