*Article* **Finite Element Approaches to Model Electromechanical, Periodic Beams**

#### **Wiktor Waszkowiak, Marek Krawczuk and Magdalena Palacz \***

Department of Mechatronics and High Voltage Engineering, Faculty of Electrical and Control Engineering, Gda ´nsk University of Technology, Narutowicza 11/12, 80-233 Gda ´nsk, Poland;

wiktor.waszkowiak@pg.edu.pl (W.W.); marek.krawczuk@pg.edu.pl (M.K.)

**\*** Correspondence: mpalacz@pg.edu.pl; Tel.: +48-58-347-25-08

Received: 6 February 2020; Accepted: 11 March 2020; Published: 14 March 2020

**Abstract:** Periodic structures have some interesting properties, of which the most evident is the presence of band gaps in their frequency spectra. Nowadays, modern technology allows to design dedicated structures of specific features. From the literature arises that it is possible to construct active periodic structures of desired dynamic properties. It can be considered that this may extend the scope of application of such structures. Therefore, numerical research on a beam element built of periodically arranged elementary cells, with active piezoelectric elements, has been performed. The control of parameters of this structure enables one for active damping of vibrations in a specific band in the beam spectrum. For this analysis the authors propose numerical models based on the finite element method (FEM) and the spectral finite element methods defined in the frequency domain (FDSFEM) and the time domain (TDSFEM).

**Keywords:** FEM; SFEM; active periodic structures; smart materials
