On the use of the wave finite element method for passive vibration control of periodic structures

Abstract

the use of the wave finite element method for passive vibration control of periodic structures.Abstract. In this work, a strategy for passive vibration control of periodic structures is proposed which involves adding a periodic array of simple resonant devices for creating band gaps. It is shown that such band gaps can be generated at low frequencies as opposed to the well known Bragg scattering effects when the wavelengths have to meet the length of the elementary cell of a periodic structure. For computational purposes, the wave finite element (WFE) method is investigated, which provides a straightforward and fast numerical means for identifying band gaps through the analysis of dispersion curves. Also, the WFE method constitutes an efficient and fast numerical means for analyzing the impact of band gaps in the attenuation of the frequency response functions of periodic structures. In order to highlight the relevance of the proposed approach, numerical experiments are carried out on a 1D academic rod and a 3D aircraft fuselage-like structure.

Application of the Wave Finite Element Approach to the Structural Frequency Response of Stiffened Structures

“…Expanding the vectors of displacements/rotations and forces/moments, on the left or right boundary of a substructure s, using wave bases [10], we get:…”

“…The version perorted is the one of Silva, [10], which proposes to make left multiply to avoid ill-conditioning of matrices, as explained by Mencik [16].…”

Design and experimental validation of a metamaterial solution for improved noise and vibration behavior of pipes

“…Recently, Silva et al have utilized WFEM to analyze the forced response of coupled flat and cylindrical systems based on substructuring [32]. They have further investigated the use of WFEM in passive vibration control of 1D academic rod and 3D aircraft cylindrical fuselage-like structures [33]. Such numerical methods can facilitate the analysis of curved structures with more geometrical and mechanical complexities.…”

Dynamic analysis of periodic structures via wave-based numerical approaches and substructuring techniques = Análise dinâmica de estruturas periódicas utilizando uma abordagem de propagação de ondas e técnicas de sub-estruturação

“…Indeed, we are interested in mechanical systems which are composed of periodic structures or structures that can be approximately modeled as one. Engineering systems like those are common in real applications; we can mention, for instance, train rails (Figure 1.1(a) 1 ), pipeline systems (Figure 1.1(b) 2 ) in the oil and gas industry, some nanostructures like the nanorods, nanobeams and nanotubes (Figure 1.1(c) 3 ), aircraft fuselages (Figure 1.1(d) 4 ) or the fuselage of a space shuttle (which can be roughly regarded as stiffened cylindrical shells) in the aerospace industry, tires and chassis frames (Figure 1.1(e) 5 ) in the automotive industry and the hull of a submarine (Figure 1.1(f) 6 ) in the naval industry. Since periodic structures are formed by a regular repetition of a periodic unit in space, by applying periodic boundary conditions, only one periodic unit needs to be modeled in order to describe the dynamics of the whole structure.…”

“…where ‖˙‖ 𝑝 denotes any of the 𝑝-norms 6 and 𝜅 denotes the condition number 7 of a given matrix. Signorelli and von Flotow (1988) showed numerical errors in their study of periodic truss beams, and attributed them to computational inaccuracy (i.e., round-off errors).…”