© 2025 Elsevier B.V.Periodic structures have attracted interest across various fields of science and engineering due to their unique ability to manipulate wave propagation. The Wave-based Finite Element Method (WFEM) is typically employed to model such systems by relying on the dynamic behavior of a single unit cell of the lattice. However, the WFEM can face challenges in handling unit cell finite element (FE) models with several degrees of freedom (DoFs), as it involves operating with large-sized matrices. Therefore, in this work, we combine the WFEM with the Generalized Bloch-Mode Synthesis (GBMS) to offer a highly efficient and accurate method for modeling periodic structures. Three different types of unit cells were investigated in this study, demonstrating that highly reduced unit cell models can be obtained using the Craig-Bampton (CB) and Local-level Characteristic Constraint (L-CC) model reduction methods. By leveraging the advantages of the WFEM and the reduced-order unit cell models, harmonic forced responses were rapidly and accurately computed. Additionally, we showed that combining the WFEM with the GBMS mitigates numerical issues when computing forced responses, as the boundary DoFs are reduced to a smaller number of equations, avoiding the computation of high-order evanescent modes, a task that can be difficult to perform accurately for some unit cells.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.This work investigates a novel metamaterial concept using the Wave-based Finite Element Method. The metamaterial comprises a periodic-like structure manufactured through fused filament deposition, featuring internal cavities filled with water. Experimental characterization of the dynamics of the periodic system without internal fluid confirms good agreement with numerical predictions obtained through frequency response function measurements. Furthermore, the dynamic behavior of the two-phase periodic metastructure is experimentally examined, where waves interact within the heterogeneous medium consisting of both fluid and solid phases. In this case, the resulting wave characteristics depend on the properties of both phases. It was shown that the fluid-filled metastructure exhibits vibration reduction through the whole frequency range compared to the case lacking internal fluid. Additionally, it was seen that the frequency range near the second attenuation band of the periodic metastructure without fluid can be enlarged after the fluid inclusion within the cavities of its unit cells, as a consequence of mass increase and damping effects. Consequently, this work presents a promising avenue for metastructure design, with potential applications in structural dynamics and acoustics.

© 2024Periodic structures have been attracting a great deal of academic and industrial interest lately, due to their distinctive vibration and wave propagation behavior, which can be explored for the development of innovative solutions to structural dynamics and vibroacoustic problems. Although such a potential has been demonstrated in a large number of studies, the investigation of detrimental effects, which can be present in practical applications, is still necessary. This paper reports investigations on the combined influence of uncertainties affecting ambient temperature — which alters material properties and induces stress-stiffening due to constrained thermal dilatation — and boundary conditions (BCs) on the bandgap characteristics of periodic beams. The space-dependent temperature fluctuations are represented as a one-dimensional stationary Gaussian random field, discretized using the Karhunen-Loève expansion, while non-ideal BCs, represented as springs, are modeled as discrete random variables. Sampling-based stochastic analyses of the central frequency and bandwidth of the beam's attenuation bands are performed using Monte Carlo simulations. The results demonstrate that the variability in the attenuation band features is influenced not only by the coefficients of variation (CVs) of the input random quantities, but also by the correlation length of the random temperature fluctuations. Numerical simulations reveal that the bandgap central frequency is primarily affected by the temperature random field, while the BCs govern the bandwidth. Although low CV and standard deviation values are obtained for the dispersion of the bandgap features, reliability analyses indicate that some designs exhibit low reliability. Increased variability in both the bandgap central frequency and bandwidth is observed for greater temperature correlation lengths and CVs. The contributions of the study include the proposal of a comprehensive stochastic modeling procedure duly accounting for relevant random influences, and evidencing that those influences can be significant, requiring consideration in the design of robust periodic structures.

© 2024 Proceedings of ISMA 2024 - International Conference on Noise and Vibration Engineering and USD 2024 - International Conference on Uncertainty in Structural Dynamics. All rights reserved.Periodic structures have been attracting increasing interest due to their potential for manipulating waves. The Wave-based Finite Element Method (WFEM) is typically employed to model such systems, involving the examination of a finite element mesh of a single unit cell of the periodic lattice. However, the utilization of the WFEM with more challenging problems, encompassing unit cell models with several degrees of freedom, can be challenging, as it involves operating with large-sized matrices. To tackle this matter, one developed a modified generalized Bloch-mode synthesis that, in conjunction with the WFEM, can efficiently and accurately model periodic structures. Simulations were performed on a plate-like elastic metamaterial, where relative errors between resonances of the reduced model and the reference solution less than 0.5% and cross signature scale factor close to one across frequency were found, demonstrating the outstanding performance of the MGBMS and WFEM in computing dispersion curves, wave shapes, and forced responses.

© 2023, Marcílio Alves. All rights reserved.Recent research on structural dynamics has steered towards elastic metamaterials, as band gap phenomena can be explored to mitigate vibration. A challenge in their design is the determination of configurations resulting in wider band gaps in lower frequency ranges. Since some level of damping is unavoidable in any real engineering structure, it is necessary to extend the current methodology of optimal design to provide a deeper understanding of how damping may affect the desired performance. Therefore, the main objective of this article is to propose and evaluate a numerical procedure for the optimization of band gaps in damped metamaterials. Specifically, a modified objective function that incorporates an evanescence index integral is used and two optimization schemes are implemented, each reflecting whether the structure is undamped or damped. It is shown that the optimal damped metamaterial has wider range of attenuation than the undamped optimal one, but with decreased attenuation levels. The optimization procedure is validated numerically for a finite structure, demonstrating reduced transmissibility of wave motions.

© 2020 Elsevier LtdThe emergence of automated manufacturing techniques has allowed the realization of the so-called tow-steered composite laminates, in which the fibers are deposited following continuous curvilinear paths. This enables to broaden the design space to satisfy a variety of design objectives. Previous studies have shown that conventional composites can be designed to maximize the modal frequencies and modal damping factors. However, similar investigations have not been devoted to tow-steered composites so far. In this context, the objective of this paper is to investigate the use of multi-objective optimization aiming at simultaneously maximizing the fundamental modal frequency and corresponding specific damping capacity of tow-steered composite laminates. The fiber trajectories are parameterized using two different schemes, and the parameters are taken as design variables. The equations of motion are derived from the combination of the Classical Lamination Theory with the Rayleigh–Ritz method. Damping is modeled by using the Strain Energy Method. Numerical optimization is performed using the evolutionary Direct Multisearch method, which provides optimal solutions forming Pareto fronts. Results obtained from various scenarios, including fully and partially steered laminates, and different boundary conditions, show that fiber steering can indeed improve substantially the dynamic characteristics, including damping, of composite laminates.

© 2020 Elsevier LtdMany studies previously reported in the literature have demonstrated, both theoretically and experimentally, the influence of thermally-induced stresses on the static and dynamic behavior of structures, due to the so-called stress-stiffening effect. In most cases of practical interest, temperature variations associated to environmental and operational conditions are governed by rather complex combinations of conduction, convection and radiation mechanisms. As a result, the temperature values at different points of a structure are very difficult to control and can rationally be considered as random quantities. In this context, the present paper addresses the stochastic modeling and characterization of the influence of thermal stresses on the natural frequencies of thin rectangular plates, assuming space-dependent temperature fluctuations modeled as stationary two-dimensional Gaussian random fields. For this purpose, based on the hypotheses of the classical Kirchhoff plate theory, a Rayleigh-Ritz-based dynamic model is first derived for the bending vibrations of plates, accounting for the presence of thermal stresses. This model is combined with the Karhunen-Loève expansion (KL), which is used to discretize the temperature random field, after which the statistics of the random natural frequencies are estimated by Monte Carlo sampling. Numerical simulations are performed for plates under free boundary conditions. Simulation results, which encompass sampling-based statistics for the thermal stresses and the first six natural frequencies of the plate, are presented and discussed. In addition, since thermal stresses can induce buckling, reliability has also been estimated considering this type of failure. Results enable to conclude that space-dependent temperature uncertainty can be significant upon the vibration and buckling behavior of plates, which justifies its consideration.

© "Advances in Acoustics, Noise and Vibration - 2021" Proceedings of the 27th International Congress on Sound and Vibration, ICSV 2021. All rights reserved.Over the last decades, the development of novel permanent magnets, especially those having rare earth metals in their composition, has led to a great improvement in their performance, as compared to conventional ferrite permanent magnets. Therefore, there has been an increasing demand for these magnets in many (including new) application fields. In particular, the strong magnetic forces exerted between magnets can be explored as a means of promoting contactless mechanical coupling between separate parts and structural components. In this context, this paper investigates the dynamic behavior of a multiphysics system composed of two parallel cantilever beams at the extremity of which cubic permanent magnets are attached. Given the nonlinear nature of the magnetic forces, the main interest is to characterize the dynamic phenomena induced by the magnetic coupling. The study also encompasses analyses of the influence of the gaps between the two magnets and the relative orientation of their polarization axes. For this purpose, an elasto-magnetic structural model is developed, accounting for the flexibility and mass distributions of the beams and also the magnetic interactions. Upon resolution of the equations of motion, this model is used to perform a number of numerical simulations, the results of which are presented and discussed.

© 2020, The Brazilian Society of Mechanical Sciences and Engineering.This article presents a novel morphing unit cell concept which relies on the combination of shape memory alloy wires for actuation and permanent magnets to enable multistability. Two distinct applications are investigated experimentally, consisting in a morphing beam metastructure made with three unit cells and a variable camber airfoil metastructure having six unit cells in the chord-wise direction. Tests are performed to assess the influence of the permanent magnets on the morphing behavior of the two referred metastructures. It is verified that the permanent magnets are able to provide new stable equilibrium configurations to the metastructure and to reduce the time necessary for morphing. Another interesting feature, which enables the reduction in energy consumption, is that, due to the magnetic interactions, the thermal activation of the SMA wires can be ceased once an equilibrium configuration is achieved. The paper describes the design premises, evaluates its limitations and devises future improvements.

© 2018 Elsevier LtdIn this work, viscoelastic materials are adopted for handling aeroelastic features of typical section models with three degrees-of-freedom, which present non-smooth, free-play type nonlinearities in their control surface. A rotational viscoelastic damper is added to the resilient element associated to the control surface motion of the typical section. Equations of motion are derived accounting for the viscoelastic damper dependence on frequency and temperature. For this, a fractional derivatives-based viscoelasticity constitutive law is considered. Aerodynamic forces are introduced based on linear potential unsteady aerodynamics accounting for arbitrary airfoil motions. The aeroelastic behavior is investigated through time domain simulations, from which bifurcation diagrams are constructed. Numerical results show that the addition of viscoelastic damping can increase the flutter speed noticeably and reduce the amplitudes of limit cycle oscillations for the system under consideration. Another observed benefit provided by the viscoelastic damper is that undesirable subcritical behavior for the bifurcation onset can be eliminated or modified to have a supercritical character. The influence of temperature on the aeroviscoelastic behavior is also investigated. Using the proposed strategy, nonlinear instabilities can be controlled, improving the safety margins of aeroelastic systems.