Metamaterials have recently emerged and shown great potential for noise and vibration reduction in specific frequency ranges, called stop bands. To predict stop bands, their often periodic nature is exploited and dispersion curves are calculated based on a single representative unit cell, typically modeled using the finite element method. Since their sub-wavelength nature and often intricate design can lead to large unit cell models, model reduction methods such as the Generalized Bloch Mode Synthesis have been proposed to greatly accelerate dispersion curve calculations. In order to calculate forced vibro-acoustic responses of finite periodic elastic metamaterial plates composed of an assembly of unit cells, however, full order finite element models rapidly become computationally unaffordable. Therefore, in this work the Generalized Bloch Mode Synthesis is incorporated in a sub-structuring approach, which enables fast forced vibration response calculations of finite elastic metamaterial plates based on a single reduced order unit cell model. The main advantage as compared to a regular Craig-Bampton approach is the additional local reduction of unit cell boundary degrees of freedom, whereby a compatible basis for the identical neighboring unit cells is incorporated. In addition, by combining this Generalized Bloch Mode Synthesis based sub-structuring approach with the Elementary Radiator Approach, efficient sound transmission loss computations of finite periodic metamaterial plates are enabled. The performance of the proposed approach for fast vibro-acoustic response predictions is demonstrated for different cases.

Recently, the potential of metamaterials and phononic crystals to cope with conflicting requirements for obtaining lightweight structures with desirable noise and vibration properties has been demonstrated. These, often periodic, structures are commonly studied based on their representative unit cell (UC) of which the vibro-acoustic performance is examined by means of their wave propagation, visualized by dispersion curves. Typically, the UC is discretized using a finite element technique to capture the possibly complex geometry. This leads to a high computation cost for the dispersion curve calculation which can be strongly reduced by applying modal-based model order reduction techniques such as the (generalized) Bloch mode synthesis (GBMS). In this paper, the choice of the UC is shown to have an impact on the dispersion curve calculation time. Moreover, the efficiency of GBMS strongly depends on the UC choice. The highest reduction in computation time is accomplished when the number of boundary degrees-of-freedom is limited.

Joined structures are of great industrial relevance. The dynamic effects of joints are, however, often practically difficult to accurately account for in numerical models, as they often lead to local changes in stiffness and damping. This paper discusses the comparison between measurements and simulations of joined panels considering four different joining techniques: adhesive bonding, metal inert gas welding, resistance spot welding and flow drill screwing. An experimental modal analysis is performed on the different systems and the power injection method is applied to determine the loss factors of single plate systems and their joined counterparts. The joined panels are modeled in a holistic simulation environment with particular focus on the joining region, by the application of predefined and generic joint models. A very good agreement is obtained between the simulated dynamic behavior and the experimental results, showing that an accurate representation of the joints has been obtained.

In the past decades, an increasing trend towards the structural combination of lightweight materials and traditional metals has been observed. For these multi-material interfaces, traditional joining technologies such as bolting and welding have to be re-thought and adhesive bonds can be a valid alternative. The substitution of the joints has an impact on the stiffness, damping, and mass distribution of the entire assembly and should be taken into account while designing for NVH, durability, and performance. The aim of this work is to experimentally compare the effect of bolts and adhesive bonding on the vibrational response of the assembly, in terms of modal frequency, shape, and damping. Plate-to-plate single lap joints are tested under transverse vibration. In particular, we compare one M4 bolted connection and three adhesive connections, respectively, realized with stiff epoxy, flexible foam tape, and toughened acrylic. Results show that, in a low-mid frequency region between 0 and 250 Hz, the substitution of bolts with adhesives has a limited influence on mode shapes but can lead up to a 6-fold increase of the modal damping values and 10% increase of the modal frequencies.

The bending wave stop band behavior of locally resonant metamaterial and phononic crystal plates can strongly improve the vibration performance of flexible plates in targeted frequency ranges. Their acoustic insulation performance, however, is found to strongly depend on the stop band mechanism, also influencing the frequency range of improvement. While sound transmission loss improvements are predicted for both infinite periodic plates, the finite phononic crystal plate performance can differ significantly.