The sound transmission loss of conventional means of passive acoustic treatment in the low-frequency range is governed by two physical mechanisms: the inertia, as stated by the mass density law, and the local resonances of the structure. Since usual partitions are flexible and lightweight, their acoustic performance is poor, especially below 300 Hz. Although conventional acoustic meta-materials can offer excellent acoustic properties, they also perform poorly in this range. Therefore, novel meta-structures are required to overcome these limitations. This proposed novel absorber optimally combines the concepts of KDamper (KD) and inertial amplification mechanisms (IAMs). The novelty of the KD-IAM absorber lies in the generation of equally deep but significantly wider attenuation bands surpassing the mass density law while requiring only a small fraction of additional mass. The absorber is implemented and demonstrated as an elastic mount for retrofitting existing panels, essentially manipulating the resonant response of the structure by controlling the panel’s boundary conditions. It is also shown that increasing the panel’s rigidity and, consequently, its fundamental eigenfrequency utilizing stiffeners results in further improvements in the bandwidth and depth of noise attenuation. A wide and deep attenuation band is demonstrated in the resonance region below 120 Hz, up to 13 dB above the reference level. An indicative design and implementation for a case study are presented. It is further demonstrated that the same concept can be utilized for the formation of meta-structures by periodic repetition of KD-IAM unit cells, leading to significant additional attenuation of the lowest vibration modes.
Phononic structures with unit cells exhibiting Bragg scattering and local resonance present unique wave propagation properties at wavelengths well below the regime corresponding to bandgap generation based on spatial periodicity. However, both mechanisms show certain constraints in designing systems with wide bandgaps in the low-frequency range. To face the main practical challenges encountered in such cases, including heavy oscillating masses, a simple dynamic directional amplification (DDA) mechanism is proposed as the base of the phononic lattice. This amplifier is designed to present the same mass and use the same damping element as a reference two-dimensional (2D) phononic metamaterial. Thus, no increase in the structure mass or the viscous damping is needed. The proposed DDA can be realized by imposing kinematic constraints to the structure’s degrees of freedom (DoF), improving inertia and damping on the desired direction of motion. Analysis of the 2D lattice via Bloch’s theory is performed, and the corresponding dispersion relations are derived. The numerical results of an indicative case study show significant improvements and advantages over a conventional phononic structure, such as broader bandgaps and increased damping ratio. Finally, a conceptual design indicates the usage of the concept in potential applications, such as mechanical filters, sound and vibration isolators, and acoustic waveguides.
The Discrete Element Method (DEM) is a well-established approach to study granular materials in numerous fields of application; modelling each granular particle individually to predict the overall behavior. This behavior can be then extracted by averaging, or coarse graining, the sample using a suitable method. The choice of appropriate coarse-graining method entails a compromise between accuracy and computational cost, especially in the large-scale simulation typically required by industry. A number of coarse-graining methods have been proposed in the literature, these are reviewed and categorized in this work. Within this contribution two novel porosity coarse-graining strategies are proposed including a Voxel method where a secondary dense grid of "pixel-cells" is implemented adopting a binary logic for the coarse graining and a Hybrid method where both analytical formulas and pixels are utilized. The proposed methods are compared with four coarsegraining schemes that have been documented in the literature, including the Particle Centroid Method (PCM), an Analytical method, a method which solves the diffusion equation and an approach which employs averaging using kernels. The novel methods are validated for problems in both two and three dimensions through comparison with the "accurate" Analytical method. It is shown that, once validated, both the proposed schemes can approximate the exact solutions quite accurately, however there is a high computational cost associated with the Voxel method. The accuracy of both methods can be adjusted allowing the user to decide between accuracy and computational time. A detailed comparison is then presented for all six schemes considering "accuracy", "smoothness" and "computational cost". Optimal parameters are obtained for all six methods and recommendations for coarse graining DEM samples are discussed.
Purpose Inertial amplification of an oscillating mass has been considered by various researchers as a means to introduce enhanced vibration control properties to a dynamic system. In this paper an experimental prototype of a novel inertial amplifier, namely the Dynamic Directional Amplification mechanism (DDA), is developed and its dynamic response is subsequently evaluated. The DDA is realized by imposing kinematic constraints to the degrees of freedom (DoFs) of a simple oscillator, hence inertia is increased by coupling the horizontal and vertical motion of the model. Methods The concept and mathematical framework of the amplifier are introduced and then validated with experimental measurements conducted on the vertical shaking table, located in the Dynamics & Acoustics Laboratory, National Technical University of Athens. Results Analysis indicates the beneficial effect of the DDA to the dynamic response of the oscillator when compared to the initial structure, showcasing a decrease in the acceleration values and shift of the resonating frequency in the derived transfer functions. Conclusions The key novelty of the DDA lies in its inertial amplification properties, introduced by a simple geometry and easy-to-apply structure. The proposed framework may be incorporated in applications such as sound and vibration isolators, acoustic panels, acoustic and seismic metamaterials and other vibration control devices that aim to explore the DDA’s dynamic amplification properties. The mechanism has been previously applied by the authors to phononic and locally resonant metamaterials aiming to introduce bandgaps within the low-frequency domain. Graphical Abstract
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