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EN
The study investigated the effect of the fill factor, lattice constant, and the shape and type of meta-atom material on the reduction of mechanical wave transmission in quasi-two-dimensional phononic structures. A finite difference algorithm in the time domain was used for the analysis, and the obtained time series were converted into the frequency domain using the discrete Fourier transform. The use of materials with large differences in acoustic impedance allowed to determine the influence of the meta-atom material on the propagation of the mechanical wave.
EN
This paper describes a homogenization model for evaluating the effective elastodynamic properties of acoustic metamaterials in problems involving wave propagation. The methodology is based on determining the constitutive equations in terms of averaged quantities observed at the macroscale. In this sense, the approach very closely follows the pioneering ideas introduced by Willis, and afterwards, followed by several authors in the last ten years. The distinctive characteristic of our approach is that we write the microscale equation in the spatial domain. The model is validated with previous results published in the literature, and our results replicate them almost exactly. The resulting homogenization model could be used as an additional tool for the topology design of acoustic metamaterials.
EN
Phononic Crystals are receiving rising attention in the field of modern acoustic materials. PCs are artificial structures of periodically arranged scatterers. Such a structure enables creating a band gap in which, due to the Bragg diffraction phenomenon, vibrations are restrained or even forbidden. In this paperwork, the fluid-fluid PC is tested and simulated - the scatterers are constructed of water cylinders with an ethylene propylene diene monomer coat (EPDM - a hyperelastic rubber) and are embedded in air. The band gap is calculated to emerge in the audible range of frequency. Every simulation is performed with the use of the finite element method.
EN
The article presents the results of the study on impact of the distribution, number and type of conglomeration of point defects on the parameters of the acoustic wave passing through the phononic crystal. For the simulation, the method of finite differences in time domain (FDTD) was used. In the paper several types of point defects distribution topology both inside and on the surface of the two-dimensional phononic crystal was examined. In order to suppress waves reflected from the edge of medium PML (Perfectly Matched Layers) algorithm was applied. In the simulation a lossless medium was considered. The study revealed that a small amount of point defects inside the body of phononic crystal has weak effect on the acoustic wave remission, while relatively small number of defects placed on the crystal's surface significantly affected the characteristics of the acoustic wave.
PL
W artykule przedstawiono wyniki badań wpływu rozmieszczenia, liczby oraz typu konglomeracji defektów punktowych na parametry fali akustycznej przechodzącej przez kryształ fononiczny. Do przeprowadzenia symulacji wykorzystano metodę różnic skończonych w domenie czasu (FDTD). W pracy zbadano kilkanaście rodzajów topologii rozmieszczenia defektów punktowych zarówno wewnątrz, jak i na powierzchni dwuwymiarowego kryształu fononicznego. W celu wytłumienia fal odbitych od krawędzi ośrodka zastosowano algorytm PML (Perfectly Matched Layers). W symulacji rozważano ośrodek bezstratny. Badania ujawniły, że niewielka liczba defektów punktowych znajdujących się wewnątrz kryształu fononicznego ma mały wpływ na reemisję fali akustycznej, natomiast relatywnie mała liczba defektów umieszczonych na powierzchni kryształu wpływa istotnie na parametry przechodzącej fali akustycznej.
5
Content available remote The influence of fill factor on the phononic crystal eigenfrequencies
EN
Purpose: The aim of this article is to determine the effect of basic cell fill factor change on the eigenfrequencies observed in two-dimensional phononic crystal. Design/methodology/approach: To perform simulation, the FDFD (finite difference frequency domain) algorithm was used. On this basis, the search for eigenfrequencies was carried out starting from lowest possible acoustic frequency range (~20 Hz) and limited to first nine search results found (up to nearly 2.2 kHz) for increasing fill factor while maintaining the shape of a rod inside cell. Findings: The fill factor has a significant influence on the eigenfrequencies of the studied system when the frequency is above 1 kHz. With the increase of this factor at relatively low frequencies (less than 1 kHz in this case) there were no major changes observed. Research limitations/implications: The results were found only for specific system consisting of materials with similar sound velocity. Therefore, more research should be carried out for other cases i.e. taking into account the different topology of primary cells and various materials with other propagation velocity of acoustic waves in these mediums. Practical implications: Simulation of two-dimensional phononic crystal systems allows for designing new specialized multi-component materials with various acoustic properties. These systems can be adapted in a variety of applications, including acoustic filters, slow-wave devices, acoustic autocollimators and many other. Originality/value: Basic research allow to improve the quality of knowledge on more advanced problems. For this reason, it is important to know in detail how simple systems work and to determine the basic properties of these systems.
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