Grapahene is a two dimensional allotrope of carbon. Since the onset of current century, particularly, upon successful exfoliation of single layer graphene, it has received significant research attention because of some of the extreme mechanical, thermal, electromagnetic and optical properties it exhibits. As various applications of graphene have been envisioned and their realizations attempted, dynamic characteristics of graphene also became an extremely important field of study. Based on solid state physics and first principle analysis, dispersion relationship of graphene has been computed using various methods. Some of these methods rely on various inter atomic potentials and force-fields. An approximate technique of mechanical characterization involves atomisticcontinuum modeling of carbon carbon bonds in graphene and its rolled 1D form carbon nanotube. In this technique, the carbon-carbon bonds are modeled as 1D frame elements. The equivalence of energies in various modes of the actual structure and the equivalent mechanical system has led to specification of various model parameters. Here, based on atomistic continuum method, we attempt to compute the dispersion relationship accounting for the bonded interactions and the next nearest non-bonded interactions. For that purpose we use frequency domain spectral finite element method with pointed inertial components. It has been shown that it is possible to obtain the dispersion relationship close to the one computed using ab-initio method.
Phononic crystals are synthetic materials with a periodic structure having spatial variations of elasto-inertial properties of constituent materials, aimed at developing devices and bulk material with engineered acoustic/ elastic properties. Multi-material structures with sides of a space filling polygonal tessellation, can constitute solid-solid phononic crystal. Coupled with inclusions and features, phononic crystals show rich and varied band structure phenomenon. We use frequency domain spectral superelement method and Bloch theory to efficiently calculate the band structures of such phononic crystals. We particularly investigate hexagonal honeycombs to assess the impacts of joint elasticity, inertia and circular and elliptical holes on band gap behavior.
The class of fabricated materials known as metamaterials, with its promises for unconventional material properties or characteristics, has opened up a whole new paradigm of possibilities and challenges. The primary enablers have been capabilities at the very low length scale and novel design configurations. Pentamode metamaterials, having fluid like properties, is one such idea to have been realized in recent past. This type of fabricated materials show high bulk modulus but low shear modulus. The fundamental constituent element is a rod like structure tapered down on both ends. Four of such elements meet at any joint, two of which in a plane orthogonal to that of the other two. The dynamics and wave propagation characteristics of such structures have been studied with an aim to obtain band structures formed because of their periodic nature.
Here, a methodology has been developed to compute the wave propagation characteristics of such pentamode structures using spectrally formulated finite elements based on frequency domain Ritz method. Bloch theory has also been used to represent the dynamics of an infinite structure through that of a unit cell. The proposed method is computationally more efficient compared to one using conventional finite element. A few variants of pentamodes are also analyzed to arrive at configurations with superior wave propagation characteristics.
A novel design for the geometric configuration of honeycombs using a seamless combination of auxetic and conventional cores-elements with negative and positive Possion ratios respectively, has been presented. The proposed design has been shown to generate a superior band gap property while retaining all major advantages of a purely conventional or purely auxetic honeycomb structure. Seamless combination ensures that joint cardinality is also retained. Several configurations involving different degree of auxeticity and different proportions auxetic and conventional elements have been analyzed. It has been shown that the preferred configurations open up wide and clean band gap at a significantly lower frequency ranges compared to their pure counterparts. In view of existence of band gaps being desired feature for the phononic applications, reported results might be appealing. Use of such design may enable superior vibration control as well. Proposed configurations can be made isovolumic and iso-weight giving designers a fairer ground of applying such configurations without significantly changing size and weight criteria.
A wave propagation based approach for the detection of damage in components of structures having periodic damage has been proposed. Periodic damage pattern may arise in a structure due to periodicity in geometry and in loading. The method exploits the Block-Floquet band formation mechanism , a feature specific to structures with periodicity, to identify propagation bands (pass bands) and attenuation bands (stop bands) at different frequency ranges. The presence of damage modifies the wave propagation behaviour forming these bands. With proper positioning of sensors a damage force indicator (DFI) method can be used to locate the defect at an accuracy level of sensor to sensor distance. A wide range of transducer frequency may be used to obtain further information about the shape and size of the damage. The methodology is demonstrated using a few 1-D structures with different kinds of periodicity and damage. For this purpose, dynamic stiffness matrix is formed for the periodic elements to obtain the dispersion relationship using frequency domain spectral element and spectral super element method. The sensitivity of the damage force indicator for different types of periodic damages is also analysed.
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