2D in-plane elastic waves in curved-tapered square lattice frame structure

2021 ◽  
pp. 1-12
Author(s):  
Rajan Prasad ◽  
Ajinkya Baxy ◽  
Arnab Banerjee
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Cross Sections ◽  
Elastic Waves ◽  
Dynamic Stiffness ◽  
Frame Structure ◽  
Square Lattice ◽  
Wave Localization ◽  
Finite Structure ◽  
Complete Bandgap

Abstract This work proposes a unique configuration of two-dimensional metamaterial lattice grid comprising of curved and tapered beams. The propagation of elastic waves in the structure is analyzed using the dynamic stiffness matrix (DSM) approach and the Floquet-Bloch theorem. The DSM for the unit cell is formulated under the extensional theory of curved beam considering the effects of shear and rotary inertia. The study considers two types of variable rectangular cross-sections, viz. single taper and double taper along the length of the beam. Further, the effect of curvature and taper on the wave propagation is analysed through the band diagram along the irreducible Brillouin zone. It is shown that a complete band gap, i.e. attenuation band in all the directions of wave propagation, in a homogeneous structure can be tailored with a suitable combination of curvature and taper. Generation of the complete bandgap is hinged upon the coupling of axial and transverse component of the lattice grid. This coupling emerges due to the presence of the curvature and further enhanced due to tapering. The double taper cross-section is shown to have wider attenuation characteristics than single taper cross-sections. Specifically, 83.36% and 63% normalized complete bandwidth is achieved for the double and single taper cross-section for a homogeneous metamaterial, respectively. Additional characteristics of the proposed metamaterial in time and frequency domain of the finite structure, vibration attenuation, wave localization in the equivalent finite structure are also studied.

Phononic Band Gaps in Al2O3/Epoxy Composite

2018 ◽  
Vol 912 ◽  
pp. 112-117 ◽  
Author(s):  
Edson Jansen Pedrosa Miranda Jr. ◽  
J.M.C. dos Santos
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Elastic Waves ◽  
Epoxy Composite ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Square Lattice ◽  
Plane Wave Expansion ◽  
Phononic Band Gaps ◽  
Angle Of Rotation

In this study, we have investigated the band structure of elastic waves propagating in a phononic crystal, consisting of an epoxy matrix reinforced by Al2O3 inclusions in a square and hexagonal lattices. We also studied the influence of the inclusion geometry cross section – circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to the x, y axes. The plane wave expansion (PWE) method is used to solve the wave equation considering the wave propagation in the xy plane (longitudinal-transverse vibration, XY mode, and transverse vibration, Z mode). The complete band gaps between the XY and Z modes are observed to circular, square and rotated square cross section inclusion and the best performance is for rotated square cross section inclusion in a square lattice. We suggest that the Al2O3/epoxy composite is feasible for vibrations management.

Dispersion study of plane-strain vibrations in poroelastic solid bars with polygonal cross-section

2016 ◽  
Vol 22 (1) ◽  
pp. 38-52 ◽  
Author(s):  
Sandhya Rani Bandari ◽  
Malla Reddy Perati ◽  
Gangadhar Reddy Gangu
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Plane Strain ◽  
Cross Section ◽  
Cross Sections ◽  
Fourier Expansion ◽  
Data Phase ◽  
Base Curve ◽  
Symmetric And Antisymmetric Modes ◽  
Relevant Material

This paper studies wave propagation in a poroelastic solid bar with polygonal cross-section under plane-strain conditions. The boundary conditions on the surface of the cylinder whose base curve is polygon are satisfied by means of the Fourier expansion collocation method. The frequency equations are discussed for both symmetric and antisymmetric modes in the framework of Biot’s theory of poroelastic solids. For illustration purposes, sandstone saturated materials and bony material are considered. The numerical results were computed as the basis of relevant material data . Phase velocity is computed against the wavenumber for various cross-sections and results are presented graphically.

Band Structure in a Sustainable Sonic Crystal

2019 ◽  
Vol 958 ◽  
pp. 75-80
Author(s):  
Edson Jansen Pedrosa Miranda Jr. ◽  
S.F. Rodrigues ◽  
J.M.C. dos Santos
Keyword(s):  
Band Structure ◽  
Cross Section ◽  
Cross Sections ◽  
Acoustic Waves ◽  
Band Gaps ◽  
Square Lattice ◽  
Host Medium ◽  
Fiber Cross Section ◽  
Sonic Crystal ◽  
Sonic Crystals

During the last few decades many researchers have been interested in acoustic wave propagation in artificial periodic composites known as sonic crystals. Sonic crystals have received renewed attention because they exhibit acoustic band gaps where there are only evanescent waves. Sonic crystals consist of a periodic array of scatterers embedded in a host medium. The host medium and/or scatterers are fluids. We investigate the band structure of acoustic waves propagating in a sustainable sonic crystal composed by miriti fibers and air, regarding square and triangular lattices. Miriti fibers are extracted from buriti palm petiole (Mauritia flexuosa Mart.), which is a typical specie that grows in Amazonian region. We also study the influence of miriti fiber cross section, i.e. circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to x, y axes. Plane wave expansion method is used to solve the wave equation. Acoustic band gaps are observed for all miriti fiber cross sections and lattices. The best performances of the sustainable sonic crystal are for triangular lattice, regarding circular and rotated square miriti fiber cross sections, and for square lattice with circular miriti fiber cross section. We suggest that the sustainable sonic crystal should be feasible for noise management.

Elastic Wave Localization in Layered Phononic Crystals With Fractal Superlattices

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Zhi-zhong Yan ◽  
Chuanzeng Zhang ◽  
Yue-sheng Wang
Keyword(s):  
Wave Propagation ◽  
Elastic Waves ◽  
Golden Section ◽  
Structure Design ◽  
Phononic Crystals ◽  
Wave Localization ◽  
Fractal Structures ◽  
Localization Factor ◽  
Time Harmonic ◽  
Approximate Similarity

In this paper, localization phenomena of in-plane time-harmonic elastic waves propagating in layered phononic crystals (PNCs) with different fractal superlattices are studied. For this purpose, oblique wave propagation in layered structures is considered. To describe wave localization phenomena, the localization factor is applied and computed by the transfer matrix method. Three typical fractal superlattices are considered, namely, the Cantorlike fractal superlattice (CLFSL), the golden-section fractal superlattice (GSFSL), and the Fibonacci fractal superlattice (FFSL). Numerical results for the localization factors of CLFSL, GSFSL, and FFSL are presented and analyzed. The results show that the localization factor of a CLFSL exhibits an approximate similarity and band-splitting properties. The number of decomposed bandgaps of the GSFSL and FFSL follows the composition of the special fractal structures. In addition, with increasing fractal series, the value of the localization factor is enlarged. These results are of great importance for structure design of fractal PNCs.

Wave propagation in tapered periodic curved meta-frame using Floquet theory

2021 ◽  
pp. 1-24
Author(s):  
Rajan Prasad ◽  
Ajinkya Baxy ◽  
Arnab Banerjee
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Cross Section ◽  
Mode Conversion ◽  
Circular Cross Section ◽  
Low Frequency ◽  
Frame Structure ◽  
Rectangular Section ◽  
Flexural Mode ◽  
Tapered Beam

Abstract In this work, the elastic wave propagation and dispersion characteristics of a curved tapered frame structure is investigated analytically. Separately, wave propagation through uniform curved and straight tapered beam were reported in the existing literature; however, no literature reports the influence of simultaneous bent and taper on the wave propagation. In particular, the band characteristics for the curved and tapered beam with two types of cross-sections, i.e., rectangular and circular, are presented. The paper elucidates that introducing a small periodic bent angle cross-section produces a complete, viz. axial and flexural band gap in the low-frequency region, and conicity enhances the width of the band. It is also evidenced that a curved tapered frame with a solid circular cross-section induces a wider band gap than the rectangular section. A complete first normalized bandwidth of 159% is achievable for the circular cross-section and 123% in the case of the rectangular section. The complete result is presented in a non-dimensional framework for wider applicability. An analysis of a finite tapered curved frame structure also demonstrates the attenuating characteristics obtained from the band structure of the infinite structure. The partial wave mode conversion, i.e., generation of coupled axial and flexural mode from a purely axial or flexural mode in an uncoupled medium is observed. This wave conversion is perceived in reflected and transmitted waves while this curved tapered frame is inserted between the two uniform cross-section straight frames.

scholarly journals Ferroelectric based fractal phononic crystals: wave propagation and band structure

2020 ◽  
Vol 557 (1) ◽  
pp. 85-91
Author(s):  
Selami Palaz ◽  
Zafer Ozer ◽  
Amirullah M. Mamedov ◽  
Ekmel Ozbay
Keyword(s):  
Wave Propagation ◽  
Band Structure ◽  
Cross Section ◽  
Phononic Crystal ◽  
Circular Cross Section ◽  
Phononic Crystals ◽  
Square Lattice ◽  
Rubber Matrix ◽  
Element Simulation ◽  
Piezoelectric Inclusion

In this study, the band structure and transmission in multiferroic based Sierpinski carpet phononic crystal are investigated based on finite element simulation. In order to obtain the band structure of the phononic crystal (PnC), the Floquet periodicity conditions were applied to the sides of the unit cell. The square lattice PnC consists of various piezoelectric inclusion in a rubber matrix with square and circular cross section.

scholarly journals Dynamic Stiffness Matrix for a Beam Element with Shear Deformation

1995 ◽  
Vol 2 (2) ◽  
pp. 155-162 ◽  
Author(s):  
Walter D. Pilkey ◽  
Levent Kitiş
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Beam Element ◽  
Stiffness Matrices ◽  
Principal Axes ◽  
Shear Beam ◽  
Shaped Cross Section

A method for calculating the dynamic transfer and stiffness matrices for a straight Timoshenko shear beam is presented. The method is applicable to beams with arbitrarily shaped cross sections and places no restrictions on the orientation of the element coordinate system axes in the plane of the cross section. These new matrices are needed because, for a Timoshenko beam with an arbitrarily shaped cross section, deflections due to shear in the two perpendicular planes are coupled even when the coordinate axes are chosen to be parallel to the principal axes of inertia.

Vibration Analysis of One-Dimensional Structures with Discontinuities Using the Acoustical Wave Propagator Technique

2004 ◽  
Vol 127 (6) ◽  
pp. 604-607
Author(s):  
S. Z. Peng
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Elastic Waves ◽  
Vibration Analysis ◽  
Fourier Transforms ◽  
Numerical Technique ◽  
Sudden Change ◽  
Computationally Efficient ◽  
Exact Analytical Solutions ◽  
One Dimensional

A numerical technique, named the acoustical wave propagator technique, is introduced to describe the dynamic characteristics of one-dimensional structures with discontinuities. A scheme combining Chebyshev polynomial expansion and fast Fourier transforms is introduced in detail. Comparison between exact analytical solutions and predicted results obtained by the acoustical wave propagator technique shows that this scheme has highly accurate and computationally efficient. Furthermore, this technique is extended to investigate the wave propagation and reflection of elastic waves in beams at the location of a sudden change in cross section.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

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