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.

Electromagnetic wave propagation in a chiroplasma-filled waveguide

1999 ◽  
Vol 62 (1) ◽  
pp. 87-94 ◽  
Author(s):  
J. GONG
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Cross Section ◽  
Electromagnetic Waves ◽  
Electromagnetic Wave Propagation ◽  
Propagation Constant ◽  
Circular Cross Section ◽  
Propagation Characteristics ◽  
Waveguide Modes ◽  
The Family

A dispersion equation is derived for a cylindrical waveguide of circular cross-section partially filled with chiroplasma. The propagation characteristics of electromagnetic waves in the family of waveguide modes are studied. The dispersion curves are given. It is found that the propagation constant changes almost linearly with the chirality admittance for the parameters that we choose, and increases with increasing filled area.

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.

Study on the Band Gap and its Influencing Factors for one Dimensional Phononic Crystal

2011 ◽  
Vol 121-126 ◽  
pp. 448-452
Author(s):  
Yu Yang He ◽  
Xiao Xiong Jin
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Band Gap ◽  
Cross Section ◽  
Phononic Crystal ◽  
Filling Rate ◽  
Lumped Mass ◽  
Height Ratio ◽  
One Dimensional ◽  
Lumped Mass Method

The width of band gap is calculated with lumped mass method in order to study the wave propagation of longitudinal and transverse elastic wave of one-dimensional phononic crystal. The starting and terminating frequency is analyzed by changing the filling rate, the density difference of two materials, cross-section height ratio, and the Young's modulus of the scatter.

Flexural waves in elastically coupled telescopic metabeams

2021 ◽  
pp. 1-28
Author(s):  
Rajan Prasad ◽  
Arnab Banerjee
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Wave Attenuation ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Length Ratio ◽  
Beam Equation ◽  
Flexural Wave ◽  
Constitutive Components

Abstract This paper investigates the flexural wave propagation through elastically coupled metabeams. It is assumed that the metabeam is formed by connecting successive beams with each other using distributed elastic springs. The equations of motion of a representative unit of the above mentioned novel structural form is established by dividing it into three constitutive components that are two side beams, modeled employing Euler-Bernoulli beam equation and an elastically coupled articulated distributed spring connection (ECADSC) at middle. ECADSC is modeled as parallel double beams connected by distributed springs. The underlying mechanics of this system in context of elastic wave propagation is unique when compared with the existing state of art in which local resonators, inertial amplifiers etc. are attached to the beam to widen the attenuation bandwidth. The dynamic stiffness matrix is employed in conjunction with Bloch-Floquet theorem to derive the band-structure of the system. It is identified that the coupling coefficient of the distributed spring layer and length ratio between the side beams and the elastic coupling plays the key role in the wave attenuation. It has been perceived that a considerable widening of the attenuation band gap in the low-frequency can be achieved while the elastically distributed springs are weak and distributed in a small stretch. Specifically, 140% normalized band gap can be obtained only by tuning the stiffness and the length ratio without adding any added masses or resonators to the structure.

scholarly journals An experimental study of the flow of water in pipes of rectangular section

1928 ◽  
Vol 119 (781) ◽  
pp. 92-107 ◽  
Keyword(s):  
Viscous Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Flat Plates ◽  
Rectangular Section ◽  
A Value ◽  
Accurate Knowledge ◽  
Wide Range ◽  
Surface Plate

During the course of study, by the authors, of the flow of fluids in the small clearances which exist between the moving and fixed parts of certain machines, an accurate knowledge was desired of the range over which the equations of viscous flow could be applied. An exhaustive search revealed an absence of any record of experimental work which could be of direct assistance. An investigation was accordingly undertaken with the object of obtaining the desired information, and as the preliminary results were of an interesting and unexpected nature, the experiments were extended to cover the whole range of velocities and dimensions permitted by the apparatus. They have shown briefly that the lower critical velocity (as ordinarily understood) for flow between flat plates occurs at a value of the Reynolds number about one-half that found for pipes of circular cross section, if the linear dimension in that number is the distance between the plates and the diameter respectively. For velocities well below this limit there is evidence, however, of a distinct deviation from true viscous flow if initial disturbing factors are present, and the influence of such disturbing factors does not disappear entirely until a second well-defined limit is reached, which has a value of about one-tenth of the lower critical number. It would appear that below this limit eddies do not exist at any point in the pipe, and the flow is truly viscous. The suggestion is accordingly made that there may be three distinct types of flow: ( a ) one in which eddies cannot exist, corresponding to truly viscous flow; ( b ) one in which eddies may exist, due to an initial disturbance, but cannot be sustained in the pipe, the initial eddies therefore ultimately disappearing; and ( c ) one in which eddies once generated will be maintained without decrement throughout the pipe, corresponding to truly turbulent flow. The use of a channel of rectangular cross section for a study of the fundamental laws of the flow of fluids possesses advantages, in point of simplicity, which were recognised at once by Reynolds in his classical research into the cause of instability of flow. In the form in which this channel is used by the present writers, an additional and important advantage is obtained over the circular pipe by the fact that the controlling dimension may be varied over a wide range whilst retaining the same surfaces as boundaries. It is, in essentials, an adjustable pipe. The upper plate A (fig. 1) and the lower plate B are brass castings suitably drilled to provide inlet and outlet passages and pressure measuring points. The surfaces forming the pipe are hand scraped to a surface plate, and are separated at the ends by brass foil shims of suitable thickness, thus providing a passage between the inlet and outlet ports. The sides of this passage are closed by the plates C and D, very thin rubber insertion providing a watertight joint. All parts are sufficiently robust to reduce distortion under pressure to an amount found to be negligible.

Damage Detection in Composite Cylindrical Multilayered Shells with Delaminations

2010 ◽  
Vol 123-125 ◽  
pp. 887-890 ◽  
Author(s):  
Aleksander Muc ◽  
Adam Stawiarski
Keyword(s):  
Wave Propagation ◽  
Numerical Analysis ◽  
Dynamic Behavior ◽  
Cross Section ◽  
Circular Cross Section ◽  
Piezoelectric Sensors ◽  
Structural Dynamic ◽  
Cylindrical Panels ◽  
The Difference ◽  
Computational Procedures

In this study, effective computational procedures are introduced and used to characterize the dynamic behavior of cylindrical panels with circular cross-section having the single delamination between laminate layers. Based on the computed results it is possible to determine the effect of delamination on the overall structural dynamic behavior. Those results are used to quantify the difference between the results of the relevant parameters in the cases of perfect and defected structures. Usually, the wave propagation can be observed with the use of piezoelectric sensors. Therefore, in the next step of our analysis we modeled delaminated structures with a finite number of PZT sensors to consider also their influence on the structural dynamic response. The numerical analysis have been conducted with the use of 3D finite elements. A lot of numerical results allow us to understand better the influence of various parameters on the form of wave propagation in cylindrical multilayered shells.

Resonant Gas Oscillations in a Linear Area Variation Cavity: Rectangular Versus Circular Cross Section

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sonu K. Thomas ◽  
T. M. Muruganandam
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Second Harmonic ◽  
Circular Cross Section ◽  
High Amplitude ◽  
Rectangular Section ◽  
Closed Cavity ◽  
Circular Section ◽  
Resonance Frequencies ◽  
Area Variation

Resonant gas oscillations in a linear area variation closed cavity are investigated, for two duct cross sections: rectangular and circular. The resonance frequencies were similar for both the ducts. Increased drive amplitude produced higher distortions in the waveform. It was found that both resonators exhibited commensurate behavior. This is opposed to noncommensurate behavior observed in nonuniform circular cross section resonators. The rectangular section duct had higher energy than circular section duct, in second harmonic for the same drive amplitude. The results reveal that in order to achieve shockless high amplitude pressure oscillations in a duct, both nonuniform area variation and circular cross section are required.

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