Wave Propagation in Exponentially Varying Cross‐Section Rods and Vibration Analysis

2008 ◽  
Author(s):  
Mansour Nikkhah‐Bahrami ◽  
Masih Loghmani ◽  
Mostafa Pooyanfar
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Vibration Analysis

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.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Free Vibration Analysis for Tapered Cross-Section Steel-Concrete Composite Material Beam

2017 ◽  
Vol 893 ◽  
pp. 380-383
Author(s):  
Jun Xia ◽  
Z. Shen ◽  
Kun Liu
Keyword(s):  
Finite Element ◽  
Composite Material ◽  
Cross Section ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Composite Beams ◽  
Shear Connection ◽  
The Common ◽  
Interlayer Slip

The tapered cross-section beams made of steel-concrete composite material are widely used in engineering constructions and their dynamic behavior is strongly influenced by the type of shear connection jointing the two different materials. The 1D high order finite element model for tapered cross-section steel-concrete composite material beam with interlayer slip was established in this paper. The Numerical results for vibration nature frequencies of the composite beams with two typical boundary conditions were compared with ANSYS using 2D plane stress element. The 1D element is more efficient and economical for the common tapered cross-section steel-concrete composite material beams in engineering.

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.

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