Traveling wave analytical solutions of vibration band gaps of composite periodic beams

2018 ◽  
Vol 25 (2) ◽  
pp. 460-472 ◽  
Author(s):  
Zhen Zhang ◽  
Tuanjie Li ◽  
Yaqiong Tang
Keyword(s):  
Explicit Expression ◽  
Analytical Solutions ◽  
Traveling Wave ◽  
Wave Theory ◽  
Intermediate Frequency ◽  
Band Gaps ◽  
Structure Theory ◽  
Vibration Band ◽  
Boundary Frequency ◽  
Uniform Cross Section

This paper is concerned with elastic wave propagation and vibration band gaps in periodic beams formed by alternating combinations of various materials with the same geometric parameters. Such composite periodic systems have the similar feature of filtering characteristics of periodic beams. The study is performed by using an exact analytical approach based on a combination of the traveling wave analysis method and periodic structure theory. Based on the wave theory, a general mathematical model of composite periodic beam with uniform cross-section is established, the band gaps mechanism and vibration characteristics of this model are discussed, and the analytical solutions of the dynamic model and the explicit expression of band gaps are derived. Based on these equations, an explicit expression is provided for the calculation of intermediate frequency boundary frequency, all the band gaps information can be obtained in an exact and simple manner, and several illustrative examples are also provided.

scholarly journals Hydromechanical Structure of the Cochlea Supports the Backward Traveling Wave in the Cochlea In Vivo

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Fangyi Chen ◽  
Dingjun Zha ◽  
Xiaojie Yang ◽  
Allyn Hubbard ◽  
Alfred Nuttall
Keyword(s):  
Traveling Wave ◽  
Basilar Membrane ◽  
Wave Theory ◽  
Otoacoustic Emission ◽  
Traditional Theory ◽  
Vibration Source ◽  
Ear Canal ◽  
Local Vibration ◽  
Membrane Vibration

The discovery that an apparent forward-propagating otoacoustic emission (OAE) induced basilar membrane vibration has created a serious debate in the field of cochlear mechanics. The traditional theory predicts that OAE will propagate to the ear canal via a backward traveling wave on the basilar membrane, while the opponent theory proposed that the OAE will reach the ear canal via a compression wave. Although accepted by most people, the basic phenomenon of the backward traveling wave theory has not been experimentally demonstrated. In this study, for the first time, we showed the backward traveling wave by measuring the phase spectra of the basilar membrane vibration at multiple longitudinal locations of the basal turn of the cochlea. A local vibration source with a unique and precise location on the cochlear partition was created to avoid the ambiguity of the vibration source in most previous studies. We also measured the vibration pattern at different places of a mechanical cochlear model. A slow backward traveling wave pattern was demonstrated by the time-domain sequence of the measured data. In addition to the wave propagation study, a transmission line mathematical model was used to interpret why no tonotopicity was observed in the backward traveling wave.

Incorporating Compressional and Shear Wave Types Into Fuzzy Structure Models for Plates

1995 ◽  
Author(s):  
Judith L. Rochat ◽  
Victor W. Sparrow
Keyword(s):  
Thin Plate ◽  
Shear Waves ◽  
Wave Theory ◽  
Structure Theory ◽  
Detailed Knowledge ◽  
Bending Waves ◽  
Incident Plane ◽  
Dependent Mass ◽  
Mass Spring ◽  
Bending Wave

Abstract Although realistic complex structures are usually difficult to model theoretically, fuzzy structure theory enables one to produce such a model without a detailed knowledge of the entire structure. Using the theory established by Pierce et al. [A. D. Pierce, V. W. Sparrow, and D. A. Russell, J. Vib. Acoust. (to be published), also ASME 93-WA/NCA-17.] regarding fundamental structural-acoustic idealizations for structures with imprecisely known or fuzzy internals, the effects that fuzzy attachments have on different wave types in a primary (or master) structure are examined in this paper. In the theory by Pierce et al., the primary structure that undergoes vibrations is a thin plate mounted in an infinite baffle. On one side of the plate are fuzzy attachments, represented as an array of attached mass-spring-dashpot systems, which are excited by an incident plane pulse. This known theory explains the effects of these attachments on bending waves in the plate. In this paper, the theory is extended to isolated compressional and shear waves in a plate. While studying this new problem, it is discovered that coupling effects occur when the plate and attachment properties are not uniform in the direction perpendicular to the wave propagation. Hence, unlike the bending wave theory which models a finite thin plate with point attached oscillators, the new wave type theory uses a thin plate infinite in one direction with line attached oscillators also infinite in the same direction. For both the compressional and shear waves, it is found that the fuzzy attachments add an apparent frequency dependent mass and damping to the plate. These results are similar to those for the bending wave theory.

Distance Protection Application Based on Wavelet Transform and Traveling Wave Ranging

2012 ◽  
Vol 150 ◽  
pp. 40-44
Author(s):  
Peng Peng Kang ◽  
Xi Fang Zhu
Keyword(s):  
Wavelet Transform ◽  
Power System ◽  
Transmission Line ◽  
Software Design ◽  
Traveling Wave ◽  
Wave Theory ◽  
Distance Measurement ◽  
Distance Protection

This paper describes the wavelet transform theory, and traveling wave theory. When the power system transmission line fault occurs, the fault signal generated by sampling and analysis, and use a method of one-end fault distance measurement in transmission line. Finally the article gives the ranging devices’ hardware and software design.

Wave Theory of a Traveling-Wave Tube Operated Near the Cutoff

2004 ◽  
Vol 47 (5/6) ◽  
pp. 356-373 ◽  
Author(s):  
A. P. Kuznetsov ◽  
S. P. Kuznetsov ◽  
A. G. Rozhnev ◽  
E. V. Blokhina ◽  
L. V. Bulgakova
Keyword(s):  
Traveling Wave ◽  
Wave Theory ◽  
Traveling Wave Tube ◽  
Wave Tube

Pseudo-Peakon, Periodic Peakons and Compactons on a Shallow Water Model with Coriolis Effect

2021 ◽  
Vol 31 (08) ◽  
pp. 2150144
Author(s):  
Zhenshu Wen ◽  
Guanrong Chen ◽  
Jibin Li
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Solitary Wave Solution ◽  
Wave Theory ◽  
Water Model ◽  
Wave System ◽  
Coriolis Effect ◽  
Bounded Solutions ◽  
Shallow Water Model

For a shallow water model with Coriolis effect, by applying the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to its traveling wave system, under different parameter conditions, all possible bounded solutions (solitary wave solution, pseudo-peakon and periodic peakons as well as compactons) are obtained. Some exact explicit parametric representations are presented.

Triply Coupled Vibration Band Gaps in Periodic Thin-Walled Open Cross Section Beams

2005 ◽  
Author(s):  
Dianlong Yu ◽  
Yaozong Liu ◽  
Jing Qiu ◽  
Gang Wang ◽  
Jihong Wen
Keyword(s):  
Cross Section ◽  
Expansion Method ◽  
Band Gaps ◽  
Vibration Band ◽  
Coupled Vibration ◽  
Plane Wave Expansion Method ◽  
Filling Fraction ◽  
Thin Walled ◽  
Gap Width ◽  
Open Cross Section

Triply coupled vibration through periodic thin-walled open cross section nonsymmetrical beams composed of two kinds of material is studied in this paper. Based on the triply coupled vibration equation, plane wave expansion method for the thin-walled beams is provided. If the filling fraction keeps constant, the lattice is one of the factors that affect the normalized gap width. If the lattice and filling fraction keep constant, the Young’s modulus contrast plays a fundamental role for the band gap width, but not density contrast. Finally, the frequency response of a finite periodic binary beam is simulated with finite element method, which provides an attenuation of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

2011 ◽  
Vol 675-677 ◽  
pp. 1085-1088
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Jian Bao Li
Keyword(s):  
Band Gap ◽  
Thin Plate ◽  
Mass Density ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Band Gaps ◽  
Physical Parameters ◽  
Vibration Band ◽  
Filling Fraction

The band structures of flexural waves in a ternary locally resonant phononic crystal thin plate are studied using the improved plane wave expansion method. And the thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps of flexural vibration with low frequency are shown. The calculation results show that the band gap width is strongly dependent on the filling fraction, the radius ratio, the mass density and the Young’s modulus contrasts between the core and the coating. So by changing these physical parameters, the required band gap could be obtained.

Vibration band gaps for elastic metamaterial rods using wave finite element method

2016 ◽  
Vol 79 ◽  
pp. 192-202 ◽  
Author(s):  
E.D. Nobrega ◽  
F. Gautier ◽  
A. Pelat ◽  
J.M.C. Dos Santos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Band Gaps ◽  
Vibration Band ◽  
Element Method
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