The influence of transverse cracks to propagation characteristics of elastic waves propagating in a non-uniform shaft

2019 ◽  
Vol 444 ◽  
pp. 35-47 ◽  
Author(s):  
Yimin Wei ◽  
Shixi Yang ◽  
Wenhua Chen ◽  
Jianmin Li
Keyword(s):  
Elastic Waves ◽  
Propagation Characteristics ◽  
Transverse Cracks

scholarly journals The Influence of Crack Modes on the Elastic Wave Propagation Characteristics in a Non-uniform Rotating Shaft

2018 ◽  
Author(s):  
Yimin Wei ◽  
Xuan Shi ◽  
Qi Liu ◽  
Wenhua Chen
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Transverse Crack ◽  
Propagation Characteristics ◽  
Mode Iii ◽  
Transverse Cracks ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Local Flexibility ◽  
The Media

The vibration propagates in a media such as a shaft in the form of elastic waves. The propagation characteristics of the waves are affected by the geometry of the media, the material properties as well as the cracks. The study to elastic waves propagating in a shaft with transverse cracks can help to detect them. The transverse crack possesses different crack modes due to different external loads. The influence of the crack mode, the location and the depth to the propagation characteristics is investigated in this paper. Firstly, the local flexibility coefficients with three different modes are deduced. And then, the transfer matrix of the elastic wave can be obtained. Finally, the influence of the crack mode, the location and the depth of the transverse crack as well as the rotating speed to the propagation characteristics is then studied, both in a numerical and an experimental way. It’s found that mode III is the most suitable mode in this paper, the location of the crack will make the stopbands fluctuating, the depth mainly affects the bandwidth of the stopbands, and the increase of the rotating speed will shift up the stopbands without changing their bandwidths.

ELASTIC WAVES IN TRIGONAL CRYSTALS

1961 ◽  
Vol 39 (1) ◽  
pp. 65-80 ◽  
Author(s):  
G. W. Farnell
Keyword(s):  
Elastic Waves ◽  
Energy Flow ◽  
Pure Mode ◽  
Sound Waves ◽  
Propagation Characteristics ◽  
Three Solutions ◽  
Transverse Waves ◽  
Plane Wavefront ◽  
Wave Normal ◽  
Quasi Longitudinal Wave

In non-isotropic single crystals the normals to the wavefronts of elastic waves are not colinear with the vectors representing either the energy flow or the particle displacement. Calculations have been carried out on the propagation characteristics of sound waves in two particular trigonal crystals, α-quartz and sapphire.The development of the eigenvalue equation for the velocity and the formulae for the components of the displacement and energy-flow vectors are summarized. The assumption that the wave has a plane wavefront normal to a given direction leads to three solutions, one representing a quasi-longitudinal wave and the other two representing quasi-transverse waves. The velocities of propagation, directions of displacement, and directions of energy flow for the three waves have been calculated for many orientations of the wave normal. Detailed results for propagation near one of the pure-mode axes are presented.

Modeling and Analysis of Nonlinear Wave Propagation in One-Dimensional Phononic Structures

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
M. Liu ◽  
W. D. Zhu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Band Structure ◽  
Band Gap ◽  
Nonlinear Wave ◽  
Elastic Waves ◽  
Propagation Characteristics ◽  
Nonlinear Wave Propagation ◽  
Weakly Nonlinear

Different from elastic waves in linear periodic structures, those in phononic crystals (PCs) with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot accurately predict band-gap variations under finite-amplitude wave motions; creating nonlinear PCs remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler–Bernoulli beam using their exact Green–Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval (BSWI) finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear PCs.

scholarly journals The Influence of Crack Modes on the Elastic Wave Propagation Characteristics in a Non-Uniform Rotating Shaft

2018 ◽  
Vol 8 (11) ◽  
pp. 2105 ◽  
Author(s):  
Yimin Wei ◽  
Xuan Shi ◽  
Qi Liu ◽  
Wenhua Chen
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Transfer Matrix ◽  
Elastic Waves ◽  
Transverse Crack ◽  
Propagation Characteristics ◽  
Mode Iii ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Local Flexibility

The transverse crack in a non-uniform shaft possesses different crack modes, and it can affect the propagation characteristics of the elastic waves in the shaft. The influence of the crack mode as well as the location and the depth of the crack and the rotating speed to the propagation characteristics is investigated in this paper. Firstly, the transfer matrix for the elastic wave in a non-uniform shaft is obtained by deducing the local flexibility coefficients of the three typical crack modes, in which the transverse crack is modeled as a local spring. After that, the influence of the crack mode to the propagation characteristics is studied both in a numerical and an experimental way. Finally, the influence of the location and the depth of the transverse crack as well as the rotating speed of the shaft is studied too. It is found that Mode III is the most suitable mode in this paper, the location of the crack will make the stopbands fluctuating, the depth mainly affects the bandwidth of the stopbands, and the increase of the rotating speed will shift up the stopbands without changing the bandwidths. The results can help to detect and locate a transverse crack.

scholarly journals Waves and damage in structured solids with multi-scale resonators

2010 ◽  
Vol 467 (2128) ◽  
pp. 964-984 ◽  
Author(s):  
I. S. Jones ◽  
A. B. Movchan ◽  
M. Gei
Keyword(s):  
Numerical Modelling ◽  
Numerical Simulations ◽  
Analytical Model ◽  
Periodic Structure ◽  
Elastic Waves ◽  
Standing Waves ◽  
Low Frequency ◽  
Asymptotic Estimates ◽  
Transverse Cracks ◽  
Multi Scale

This paper presents asymptotic and numerical modelling of elastic waves interacting with micro-structured solids containing multi-scale resonators. The resonators may be damaged by transverse cracks at their foundations. One particular feature of the resonators used here is the presence of low-frequency eigenmodes. Asymptotic estimates of low eigenfrequencies are included in the model. Hence, the overall periodic structure containing such resonators may support low-frequency standing waves and possess low-frequency stop bands. The analytical model is accompanied by numerical simulations illustrating dispersion, localization and focusing within the structured multi-scale solids.

Band Gaps of 2D Phononic Crystal with Graded Interphase

2011 ◽  
Vol 121-126 ◽  
pp. 2567-2571
Author(s):  
Bei Cai ◽  
Pei Jun Wei
Keyword(s):  
Multiple Scattering ◽  
Brillouin Zone ◽  
Elastic Waves ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Scattering Method ◽  
Propagation Characteristics ◽  
Dispersive Equation ◽  
Host Medium ◽  
Multiple Scattering Method

Propagation characteristics of elastic waves in 2D phononic crystal consisting of parallel cylinders embedded periodically in a homogeneous host medium are investigated. The multiple scattering method and the Bloch theorem are used to derive the dispersive equation. The dispersive curves and the band gaps between them are evaluated numerically in the reduced Brillouin zone. The graded interphase between the cylinders and the host are considered. The influences of the graded interphase with different gradient profiles are discussed based on the numerical results.

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