Dispersion of Axially Symmetric Waves in Elastic Rods

1962 ◽  
Vol 29 (4) ◽  
pp. 729-734 ◽  
Author(s):  
Morio Onoe ◽  
H. D. McNiven ◽  
R. D. Mindlin
Keyword(s):  
Poisson’S Ratio ◽  
Large Range ◽  
Propagation Constant ◽  
Poisson's Ratio ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Complex Propagation

The relation between frequency and propagation constant, for axially symmetric waves in an infinitely long, isotropic, circular rod, as given by Pochhammer’s equation, is explored. A spectrum, covering a large range of frequencies, is developed for real, imaginary, and complex propagation constants, and the influence of Poisson’s ratio is described.

Dependence of the Frequency Spectrum of a Circular Disk on Poisson’s Ratio

1957 ◽  
Vol 24 (1) ◽  
pp. 53-54
Author(s):  
R. L. Sharma
Keyword(s):  
Frequency Spectrum ◽  
Poisson’S Ratio ◽  
Circular Disk ◽  
Intermediate Frequency ◽  
Poisson's Ratio ◽  
Axially Symmetric ◽  
Frequency Range ◽  
Flexural Vibrations ◽  
Circular Disks

Abstract The results of computations of frequencies of axially symmetric flexural vibrations of circular disks are given for an intermediate frequency range and for several values of Poisson’s ratio.

scholarly journals Localization of maximal stresses in axisymmetric waves in elastic rods for positive Poisson’s ratio

2020 ◽  
pp. 95-100
Author(s):  
Вячеслав Викторович Мокряков
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Elastic Rods ◽  
Maximal Extension ◽  
Maximum Stresses

Рассмотрены максимальные напряжения в осесимметричных волнах в упругих стержнях для положительных значений коэффициента Пуассона. Обнаружена особая длина волны, для которой имеет место наибольшее значение максимального растяжения на оси по отношению к максимальному растяжению на поверхности. Показано, что и особая длина волна, и наибольшее значение отношений растяжений не зависят от коэффициента Пуассона. The maximum stresses in axisymmetric waves in elastic rods for positive values of the Poisson’s ratio are considered. A special wavelength has been found for which the ratio of axial maximal extension to surface maximal extension has the largest value. It is shown that both the special wavelength and the largest value of the extensions ratio are independent of the Poisson’s ratio.

Longitudinal Pochhammer — Chree Waves in Mild Auxetics and Non-Auxetics

2018 ◽  
Vol 35 (3) ◽  
pp. 327-334 ◽  
Author(s):  
A. V. Ilyashenko ◽  
S. V. Kuznetsov
Keyword(s):  
Poisson’S Ratio ◽  
Wave Speed ◽  
Poisson's Ratio ◽  
Abnormal Behavior ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Shear Wave Speed ◽  
The Matrix ◽  
The Waves ◽  
Analytical Expressions

ABSTRACTThe exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.

The Model for Calculating Elastic Modulus and Poisson's Ratio of Coal Body

2013 ◽  
Vol 6 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Ai Chi ◽  
Li Yuwei
Keyword(s):  
Elastic Modulus ◽  
Poisson’S Ratio ◽  
Fractured Rock ◽  
Rock Block ◽  
Poisson's Ratio ◽  
Linear Elastic ◽  
Study Results ◽  
The Face ◽  
Block Face ◽  
Coal Rock

Coal body is a type of fractured rock mass in which lots of cleat fractures developed. Its mechanical properties vary with the parametric variation of coal rock block, face cleat and butt cleat. Based on the linear elastic theory and displacement equivalent principle and simplifying the face cleat and butt cleat as multi-bank penetrating and intermittent cracks, the model was established to calculate the elastic modulus and Poisson's ratio of coal body combined with cleat. By analyzing the model, it also obtained the influence of the parameter variation of coal rock block, face cleat and butt cleat on the elastic modulus and Poisson's ratio of the coal body. Study results showed that the connectivity rate of butt cleat and the distance between face cleats had a weak influence on elastic modulus of coal body. When the inclination of face cleat was 90°, the elastic modulus of coal body reached the maximal value and it equaled to the elastic modulus of coal rock block. When the inclination of face cleat was 0°, the elastic modulus of coal body was exclusively dependent on the elastic modulus of coal rock block, the normal stiffness of face cleat and the distance between them. When the distance between butt cleats or the connectivity rate of butt cleat was fixed, the Poisson's ratio of the coal body initially increased and then decreased with increasing of the face cleat inclination.

scholarly journals A Hybrid Artificial Intelligence Model to Predict the Elastic Behavior of Sandstone Rocks

2019 ◽  
Vol 11 (19) ◽  
pp. 5283 ◽  
Author(s):  
Gowida ◽  
Moussa ◽  
Elkatatny ◽  
Ali
Keyword(s):  
Poisson’S Ratio ◽  
Accurate Determination ◽  
Oil And Gas Industry ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Percentage Error ◽  
Ann Model ◽  
Field Development ◽  
Well Completion

Rock mechanical properties play a key role in the optimization process of engineering practices in the oil and gas industry so that better field development decisions can be made. Estimation of these properties is central in well placement, drilling programs, and well completion design. The elastic behavior of rocks can be studied by determining two main parameters: Young’s modulus and Poisson’s ratio. Accurate determination of the Poisson’s ratio helps to estimate the in-situ horizontal stresses and in turn, avoid many critical problems which interrupt drilling operations, such as pipe sticking and wellbore instability issues. Accurate Poisson’s ratio values can be experimentally determined using retrieved core samples under simulated in-situ downhole conditions. However, this technique is time-consuming and economically ineffective, requiring the development of a more effective technique. This study has developed a new generalized model to estimate static Poisson’s ratio values of sandstone rocks using a supervised artificial neural network (ANN). The developed ANN model uses well log data such as bulk density and sonic log as the input parameters to target static Poisson’s ratio values as outputs. Subsequently, the developed ANN model was transformed into a more practical and easier to use white-box mode using an ANN-based empirical equation. Core data (692 data points) and their corresponding petrophysical data were used to train and test the ANN model. The self-adaptive differential evolution (SADE) algorithm was used to fine-tune the parameters of the ANN model to obtain the most accurate results in terms of the highest correlation coefficient (R) and the lowest mean absolute percentage error (MAPE). The results obtained from the optimized ANN model show an excellent agreement with the laboratory measured static Poisson’s ratio, confirming the high accuracy of the developed model. A comparison of the developed ANN-based empirical correlation with the previously developed approaches demonstrates the superiority of the developed correlation in predicting static Poisson’s ratio values with the highest R and the lowest MAPE. The developed correlation performs in a manner far superior to other approaches when validated against unseen field data. The developed ANN-based mathematical model can be used as a robust tool to estimate static Poisson’s ratio without the need to run the ANN model.

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