The Relation Between Helical Spring Compliances With Free and Fixed End Rotations

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
S. J. Burns
Keyword(s):  
Poisson’S Ratio ◽  
Substantial Reduction ◽  
Beam Theory ◽  
Helix Angle ◽  
Poisson's Ratio ◽  
Helical Spring ◽  
Free Rotation ◽  
Spring Wire ◽  
Dimensionless Ratio ◽  
Fixed End

A helical spring that is constrained to no rotation has a compliance that is typically more than 95% of the compliance of springs constrained to free rotation when restricted to symmetric wires made from materials with Poisson’s ratio between 0 and 1/2. It is shown that the shape of the spring wire can be designed so the spring will not twist when it is extended nor extend when it is twisted. The constrained spring versus a freely rotating spring with the helix angle equal to π/4 has the largest reduction in compliance in the limits of beam theory. Spring compliances for torsion and extension with quite complex helical spring geometries are found to be related by a dimensionless ratio of compliances in a very simple equation that only depends on Poisson’s ratio and the helical, spring angle, ψ. Springs made from materials with negative Poisson’s ratio, however, can have a very substantial reduction in compliance; the no rotation compliance is zero when Poisson’s ratio is −1. There are large changes in spring compliances for springs with geometric coils that are elongated rectangles or flattened ellipses.

ANALYSIS OF AUXETIC BEAMS AS RESONANT FREQUENCY BIOSENSORS

2012 ◽  
Vol 12 (05) ◽  
pp. 1240027 ◽  
Author(s):  
TEIK-CHENG LIM
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
Poisson’S Ratio ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Poisson's Ratio ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

The mechanics of beam vibration is of fundamental importance in understanding the shift of resonant frequency of microcantilever and nanocantilever sensors. Unlike the simpler Euler–Bernoulli beam theory, the Timoshenko beam theory takes into consideration rotational inertia and shear deformation. For the case of microcantilevers and nanocantilevers, the minute size, and hence low mass, means that the topmost deviation from the Euler–Bernoulli beam theory to be expected is shear deformation. This paper considers the extent of shear deformation for varying Poisson's ratio of the beam material, with special emphasis on solids with negative Poisson's ratio, which are also known as auxetic materials. Here, it is shown that the Timoshenko beam theory approaches the Euler–Bernoulli beam theory if the beams are of solid cross-sections and the beam material possess high auxeticity. However, the Timoshenko beam theory is significantly different from the Euler–Bernoulli beam theory for beams in the form of thin-walled tubes regardless of the beam material's Poisson's ratio. It is herein proposed that calculations on beam vibration can be greatly simplified for highly auxetic beams with solid cross-sections due to the small shear correction term in the Timoshenko beam deflection equation.

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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