Fundamental Frequencies of U-Tubes in Tube Bundles

1985 ◽  
Vol 107 (2) ◽  
pp. 207-209
Author(s):  
P. M. Moretti
Keyword(s):  
Poisson’S Ratio ◽  
Estimation Procedure ◽  
Moment Of Inertia ◽  
Poisson's Ratio ◽  
Dimensionless Number ◽  
Bend Radius ◽  
Cross Sectional ◽  
Strong Function ◽  
Fundamental Frequencies ◽  
Axial Moment

The natural frequencies of U-tubes on multiple supports have been studied as a complement to the author’s previous work on the vibration of straight heat-exchanger tubes (reference [1]). A rapid estimation procedure for fundamental frequencies of tubes on symmetrical support spacings has been developed by expressing the frequency in the form f1≥12π•a1•1Ls2•EIμ where the square root contains the tube properties of Young’s modulus, cross-sectional second moment, and linear density; Ls is a characteristic length of support spacing; and a1 is a dimensionless number which is a strong function of the support geometry (as expressed by the ratio of bend radius to span lengths) and weak function of Poisson’s ratio and of tube axial moment of inertia. a1 has been plotted as a function of the ratio of the bend radius to the straight-span length, for usual values of Poisson’s ratio and small axial moment of inertia. The underlying assumptions for the use of such plots are examined and the theoretical basis for the statement of a lower bound is given, in order to show where the use of this method is applicable.

PROPAGATION AND RESONANCE OF LONGITUDINAL WAVES IN PRISMATIC RODS

1936 ◽  
Vol 14a (2) ◽  
pp. 48-55
Author(s):  
R. Ruedy
Keyword(s):  
Boundary Conditions ◽  
Poisson’S Ratio ◽  
Equations Of Motion ◽  
Poisson's Ratio ◽  
Longitudinal Waves ◽  
Fundamental Frequencies ◽  
Cubic Equation ◽  
Resonance Frequencies ◽  
Fourth Series ◽  
Shearing Motion

For vibrations involving shearing and rotation, and for those involving both distortion and dilatation, the equations of motion combined with the boundary conditions yield in the simplest case a cubic equation for the resonance frequencies; its solution depends on Poisson's ratio and on the resonance frequencies fx, fy, fz, which the rod possesses when in pure shearing motion in the direction of its three axes. Three series of resonance frequencies are obtained when fy and fz are constant and the frequencies of the overtones are inserted for fx. A fourth series of resonance frequencies begins above the highest of the fundamental frequencies fx, fy, fz.

scholarly journals Development of a New Span-Morphing Wing Core Design

Designs ◽  
2019 ◽  
Vol 3 (1) ◽  
pp. 12 ◽  
Author(s):  
Peter L. Bishay ◽  
Erich Burg ◽  
Akinwande Akinwunmi ◽  
Ryan Phan ◽  
Katrina Sepulveda
Keyword(s):  
Carbon Fiber ◽  
Poisson’S Ratio ◽  
Fuel Efficiency ◽  
Poisson's Ratio ◽  
Cross Sectional ◽  
Structural Support ◽  
Roll Control ◽  
Wing Model ◽  
Transverse Rigidity ◽  
Main Components

This paper presents a new design for the core of a span-morphing unmanned aerial vehicle (UAV) wing that increases the spanwise length of the wing by fifty percent. The purpose of morphing the wingspan is to increase lift and fuel efficiency during extension, to increase maneuverability during contraction, and to add roll control capability through asymmetrical span morphing. The span morphing is continuous throughout the wing, which is comprised of multiple partitions. Three main components make up the structure of each partition: a zero Poisson’s ratio honeycomb substructure, telescoping carbon fiber spars and a linear actuator. The zero Poisson’s ratio honeycomb substructure is an assembly of rigid internal ribs and flexible chevrons. This innovative multi-part honeycomb design allows the ribs and chevrons to be 3D printed separately from different materials in order to offer different directional stiffness, and to accommodate design iterations and future maintenance. Because of its transverse rigidity and spanwise compliance, the design maintains the airfoil shape and the cross-sectional area during morphing. The telescoping carbon fiber spars interconnect to provide structural support throughout the wing while undergoing morphing. The wing model has been computationally analyzed, manufactured, assembled and experimentally tested.

A geophysical model for the Kapuskasing uplift from seismic and gravity studies

1991 ◽  
Vol 28 (3) ◽  
pp. 342-354 ◽  
Author(s):  
A. V. Boland ◽  
R. M. Ellis
Keyword(s):  
Cross Section ◽  
Wave Velocity ◽  
Poisson’S Ratio ◽  
Gravity Anomalies ◽  
P Wave ◽  
Poisson's Ratio ◽  
S Wave ◽  
Low Velocity ◽  
Cross Sectional ◽  
P Wave Velocity

The Kapuskasing uplift is an oblique cross section of Archean crust exposed by a major thrusting event in Early Proterozoic times. Previous results from the traveltime and amplitude analysis of compressional-wave (P-wave) arrivals from a seismic-refraction experiment have been used to constrain the modelling of shear-wave (S-wave) arrivals and gravity anomalies along the seismic profiles. S-wave and P-wave velocity information have been combined to obtain the variations of Poisson's ratio within the crust. High and low Poisson's ratio values have been linked to the mafic and felsic content, respectively, of the Shield rocks. Density variations along the profiles, constrained by the P-wave velocity structures and the observed gravity anomalies, again have been linked to the lithological variations as observed in the exposed cross section. Geological models, constrained by the geophysical observations and the cross-sectional exposure, have been constructed for profiles across the northern and southern portions of the main uplift region. The results indicate an increase in pyroxene and garnetiferous gneisses with depth in the crust, as suggested by the high P-wave velocities (7.0–7.6 km/s), high densities (3050–3150 kg/m3, high Poisson's ratio values (0.26–0.28), and the petrological variations within the exposure. The presence of a low-velocity and low-density layer of tonalites under the surface greenstones has been established and can account for the low-velocity zones imaged along the Abitibi profile of this experiment and those imaged in other Shield refraction experiments.

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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