Flow-Induced Vibrations Caused by Roughness in Pipes Conveying Fluid

1986 ◽  
Vol 53 (1) ◽  
pp. 181-186 ◽  
Author(s):  
A. Shulemovich
Keyword(s):  
Differential Operator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Negative Slope ◽  
Friction Characteristic ◽  
Fluid Velocities ◽  
Flow Induced Vibrations ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid ◽  
Loop Motion

This paper presents a theoretical investigation of self-excited vibrations of pipes conveying fluid due to roughness. A model of a laminar friction, considered as the excitation mechanism, is based on Prandtl’s universal velocity distribution for the turbulent boundary layer and on Nikuradse’s experiments. The analysis has shown that the friction characteristic has a negative slope in a certain range of fluid velocities. This range is a function of pipe roughness and is shifted to lower flow velocities due to roughness growth during pipe operation. It was found that the differential operator of a piping loop motion based on the nonlinear restoring characteristic coincides with the differential operator of Duffing’s equation for the hardening system. The energy method was used to obtain the approximate closed-form solution for the amplitude of steady self-excited vibrations. The unstable response with jump phenomena can appear due to interaction of small turbulent disturbances in conveying fluid with a given nonlinear system.

A Generalized Impact-Sliding Fretting Wear Model Based on Fracture Mechanics Approach

2004 ◽  
Author(s):  
Yemane Gessesse ◽  
Helmi Attia ◽  
M. O. M. Osman
Keyword(s):  
Fracture Mechanics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fretting Wear ◽  
Simultaneous Action ◽  
Wear Process ◽  
Inconel 600 ◽  
Order Of Magnitude ◽  
Flow Induced Vibrations ◽  
Physical Attributes

Impact-sliding fretting wear is a complex phenomenon due to the random nature of the flow-induced vibrations, and the self-induced tribological changes. Available models, which relate wear losses to the process variables, are empirical in nature and bear no physical similarity to the actual mathematical and physical attributes of the wear process. A generalized model is developed in the present work to mathematically describe the fretting wear process under various modes of motion, namely, impact, sliding and oscillatory. This model, which is based on the findings from the fracture mechanics analysis of the crack initiation and propagation processes, takes into consideration the simultaneous action of both the surface adhesion and subsurface fatigue mechanisms. The model also accounts for the micro-, and macro- contact configuration of the tube-support system. The closed form solution requires the calibration of single parameter, using a limited number of experiments, to account for the effect of environment and the support material. The model was validated using experimental data that are generated for Inconel 600 and Incology 800 tube materials at room and high temperature environment, and for different types of motion. The results showed that model can accurately predict wear losses within a factor of < ±3. This narrow range presents better than an order of magnitude improvement over the current state-of-the-art models.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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