Statistical Response of a Simplified Nonlinear Fluid Model Under Random Parameters

2007 ◽  
Author(s):  
T-P. Chang
Keyword(s):  
Fluid Model ◽  
Closed Form Solution ◽  
Mean Value ◽  
Form Solution ◽  
Viscoelastic Materials ◽  
Nonlinear Springs ◽  
Constant Rate ◽  
Viscoelastic Modeling ◽  
Spring Constants ◽  
Nonlinear Fluid

In this paper, a simplified spring-dashpot model is proposed to represent the complicated nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been adopted by many researchers to characterize some parts of human body in bioengineering. Among others, the following researchers have already contributed to the development of this field (Weiss et al., [1]; Guedes et al., [2]). Sometimes it is impossible to estimate the constant parameters in the model deterministically, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to characterize the random properties of the viscoelastic materials. The mean value of the displacement of the nonlinear model, subjected to constant rate displacement, can be solved analytically. Based on the closed-form solution, the proposed method produces the statistical responses of the simplified nonlinear fluid model, which is fairly useful in estimating the reliability of the nonlinear system.

Stochastic Dynamic Response of a Simplified Nonlinear Fluid Model for Viscoelastic Materials

2012 ◽  
Vol 28 (2) ◽  
pp. 365-372 ◽  
Author(s):  
T.-P. Chang
Keyword(s):  
Dynamic Response ◽  
Closed Form ◽  
Fluid Model ◽  
Closed Form Solution ◽  
Mean Value ◽  
Form Solution ◽  
Stochastic Dynamic ◽  
Viscoelastic Materials ◽  
Viscoelastic Modeling ◽  
Nonlinear Fluid

AbstractIn the present study, we propose a simplified nonlinear fluid model to characterize the complex nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been utilized by many researchers to simulate some parts of human body in bioengineering and to represent many material properties in mechanical engineering, electronic engineering and construction engineering. Occasionally it is almost impossible to evaluate the constant parameters in the model in the deterministic sense, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to model the stochastic properties of the viscoelastic materials. After some transformations, the closed-form solution can be obtained for the mean value of the displacement of the simplified nonlinear fluid model, subjected to constant rate of displacement. Based on the closed-form solution, the proposed method generates the stochastic dynamic response of the simplified nonlinear model, which plays an important role in performing the reliability analysis of the nonlinear system.

Eulerian Multi-Fluid Model of Air Blast Atomization

2006 ◽  
Author(s):  
Srimani Bhamidipati ◽  
Mahesh Panchagnula ◽  
John Peddieson
Keyword(s):  
Closed Form ◽  
Recurrence Relations ◽  
Model Problem ◽  
Fluid Model ◽  
Closed Form Solution ◽  
Fluid Phase ◽  
Form Solution ◽  
Air Blast ◽  
Carrier Fluid ◽  
Selection Of

The application of fully Eulerian "multi-fluid" models to air blast atomization is discussed. Such models envision the system as consisting one carrier fluid phase and multiple drop phases, each having a discrete size. A model problem is formulated which allows a general closed form solution in terms of recurrence relations. This closed form solution is employed to produce representative results. A selection of these is used to illustrate interesting aspects of the predictions.

A Nonlinear Generalized Maxwell Fluid Model for Viscoelastic Materials

2001 ◽  
Vol 68 (5) ◽  
pp. 787-790 ◽  
Author(s):  
D. T. Corr ◽  
M. J. Starr ◽  
R. Vanderby, ◽  
T. M. Best
Keyword(s):  
Fluid Model ◽  
Maxwell Fluid ◽  
Viscoelastic Materials ◽  
Force Equation ◽  
Constant Rate ◽  
Parallel Arrangement ◽  
Noteworthy Feature ◽  
In Series ◽  
Linear Spring ◽  
Generalized Maxwell Fluid

A nonlinear Maxwell fluid model consisting of a linear dashpot in series with a parallel arrangement of a linear spring and a second-order nonlinear spring, was developed. This configuration provides the flexibility necessary to describe both the stiffening and the softening responses of some viscoelastic materials. A noteworthy feature of the model is that under constant rate displacement, the force equation can be solved in closed form, thereby providing a continuous, exact general solution.

BIOMECHANICS OF ELECTRO-KINETICALLY MODULATED PERISTALTIC MOTION OF BIO-FLUID THROUGH A DIVERGENT COMPLEX WAVY CHANNEL

2020 ◽  
Author(s):  
Khurram Javid ◽  
Zeeshan Asghar ◽  
Fiaz Ur Rehman
Keyword(s):  
Fluid Model ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Volumetric Flow Rate ◽  
Axial Direction ◽  
Mechanical Efficiency ◽  
Form Solution ◽  
Long Wavelength ◽  
Electro Magnetic ◽  
Physical Quantities

The utility of electrically driven peristaltic flow to enhance the mechanical efficiency of a biological system is diverse. This motivates us to discuss the mathematical modelling of magnetic fluid flow via complex wavy walls. Additionally, an electric field is also applied in the axial direction. The non-Newtonian couple stress fluid model is used here. The analysis is performed under the Debye–Hückel linearization. The governing equations are modelled under long wavelength and low Reynolds number assumption. A closed form solution is obtained for the stream function, which is further used to calculate other physical quantities. To observe the remarkable effects of eminent parameters on the velocity distribution and volumetric flow rate, we have plotted graphs in both two- and three-dimensional axes. Comparison between simple and complex peristaltic wave is also provided. This study is very useful for designing a non-uniform micro-peristaltic pump, in which a flow can be controlled by electro-magnetic forces.

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.

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