scholarly journals Limiting Vibroisolation Control of an Oscillating String on a Moving Base

1995 ◽  
Vol 2 (2) ◽  
pp. 163-171 ◽  
Author(s):  
Dmitry V. Balandin
Keyword(s):  
Solution Method ◽  
Solution Technique ◽  
Quadratic Functional ◽  
Numerical Example ◽  
Guaranteed Quality ◽  
Moving Base ◽  
Elastic Object

The vibroisolating capability of an elastic object that is assumed to be protected against a class of excitations is studied. It is proposed that this capability be estimated by a quadratic functional. The solution method gives an estimate of the optimal isolation with a criterion of minimum guaranteed quality. A numerical example of the solution technique is presented.

Modeling Low Knudsen Number Transition Flows Using a Computationally Efficient Continuum-Based Methodology

2006 ◽  
Author(s):  
Simon Mizzi ◽  
David R. Emerson ◽  
Robert W. Barber ◽  
Jason M. Reese
Keyword(s):  
Boundary Conditions ◽  
Solution Method ◽  
Computational Cost ◽  
Solution Technique ◽  
Moment Equations ◽  
Transition Flow ◽  
Transition Flow Regime ◽  
Present Solution ◽  
Fully Coupled ◽  
Non Equilibrium

This paper presents a new technique that combines Grad’s 13-moment equations (G13) with a phenomenological approach. The combination of these approaches and the proposed solution technique manages to capture important non-equilibrium phenomena that start to appear in the early transition-flow regime. In contrast to the fully-coupled 13-moment equations, a significant advantage of the present solution technique is that it does not require extra boundary conditions. The solution method is similar in form to the Maxwellian iteration used in the kinetic theory of gases. In our approach, Grad’s equations for viscous stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations of transport. This novel technique manages to capture non-equilibrium effects and its relative computational cost is low in comparison to other methods such as fully-coupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is applied to a planar Couette flow and the results are compared to predictions obtained from the direct simulation Monte Carlo method. In the transition regime, this test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from non-equilibrium phenomena. These effects cannot be captured by the Navier-Stokes-Fourier constitutive equations or phenomenological modifications thereof. Moreover, simply using the G13 equations, along with the decoupled solution method, does not capture the nonlinearities occurring in the proximity of a solid wall. However, combining phenomenological scaling functions and slip boundary conditions with the G13 equations provides a better representation of these important non-equilibrium phenomena but at a relatively low computational cost.

Simulation of Piping Process Based on Coupling Seepage and Erosion

2014 ◽  
Vol 602-605 ◽  
pp. 558-561
Author(s):  
Jin Zhang
Keyword(s):  
Solution Technique ◽  
Governing Equations ◽  
Theory Analysis ◽  
Preliminary Stage ◽  
Seepage Erosion ◽  
Numerical Example ◽  
Dynamic Constraint ◽  
Solution Accuracy

Only the preliminary stage of piping process can be simulated by current seepage-erosion coupled piping model. In order to enhance the simulation capability, a modified piping model is presented. Theory analysis shows that the governing equations of the modified piping model have significant advantages in practicality and solution accuracy. The solving process of the model is analyzed, with the result showing that the out-of-bounds appearance of the field variables is the major factor interrupting the solving process. Then a new solution technique called dynamic constraint is proposed, which can ensure the validity of field variables. Numerical example indicates that the new governing equations and dynamic constraint technique can enormously enhance the simulation capability of the model, and the piping process can be effectively simulated.

scholarly journals Solution of Plane Cascade Flow Using Improved Surface Singularity Methods

1981 ◽  
Author(s):  
E. R. McFarland
Keyword(s):  
Solution Method ◽  
External Flow ◽  
Surface Singularity ◽  
Solution Technique ◽  
Linear Cascade ◽  
Cascade Flow ◽  
Flow Through

A solution method has been developed for calculating compressible in viscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those found in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method’s capabilities are presented.

scholarly journals Improvement for Amelioration Inventory Model with Weibull Distribution

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Han-Wen Tuan ◽  
Shu-Cheng Lin ◽  
Peterson Julian
Keyword(s):  
Weibull Distribution ◽  
Solution Method ◽  
Shape Parameter ◽  
Optimal Solution ◽  
Inventory Model ◽  
Inventory Systems ◽  
Inventory Models ◽  
Numerical Example ◽  
Analytical Work

Most inventory models dealt with deteriorated items. On the contrary, just a few papers considered inventory systems under amelioration environment. We study an amelioration inventory model with Weibull distribution. However, there are some questionable results in the amelioration paper. We will first point out those questionable results in the previous paper that did not derive the optimal solution and then provide some improvements. We will provide a rigorous analytical work for different cases dependent on the size of the shape parameter. We present a detailed numerical example for different ranges of the sharp parameter to illustrate that our solution method attains the optimal solution. We developed a new amelioration model and then provided a detailed analyzed procedure to find the optimal solution. Our findings will help researchers develop their new inventory models.

scholarly journals Solution of Plane Cascade Flow Using Improved Surface Singularity Methods

1982 ◽  
Vol 104 (3) ◽  
pp. 668-674 ◽  
Author(s):  
E. R. McFarland
Keyword(s):  
Solution Method ◽  
Inviscid Flow ◽  
External Flow ◽  
Surface Singularity ◽  
Solution Technique ◽  
Linear Cascade ◽  
Cascade Flow ◽  
Flow Through

A solution method has been developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those found in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method’s capabilities are presented.

A Consistent Approach to Problem Solving in Mechanical Vibrations

2018 ◽  
Author(s):  
Amir H. Danesh-Yazdi ◽  
Yi Wu ◽  
Oladipo Onipede
Keyword(s):  
State Space ◽  
Degrees Of Freedom ◽  
Solution Method ◽  
Traditional Approach ◽  
Solution Technique ◽  
Mdof Systems ◽  
Solution Methods ◽  
Vibration Problems ◽  
The Mathematical Model ◽  
Consistent Approach

A consistent approach to solving problems in an undergraduate vibrations course in Mechanical Engineering is presented in this paper. The traditional approach of solving vibration problems involves several steps such as classifying the system according to degrees of freedom, free or forced vibrations and with or without damping. Based on the classification, an appropriate solution technique is applied and the results are obtained. Since the mathematical solution technique is strictly tied to the classification, students have to learn and apply a variety of solution methods based on the particular form of the mathematical model. The course was literally more like a math course rather than an engineering course. By introducing students to the state-space solution method early in the course and using it as the main/dominant solution method, students can focus more on learning both the physical modeling and mathematical modeling of the vibration systems as well as interpreting results in the engineering context. Since state-space computational solvers are readily available to students (MATLAB, Mathcad, etc.) and they can be applied to solve most (but not all) vibration problems including free or forced SDOF, 2DOF, MDOF systems with or without damping, it allows for consistency when teaching students how to solve vibration problems. State-space solvers can solve for either the time or the frequency response and provides a graphical solution. The students can go from modeling to visually exploring and interpreting results. The students’ response to this approach is also discussed.

A study of moving base simulation motion cues utilizing washout technique

1975 ◽  
Author(s):  
Mark Kirkpatrick ◽  
Nicholas Shields ◽  
Ronald Brye ◽  
Frank L. Vinz
Keyword(s):  
Motion Cues ◽  
Moving Base

SIMPLIFIED MATHEMATICS FOR MULTIPLE BIOASSAYS

1960 ◽  
Vol XXXV (III) ◽  
pp. 454-468 ◽  
Author(s):  
R. Borth
Keyword(s):  
Parallel Line ◽  
Numerical Example ◽  
Dose Levels

ABSTRACT Gaddum's simplified system of computation for the analysis of biological parallel-line assays is extended to the assay of several unknown preparations simultaneously against the same standard, using up to four dose levels of each preparation. Complete working directions and formulae are provided and illustrated by a numerical example. Limiting conditions are briefly discussed.

Elasto-plastic state of curve beam system subjected to complex loading

1996 ◽  
Vol 18 (4) ◽  
pp. 14-22
Author(s):  
Vu Khac Bay
Keyword(s):  
Cylindrical Shell ◽  
Solution Method ◽  
Complex Loading ◽  
Numerical Results ◽  
Elastic Solution ◽  
Plastic State ◽  
Curve Beam ◽  
Elastic State ◽  
Elastic Plastic ◽  
Beam System

Investigation of the elastic state of curve beam system had been considered in [3]. In this paper the elastic-plastic state of curve beam system in the form of cylindrical shell is analyzed by the elastic solution method. Numerical results of the problem and conclusion are given.

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