Numerical Solution for Two-Dimensional Elastic Wave Propagation in Finite Bars

1967 ◽  
Vol 34 (3) ◽  
pp. 725-734 ◽  
Author(s):  
L. D. Bertholf
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Numerical Solutions ◽  
Step Change ◽  
Two Dimensional ◽  
One Dimensional ◽  
Elastic Bar ◽  
The One ◽  
The Impact

Numerical solutions of the exact equations for axisymmetric wave propagation are obtained with continuous and discontinuous loadings at the impact end of an elastic bar. The solution for a step change in stress agrees with experimental data near the end of the bar and exhibits a region that agrees with the one-dimensional strain approximation. The solution for an applied harmonic displacement closely approaches the Pochhammer-Chree solution at distances removed from the point of application. Reflections from free and rigid-lubricated ends are studied. The solutions after reflection are compared with the elementary one-dimensional stress approximation.

Study of Stress Wave Propagation in SHPB with NHDMOC

2013 ◽  
Vol 444-445 ◽  
pp. 158-162
Author(s):  
Ming Li Xu ◽  
Guang Ying Zhang ◽  
Ruo Qi Zhang
Keyword(s):  
Wave Propagation ◽  
Stress Wave ◽  
Elastic Stress ◽  
Constitutive Relationship ◽  
Stress Wave Propagation ◽  
One Dimensional ◽  
Elastic Bar ◽  
The One ◽  
Dispersion And Attenuation ◽  
Elastic Stress Wave

In this paper the NHDMOC method which succeeded in studying stress wave propagation with one dimensional strain was applied to study the one-dimensional stress wave propagation. In this paper, the ZWT nonlinear visco-elastic constitutive relationship with 7 parameters to NHDMOC, and corresponding equations were deduced The equations was verified from the comparison of elastic stress wave propagation in SHPB with elastic bar and visco-elastic bar respectively. Finally the dispersion and attenuation of stress wave in SHPB with visco-elastic bar was studied.

scholarly journals Flow Simulation in a combined Region

2021 ◽  
Vol 264 ◽  
pp. 01016
Author(s):  
Umurdin Dalabaev
Keyword(s):  
Experimental Data ◽  
Porous Medium ◽  
Flow Simulation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Heterogeneous Model ◽  
One Dimensional ◽  
Free Zone ◽  
Porous Framework ◽  
The One

The article deals with the flow in a complex area. The composition of this region consists of a porous medium through the pores of which the liquid moves and a zone without a porous framework (free zone). The flow is modeled using an interpenetrating heterogeneous model. In the one-dimensional case, an analytical solution is obtained. This solution is compared with the solution learned by the move node method. An analysis is made with experimental data with a Brinkman layer. A numerical solution of a two-dimensional problem is also obtained.

scholarly journals Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation

2014 ◽  
Vol 61 (3-4) ◽  
pp. 111-125 ◽  
Author(s):  
Dariusz Gąsiorowski
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Numerical Solutions ◽  
Numerical Algorithms ◽  
Finite Volume Methods ◽  
Flood Wave ◽  
One Dimensional ◽  
Benchmark Solution ◽  
The One ◽  
Water Depths

Abstract A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of a moving wet-dry front, which lead to instability in numerical solutions. To overcome these difficulties, a simplified model in the form of a non-linear diffusive wave equation (DWE) can be used. The diffusive wave approach requires numerical algorithms that are much simpler, and consequently, the computational process is more effective than in the case of the SWE. In this paper, the numerical solution of the one-dimensional DWE based on the modified finite element method is verified in terms of accuracy. The resulting solutions of the DWE are compared with the corresponding benchmark solution of the one-dimensional SWE obtained by means of the finite volume methods. The results of numerical experiments show that the algorithm applied is capable of reproducing the reference solution with satisfactory accuracy even for a rapidly varied wave over a dry bottom.

Temperature Depression Under Heat Sources With Cylindrical Contact Thermocouples

2015 ◽  
Author(s):  
Kayvan Abbasi ◽  
Sukhvinder Kang
Keyword(s):  
Heat Sink ◽  
Numerical Solutions ◽  
Heat Sources ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Dimensionless Groups ◽  
Dimensional Approximation ◽  
The One ◽  
Temperature Depression

The thermal performance of heat sinks is commonly measured using heat sources with spring loaded thermocouples contained within plastic poppets that press against the heat sink to measure its surface temperature where the heat is applied. However, when the thickness of the heat sink base is small or the effective heat transfer coefficient on the fin side is large, the temperature at the thermocouple contact point is less than the nearby temperature where the heat source contacts the heat sink. This temperature depression under the contact thermocouples has been studied. The heat conduction equation is solved analytically to determine the temperature distribution around the contact thermocouple using a one-dimensional approximation and also a detailed two-dimensional approach. Two dimensionless groups are identified that characterize the detailed two-dimensional solution. The combination of the two dimensionless groups also appears in the one dimensional solution. The temperature distributions are validated using finite difference numerical solutions. It is shown that the one dimensional solution is the limit of the detailed solution when one of the dimensionless groups tends to infinity. A simple equation is provided to estimate the temperature measurement error on the heat sink surface.

Results from the multi-species Benchmark Problem 3 (BM3) using two-dimensional models

2004 ◽  
Vol 49 (11-12) ◽  
pp. 169-176 ◽  
Author(s):  
D.R. Noguera ◽  
C. Picioreanu
Keyword(s):  
Numerical Solutions ◽  
Mathematical Framework ◽  
Two Dimensional ◽  
Benchmark Problem ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Bulk Substrate ◽  
The One ◽  
Definition Of ◽  
Multidimensional Models

In addition to the one-dimensional solutions of a multi-species benchmark problem (BM3) presented earlier (Rittmann et al., 2004), we offer solutions using two-dimensional (2-D) models. Both 2-D models (called here DN and CP) used numerical solutions to BM3 based on a similar mathematical framework of the one-dimensional AQUASIM-built models submitted by Wanner (model W) and Morgenroth (model M1), described in detail elsewhere (Rittmann et al., 2004). The CP model used differential equations to simulate substrate gradients and biomass growth and a particle-based approach to describe biomass division and biofilm growth. The DN model simulated substrate and biomass using a cellular automaton approach. For several conditions stipulated in BM3, the multidimensional models provided very similar results to the 1-D models in terms of bulk substrate concentrations and fluxes into the biofilm. The similarity can be attributed to the definition of BM3, which restricted the problem to a flat biofilm in contact with a completely mixed liquid phase, and therefore, without any salient characteristics to be captured in a multidimensional domain. On the other hand, the models predicted significantly different accumulations of the different types of biomass, likely reflecting differences in the way biomass spread within the biofilm is simulated.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

A CALIBRATED MODEL SEISMIC SYSTEM

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 445-455 ◽  
Author(s):  
C. N. G. Dampney ◽  
B. B. Mohanty ◽  
G. F. West
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Critical Examination ◽  
Two Dimensional ◽  
Linear Filtering ◽  
Analog Model ◽  
Basic Assumptions ◽  
Electronic Circuitry ◽  
Seismic System

Simple electronic circuitry and axially polarized ceramic transducers are employed to generate and detect elastic waves in a two‐dimensional analog model. The absence of reverberation and the basic simplicity. of construction underlie the advantages of this system. If the form of the fundamental wavelet in the model itself, as modified by the linear filtering effects of the remainder of the system, can be found, then calibration is achieved. This permits direct comparison of theoretical and experimental seismograms for a given model if its impulse response is known. A technique is developed for calibration and verified by comparing Lamb’s theoretical and experimental seismograms for elastic wave propagation over the edge of a half plate. This comparison also allows a critical examination of the basic assumptions inherent in a model seismic system.

MUTUAL EXCLUSION ON OPTICAL BUSES

2002 ◽  
Vol 12 (03n04) ◽  
pp. 341-358
Author(s):  
KRISHNA M. KAVI ◽  
DINESH P. MEHTA
Keyword(s):  
Mutual Exclusion ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Array ◽  
Propagation Delays ◽  
Optical Buses ◽  
The One

This paper presents two algorithms for mutual exclusion on optical bus architectures including the folded one-dimensional bus, the one-dimensional array with pipelined buses (1D APPB), and the two-dimensional array with pipelined buses (2D APPB). The first algorithm guarantees mutual exclusion, while the second guarantees both mutual exclusion and fairness. Both algorithms exploit the predictability of propagation delays in optical buses.

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