Exact Solutions of the Generalized Equal Width Wave Equation

Hamdi, Samir; Enright, W. H.; Schiesser, William E.; Gottlieb, J. J.

doi:10.1007/3-540-44843-8_79

Cited by 21 publications

(28 citation statements)

References 7 publications

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“…From (1)(2)(3)(4)(5)(6)(7)(8) This result is very close to the experimentally observed minimum velocity needed for full penetration. In Figure 7, we compare the penetration depth of the reference 'BB' projectile and a polypropylene projectile using the small-depth penetration model.…”

Section: Determine Penetration Threshold Velocity C V Revisitedsupporting

confidence: 84%

“…In Figure 7, we compare the penetration depth of the reference 'BB' projectile and a polypropylene projectile using the small-depth penetration model. It should be recalled that for a large depth of penetration, penetration depth is proportional to ln( ) v instead of 2 v shown in Equation (1)(2)(3)(4)(5)(6)(7)(8) for the small depth of penetration model. …”

Section: Determine Penetration Threshold Velocity C V Revisitedmentioning

confidence: 99%

“…In the case of a finite sized rigid body penetrating a given target, we assume that the body surface is composed of an ensemble of small elementary surfaces, and the force of resistance on an elementary area dA depends on the inward velocity at P and three retardation coefficients obtained from Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and experimental data. By using a scaling analysis, we have extended the nature of the retardation force to unknown bodies for which no experimental data is available.…”

Section: Analysis Of New Penetration Datamentioning

confidence: 99%

“…In equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), subscripts P in the retardation coefficients , and    indicate that these coefficients depend on the target material properties at P . In Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), G v is the velocity of the center of mass G. In Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), G M is the moment of the retardation forces about G, and G H is the angular momentum of the rigid body about G, and /  G P r GP (Equation 1-15 and Figure 10).…”

Section: Analysis Of New Penetration Datamentioning

confidence: 99%

“…Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) about the center of mass G with axes along the Gxyz (Figure 10), and the angular velocity  of the rigid body -17) where the components are along the axes of the rotating frame …”

Section: Using the Inertia Matrixmentioning

confidence: 99%

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Analytic Simulation of Tissue Damage from Penetrating Wounds to the Heart

Eisler¹,

Chatterjee²,

Stone³

et al. 2006

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE 01-12-2006 REPORT TYPE PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER ATK Mission ResearchLaguna Hills, CA 92653-1327 SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) U.S. Army Medical Research and Materiel Command Fort Detrick, Maryland 21702-5012 SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for Public Release; Distribution Unlimited SUPPLEMENTARY NOTESOriginal contains colored plates: ALL DTIC reproductions will be in black and white. ABSTRACTATKMissionResearchwassponsoredbyDARPA'sVirtualSoldierprogramtoanalyticallysimulateresidualwoundtractsandtissuedyna micsassociatedwithasurvivablewoundfromanexplosivelydrivenfragmentpenetratingtheleftventricularwallofthehumanheart. LIST OF FIGURESFIGURE 1. Models for three fragment categories………………………………………… 9 FIGURE 2. 30 Caliber "Wedge Projectile" used in Task 3 Ballistic Experiments………. 10 FIGURE 3. Penetration Depth and Retardation forces vs. Velocity……………………… 11 FIGURE 4. Correlation between analytical predictions and ballistic test data for three different diameter spheres shot into 20% ordnance gelatin …………. 14 FIGURE 5. Schematic of Loading on a Flat Fragment …………………………………… 15 FIGURE 6. Schematic and Loading on a Cut Cylinder …………………………………… 15 The Mission Research effort consisted of three related tasks. In the first task entitled Analytical Simulation of Projectile Trajectory, Mission Research divided up fragments into three geometric categories -platelet, "chunky" fragment, and slender high aspect ratio projectile -with different governing parameters. For each fragment geometry, algorithms were developed that describe interaction of the fragment with human tissue and resulting projectile kinematics through different tissue layers of the human left ventricular wall. Prof. Andrew McCulloch, Ph.D. (University of California, San Diego -UCSD) and his team assisted Mission Research in executing the UCSD Continuity code to develop quasistatic constitutive models for the various layers of tissue through the left ventricular wall. From these qu...

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