A Three-Dimensional Lumped Parameter Model of Nanoscale Phononic Crystals

2009 ◽  
Author(s):  
Bruce L. Davis ◽  
Mahmoud I. Hussein
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Phononic Crystals ◽  
Lumped Parameter Model ◽  
Lagrangian Equations ◽  
Area Of Interest ◽  
Simple Cubic ◽  
Lumped Parameter ◽  
Mass Spring Model ◽  
Mass Spring

This work focuses on modeling nanoscale phononic crystals by setting up the appropriate Lagrangian equations of motion. The atomic structure and force constants are accounted for by means of a lumped parameter mass-spring model. In particular we focus on a simple cubic lattice with one mass per primitive unit cell. We use the model to predict the wave propagation frequency spectrum. We then use the model to conduct a series of studies on the influence of defects intentionally introduced to the lattice at a supercell level. One area of interest is the effect of such alterations on the size and location of band gaps.

Modeling of Spur and Helical Gear Planetary Drives With Flexible Ring Gears and Planet Carriers

2006 ◽  
Vol 129 (1) ◽  
pp. 95-106 ◽  
Author(s):  
V. Abousleiman ◽  
P. Velex ◽  
S. Becquerelle
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Lumped Parameter Model ◽  
Integration Scheme ◽  
Ring Gear ◽  
Time Step ◽  
Contact Algorithm ◽  
Lumped Parameter ◽  
Epicyclic Gear ◽  
Internal Gear

A model is presented which enables the simulation of the three-dimensional static and dynamic behavior of planetary/epicyclic spur and helical gears with deformable parts. The contributions of the deflections of the ring gear and the carrier are introduced via substructures derived from 3D finite element models. Based on a modal condensation technique, internal gear elements are defined by connecting the ring-gear substructure and a planet lumped parameter model via elastic foundations which account for tooth contacts. Discrete mesh stiffness and equivalent normal deviations are introduced along the contact lines, and their values are recalculated as the mating flank positions vary with time. A constraint mode substructuring technique is used to simulate the planet carrier as a superelement which is connected to the planet center. Planetary/epicyclic gear models are completed by assembling lumped parameter sun gear/planet elements along with shaft elements, lumped stiffness, masses and inertias. The corresponding equations of motion are solved by combining a time-step integration scheme and a contact algorithm for all simultaneous meshes. Several quasistatic and dynamic results are given which illustrate the potential of the proposed hybrid model and the interest of taking into account ring gear and carrier deflections.

Mitigation of Biodynamic Response to Shock Loads Using Semi-Active Vertically Stroking Crew Seats

2010 ◽  
Author(s):  
Harinder J. Singh ◽  
Norman M. Wereley
Keyword(s):  
Human Body ◽  
Control Algorithm ◽  
Equations Of Motion ◽  
Comprehensive Analysis ◽  
Lumped Parameter Model ◽  
Force Model ◽  
Body Parts ◽  
Governing Equations ◽  
Lumped Parameter ◽  
Yield Force

This study addresses mitigation of biodynamic response due to an initial velocity impact of a vertically stroking crew seat using an adaptive magnetorheological energy absorber. Under consideration is a multiple degree-of-freedom detailed lumped parameter model of a human body falling with prescribed initial crash velocity (sink rate). The lumped parameter model of the human body consisted of four main parts: pelvis, upper torso, viscera and head. The governing equations of motion of a vertically stroking crew seat incorporating a human body were derived using parameters such as available damper stroke as well as MR yield force. The control algorithm for smooth landing of a rigid occupant was examined for compliant occupant and was modified accordingly. Four MR yield force models were analyzed to shape decelerations experienced by human body and an appropriate model was selected for comprehensive analysis. The simulated responses were analyzed with selected MR yield force model for a crew seat with an occupant corresponding to 90th percentile male at sink rates varying from 8 to 12 m/s. In addition, the mitigation of injuries to the human body parts due to load transmissions corresponding to crash velocities was also evaluated for the selected MR yield force model along with terminal conditions necessary for smooth landing.

scholarly journals The total cavopulmonary connection resistance: a significant impact on single ventricle hemodynamics at rest and exercise

2008 ◽  
Vol 295 (6) ◽  
pp. H2427-H2435 ◽  
Author(s):  
Kartik S. Sundareswaran ◽  
Kerem Pekkan ◽  
Lakshmi P. Dasi ◽  
Kevin Whitehead ◽  
Shiva Sharma ◽  
...  
Keyword(s):  
Heart Rate ◽  
Single Ventricle ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Lumped Parameter Model ◽  
Total Cavopulmonary Connection ◽  
Dynamic Simulations ◽  
Lumped Parameter ◽  
The Impact ◽  
Cavopulmonary Connection

Little is known about the impact of the total cavopulmonary connection (TCPC) on resting and exercise hemodynamics in a single ventricle (SV) circulation. The aim of this study was to elucidate this mechanism using a lumped parameter model of the SV circulation. Pulmonary vascular resistance (1.96 ± 0.80 WU) and systemic vascular resistances (18.4 ± 7.2 WU) were obtained from catheterization data on 40 patients with a TCPC. TCPC resistances (0.39 ± 0.26 WU) were established using computational fluid dynamic simulations conducted on anatomically accurate three-dimensional models reconstructed from MRI ( n = 16). These parameters were used in a lumped parameter model of the SV circulation to investigate the impact of TCPC resistance on SV hemodynamics under resting and exercise conditions. A biventricular model was used for comparison. For a biventricular circulation, the cardiac output (CO) dependence on TCPC resistance was negligible (sensitivity = −0.064 l·min−1·WU−1) but not for the SV circulation (sensitivity = −0.88 l·min−1·WU−1). The capacity to increase CO with heart rate was also severely reduced for the SV. At a simulated heart rate of 150 beats/min, the SV patient with the highest resistance (1.08 WU) had a significantly lower increase in CO (20.5%) compared with the SV patient with the lowest resistance (50%) and normal circulation (119%). This was due to the increased afterload (+35%) and decreased preload (−12%) associated with the SV circulation. In conclusion, TCPC resistance has a significant impact on resting hemodynamics and the exercise capacity of patients with a SV physiology.

A Lumped-Parameter Model for Stagnant Thermal Conductivity of Spatially Periodic Porous Media

1995 ◽  
Vol 117 (2) ◽  
pp. 264-269 ◽  
Author(s):  
C. T. Hsu ◽  
P. Cheng ◽  
K. W. Wong
Keyword(s):  
Thermal Conductivity ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Lumped Parameter Model ◽  
Circular Cylinders ◽  
Parameter Method ◽  
Two Dimensional ◽  
Algebraic Expressions ◽  
Lumped Parameter ◽  
Spatially Periodic

Based on a lumped-parameter method, algebraic expressions for the stagnant thermal conductivity of some two-dimensional and three-dimensional spatially periodic media are obtained. The geometries under consideration include arrays of touching and non-touching in-line square and circular cylinders (two-dimensional), as well as touching and nontouching in-line cubes (three-dimensional). A comparison of results based on these algebraic expressions with existing numerical solutions and experimental data shows that they are in excellent agreement.

A Discrete Lumped-Parameter Dynamic Model for a Planetary Gear Set with Flexible Ring Gear

2011 ◽  
Vol 86 ◽  
pp. 756-761 ◽  
Author(s):  
Jun Zhang ◽  
Yi Min Song ◽  
Jin You Xu
Keyword(s):  
Individual Component ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Ring Gear ◽  
Lumped Parameter ◽  
Planetary Gear System ◽  
Flexible Ring

A discrete lumped-parameter model for a general planetary gear set is proposed, which models the continuous flexible ring gear as discrete rigid ring gear segments connected with each other through virtual springs. The ring-planet mesh is analyzed to derive equations of motion of ring segments and planet. By assembling equations of motion of each individual component, the governing equations of planetary gear system are obtained. The solution for eigenvalue problem yields to natural frequencies and corresponding vibration modes. The simulations of example system reveal that the ring gear flexibility decreases system lower natural frequencies and the vibration modes can be classified into rotational, translational, planet and ring modes.

Vibration Modes of Helical Planetary Gears

2009 ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Modal Properties ◽  
Lumped Parameter

This paper examines the vibration modes of single stage helical planetary gears in three dimensions with equally spaced planets. A lumped-parameter model is formulated to obtain the equations of motion. The gears and shafts are modeled as rigid bodies with compliant bearings at arbitrary axial locations on the shafts. A translational and a tilting stiffness account for the force and moment transmission at the gear mesh interface. The modal properties generalize those of two-dimensional spur planetary gears; there are twice as many degrees of freedom and natural frequencies due to the added tilting and axial motion. All vibration modes are categorized as planet, rotational-axial, and translational-tilting modes. The modal properties are shown to hold even for configurations that are not symmetric about the gear plane, due to, for example, shaft bearings not being equidistant from the gear plane. Computational modal analysis are performed to numerically verify the findings.

scholarly journals Fast image-based model of mitral valve closure for surgical planning

2008 ◽  
Author(s):  
Peter Hammer ◽  
Nikolay Vasilyev ◽  
Douglas Perrin ◽  
Pedro del Nido ◽  
Robert Howe
Keyword(s):  
Mitral Valve ◽  
Surgical Planning ◽  
Equations Of Motion ◽  
Planning System ◽  
Patient Specific ◽  
Valve Closure ◽  
Spring Model ◽  
Closed State ◽  
Mass Spring Model ◽  
Mass Spring

Surgical repair of the mitral valve results in better outcomes than valve replacement, yet diseased valves are often replaced due to the technical difficulty of the repair process. A surgical planning system based on patient-specific medical images that allows surgeons to simulate and compare potential repair strategies could greatly improve surgical outcomes. The system must simulate valve closure quickly and handle the complex boundary conditions imposed by the chords that tether the valve leaflets. We have developed a process for generating a triangulated mesh of the valve surface from volumetric image data of the opened valve. The closed position of the mesh is then computed using a mass-spring model of dynamics. In the mass-spring model, triangle sides are treated as linear springs supporting only tension. Chords are also treated as linear springs, and self-collisions are detected and handled inelastically. The equations of motion are solved using implicit numerical integration. The simulated closed state is compared with an image of the same valve taken in the closed state to assess accuracy of the model. The model exhibits rapid valve closure and is able to predict the closed state of the valve with reasonable accuracy.

scholarly journals Rail Car Impact Tests With Steel Coil: Collision Dynamics

Joint Rail ◽  
2003 ◽  
Author(s):  
Karina Jacobson ◽  
David Tyrell ◽  
Benjamin Perlman
Keyword(s):  
Three Dimensional ◽  
Full Scale ◽  
Dynamic Responses ◽  
Lumped Parameter Model ◽  
Collision Dynamics ◽  
Dynamics Model ◽  
Steel Coil ◽  
Impact Tests ◽  
Lumped Parameter ◽  
Grade Crossing

Two full-scale oblique grade-crossing impact tests were conducted in June 2002 to compare the crashworthiness performance of alternative corner post designs on rail passenger cab cars. On June 4, 2002 a cab car fitted with an end structure built to pre-1999 requirements impacted a steel coil at approximately 14 mph. Following, on June 7, 2002 a cab car fitted with an end structure built to current requirements underwent the same test. Each car was equipped with strain gauges, string potentiometers and accelerometers to measure the deformation of specific structural elements, and the longitudinal, lateral and vertical displacements of the car body. The gross motions of the cars and steel coil, the force/crush behavior of the end structures, and the deformation of major elements in the end structures were measured during the tests. During the first test, the car fitted with the 1990’s design end structure acquired more than 20 inches of longitudinal deformation causing failure at the corner post and resulting in the loss of operator survival space. During the second test, the corner post on the car fitted with the State-of-the-Art design deformed longitudinally by about 8 inches, causing no failure and consequently preserving the survivable operator volume. In both cases, the steel coil was thrown to the side of the train after impacting the end structure. Prior to the tests, the crush behaviors of the cars and their dynamic responses were simulated with car crush and collision dynamics models. The car crush model was used to determine the force/crush characteristics of the corner posts, as well as their modes of deformation. The collision dynamics model was used to predict the extent of crush of the corner posts as functions of impact velocity, as well as the three-dimensional accelerations, velocities, and displacements of the cars and coil. Both models were used in determining the instrumentation and its locations. This paper describes the collision dynamics model and compares predictions for the gross motions of the cars and coils made with this model with measurements from the tests. A companion paper describes the car crush model and compares predictions made of car crush with measurements from the test. The collision dynamics was analyzed using a lumped-parameter model, with non-linear stiffness characteristics. The suspension of the car is included in the model in sufficient detail to predict derailment. The model takes the force/crush characteristic developed in the car crush analysis as input, and includes the lateral force that develops as the corner post is loaded longitudinally. The results from the full-scale grade-crossing impact tests largely agree with and confirm the preliminary results of the three-dimensional lumped parameter computer model of the collision dynamics. The predictions of the model for the three-dimensional accelerations, velocities, and displacements of the car and the coil are in very close agreement with the measurements made in the tests of both cars, up to the time of failure of the corner post. The cars remained on the track in both tests, as predicted with the model.

Optimized Biodynamic Shock Attenuation Performance Using an Adaptive Seat Suspension

2011 ◽  
Author(s):  
Harinder J. Singh ◽  
Norman M. Wereley
Keyword(s):  
Equations Of Motion ◽  
Lumped Parameter Model ◽  
Local Optimum ◽  
Shock Attenuation ◽  
Energy Absorber ◽  
Seat Suspension ◽  
Lumped Parameter ◽  
Cubic Polynomial ◽  
Yield Force ◽  
Vertical Impact

Design optimization-based techniques are presented for the minimization of biodynamic loads of a seated occupant subjected to a shock due to an initial velocity vertical impact. A 95th percentile male occupant was modeled using a multiple degree-of-freedom biodynamic lumped parameter model (BLPM) seated on a vertically stroking adaptive seat suspension with a semi-active magnetorheological energy absorber (MREA). The governing equations of motion of the adaptive MREA-based seat suspension with biodynamic lumped parameter model were developed. The variation of magnetorheological yield force with respect to the energy absorber stroke was shaped using cubic polynomial for the maximum shock attenuation. Three cost functions were devised with a common goal of minimizing biodynamic decelerations. Constraints were established based on limitation of MREA stroke and, yield force as well as stroking load. The MREA yield force and damper stroke were crucial parameters for improved biodynamic response mitigation to shock loads. A globally optimized biodynamic response was analyzed among several local optimum responses for better shock attenuation.

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