Three-Dimensional Frictional Rigid-Body Impact

1995 ◽  
Vol 62 (4) ◽  
pp. 893-898 ◽  
Author(s):  
V. Bhatt ◽  
Jeff Koechling
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Local Analysis ◽  
Integration Scheme ◽  
Numerical Integration Scheme ◽  
Rigid Body Model ◽  
Global Nature ◽  
The Impact

We present an analysis of the rigid-body model for frictional three-dimensional impacts, which was originally studied by Routh. Using Coulomb’s law for friction, a set of differential equations describing the progress and outcome of the impact process for general bodies can be obtained. The differential equations induce a flow in the tangent velocity space for which the trajectories cannot be solved for in a closed form, and a numerical integration scheme is required. At the point of sticking, the numerical problem becomes ill-conditioned and we have to analyze the flow at the singularity to determine the rest of the process. A local analysis at the point of sticking provides enough information about the global nature of the flow to let us enumerate all the possible dynamic scenarios for the sliding behavior during impact. The friction coefficient, and the mass parameters at the point of contact, determine the particular sliding behavior that would occur for a given problem. Once the initial conditions are specified, the possible outcome of the impact can then be easily determined.

A Simple and Accurate Method for Determining Large Deflections in Complaint Mechanisms Subjected to End Forces and Moments

1998 ◽  
Author(s):  
A. Saxena ◽  
Steven N. Kramer
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Beam Equation ◽  
Integration Scheme ◽  
Large Deflections ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Abstract Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads for which, traditional methods of deflection analysis do not apply Nonlinearities introduced by these large deflections make the system comprising such members difficult to solve Parametric deflection approximations are then deemed helpful in the analysis and synthesis of compliant mechanisms This is accomplished by seeking the pseudo-rigid-body model representation of the compliant mechanism A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads with positive end moments A numerical integration technique using quadrature formulae has been employed to solve the nonlinear Bernoulli-Euler beam equation for the tip deflection Implementation of this scheme is relatively simpler than the elliptic integral formulation and provides nearly accurate results Results of the numerical integration scheme are compared with the beam finite element analysis An example for the synthesis of a compliant mechanism using the proposed model is also presented.

Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

2022 ◽  
pp. 108128652110679
Author(s):  
Emilio Turco
Keyword(s):  
Kinetic Energy ◽  
Strain Energy ◽  
Nonlinear Vibrations ◽  
Three Dimensional ◽  
Integration Scheme ◽  
Beam Model ◽  
Model Formulation ◽  
Discrete Approach ◽  
Numerical Integration Scheme ◽  
Proposed Model

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

scholarly journals Impact of nuclear inertia momenta on fission observables

2018 ◽  
Vol 193 ◽  
pp. 01004
Author(s):  
P. Tamagno ◽  
O. Litaize
Keyword(s):  
Rigid Body ◽  
Excitation Energy ◽  
Nuclear Fission ◽  
Particle Model ◽  
Rotational Inertia ◽  
Neutron Fission ◽  
Fission Fragments ◽  
Rigid Body Model ◽  
Two Parameters ◽  
The Impact

Fission is probably the nuclear process the less accurately described with current models because it involves dynamics of nuclear matter with strongly coupled manybody interactions. It is thus diffcult to find models that are strongly rooted in good physics, accurate enough to reproduce target observables and that can describe many of the nuclear fission observables in a consistent way. One of the most comprehensive current modeling of the fission process relies on the fission sampling and Monte-Carlo de-excitation of the fission fragments. This model is implemented for instance in the FIFRELIN code. In this model fission fragments and their state are first sampled from pre-neutron fission yields, angular momentum distribution and excitation energy repartition law then the decay of both initial fragments is simulated. This modeling provides many observables: prompt neutron and gamma fission spectra, multiplicities and also fine decompositions: number of neutrons emitted as a function of the fragment mass, spectra per fragments, etc. This model relies on nuclear structure databases and on several basic nuclear models describing for instance gamma strength functions or level densities. Additionally some free parameters are still to be determined, namely two parameters describing the excitation energy repartition law, the spin cutoff of the heavy and light fragments and a rescaling parameter for the rotational inertia momentum of the fragments with respect of the rigid-body model. In the present work we investigate the impact of this latter parameter. For this we mainly substitute the corrected rigid-body value by a quantity obtained from a microscopic description of the fission fragment. The independent-particle model recently implemented in the CONRAD code is used to provide nucleonic wave functions that are required to compute inertia momenta with an Inglis-Belyaev cranking model. The impact of this substitution is analyzed on different fission observables provided by the FIFRELIN code.

Research on Dynamic Modelling and Simulation of Erection System of Mobile Equipment in Absolute Coordinates

2011 ◽  
Vol 66-68 ◽  
pp. 2034-2040
Author(s):  
Qin He Gao ◽  
Xiang Yang Li
Keyword(s):  
Rigid Body ◽  
Dynamic Models ◽  
Dynamic Modelling ◽  
Hydraulic Cylinder ◽  
Correction Method ◽  
Integration Time ◽  
Multi Stage ◽  
Rigid Body Model ◽  
Absolute Coordinates ◽  
The Impact

This paper employed the theories of multibody system dynamics to analyze the multi-rigid-body model of erection system and build the general dynamic models in absolute coordinates. The impact theory of contact mechanics and nonlinear spring-damper force function were used to model the impact problems between rods of multi-stage hydraulic cylinder of erection system and educe the dynamic models of multi-rigid-body erection system with impact. An automatic violation correction method according to the step of integration time was given to solve the violation which is an incident problem in numerical integration of dynamic models in absolute coordinates. Simulation results show that these dynamic models are effective.

scholarly journals CIRA/CSU Four-Dimensional Variational Data Assimilation System

2005 ◽  
Vol 133 (4) ◽  
pp. 829-843 ◽  
Author(s):  
Milija Zupanski ◽  
Dusanka Zupanski ◽  
Tomislava Vukicevic ◽  
Kenneth Eis ◽  
Thomas Vonder Haar
Keyword(s):  
Data Assimilation ◽  
Initial Conditions ◽  
Control Variable ◽  
Three Dimensional ◽  
Atmospheric Modeling ◽  
Variational Data Assimilation ◽  
Regional Atmospheric Modeling ◽  
The Impact ◽  
Data Assimilation System ◽  
Assimilation System

A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Prediction (NCEP) Eta 4DVAR system, however with added improvements addressing its use in a research environment. Preliminary results with RAMDAS are presented, focusing on the minimization performance and the impact of vertical correlations in error covariance modeling. A three-dimensional formulation of the background error correlation is introduced and evaluated. The Hessian preconditioning is revisited, and an alternate algebraic formulation is presented. The results indicate a robust minimization performance.

scholarly journals Analysis and Forecast of a Tornadic Thunderstorm Using Multiple Doppler Radar Data, 3DVAR, and ARPS Model

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Edward Natenberg ◽  
Jidong Gao ◽  
Ming Xue ◽  
Frederick H. Carr
Keyword(s):  
Doppler Radar ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Radar Data ◽  
Advanced Regional Prediction System ◽  
Regional Prediction ◽  
Upper Level ◽  
Using Data ◽  
Nwp Model ◽  
The Impact

A three-dimensional variational (3DVAR) assimilation technique developed for a convective-scale NWP model—advanced regional prediction system (ARPS)—is used to analyze the 8 May 2003, Moore/Midwest City, Oklahoma tornadic supercell thunderstorm. Previous studies on this case used only one or two radars that are very close to this storm. However, three other radars observed the upper-level part of the storm. Because these three radars are located far away from the targeted storm, they were overlooked by previous studies. High-frequency intermittent 3DVAR analyses are performed using the data from five radars that together provide a more complete picture of this storm. The analyses capture a well-defined mesocyclone in the midlevels and the wind circulation associated with a hook-shaped echo. The analyses produced through this technique are used as initial conditions for a 40-minute storm-scale forecast. The impact of multiple radars on a short-term NWP forecast is most evident when compared to forecasts using data from only one and two radars. The use of all radars provides the best forecast in which a strong low-level mesocyclone develops and tracks in close proximity to the actual tornado damage path.

The Analysis of a Simplified 2R Pseudo-Rigid-Body Model with Moment Load

2012 ◽  
Vol 224 ◽  
pp. 18-23
Author(s):  
Yun Jiao Zhang ◽  
Guo Wu Wei ◽  
Jian Sheng Dai
Keyword(s):  
Rigid Body ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Body Model ◽  
Design Variables ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Moment Load

Pseudo-rigid-body model (PRBM) method, which simplifies the geometrical nonlinear analysis, has become an important tool for the analysis and synthesis of compliant mechanisms. In this paper, a simplified 2R PRBM with two rigid links and two torsion springs is proposed. The characteristic radius factor and stiffness coefficients are selected as the design variables; in order to be better to simulate the tip point and tip slope, a three-dimensional objective function is formulated to optimize the new pseudo-rigid-body model. It is revealed in this paper that the precision of the tip point simulation can be improved when the coefficient of the tip slope error in the objective function is reduced.

scholarly journals Thermal Analysis of 3D Electromagnetic Radiative Nanofluid Flow with Suction/Blowing: Darcy–Forchheimer Scheme

Micromachines ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1395
Author(s):  
Hammad Alotaibi ◽  
Mohamed R. Eid
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Melt Spinning ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Brownian Diffusion ◽  
Force Coefficient ◽  
Catalytic Reactors ◽  
Nanofluid Flow ◽  
The Impact

This paper discusses the Darcy–Forchheimer three dimensional (3D) flow of a permeable nanofluid through a convectively heated porous extending surface under the influences of the magnetic field and nonlinear radiation. The higher-order chemical reactions with activation energy and heat source (sink) impacts are considered. We integrate the nanofluid model by using Brownian diffusion and thermophoresis. To convert PDEs (partial differential equations) into non-linear ODEs (ordinary differential equations), an effective, self-similar transformation is used. With the fourth–fifth order Runge–Kutta–Fehlberg (RKF45) approach using the shooting technique, the consequent differential system set is numerically solved. The influence of dimensionless parameters on velocity, temperature, and nanoparticle volume fraction profiles is revealed via graphs. Results of nanofluid flow and heat as well as the convective heat transport coefficient, drag force coefficient, and Nusselt and Sherwood numbers under the impact of the studied parameters are discussed and presented through graphs and tables. Numerical simulations show that the increment in activation energy and the order of the chemical reaction boosts the concentration, and the reverse happens with thermal radiation. Applications of such attractive nanofluids include plastic and rubber sheet production, oil production, metalworking processes such as hot rolling, water in reservoirs, melt spinning as a metal forming technique, elastic polymer substances, heat exchangers, emollient production, paints, catalytic reactors, and glass fiber production.

scholarly journals The Impact of Airborne Doppler Aerosol Wind (DAWN) Lidar Wind Profiles on Numerical Simulations of Tropical Convective Systems during the NASA Convective Processes Experiment (CPEX)

2020 ◽  
Vol 37 (4) ◽  
pp. 705-722 ◽  
Author(s):  
Zhiqiang Cui ◽  
Zhaoxia Pu ◽  
G. David Emmitt ◽  
Steven Greco
Keyword(s):  
Data Assimilation ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Tropical Storm ◽  
Convective System ◽  
Spatiotemporal Resolution ◽  
Convective Systems ◽  
Convective Processes ◽  
Wind Profiles ◽  
The Impact

AbstractHigh-spatiotemporal-resolution airborne Doppler Aerosol Wind (DAWN) lidar profiles over the Caribbean Sea and Gulf of Mexico region were collected during the NASA Convective Processes Experiment (CPEX) field campaign from 27 May to 24 June 2017. This study examines the impact of assimilating these wind profiles on the numerical simulation of moist convective systems using an Advanced Research version of the Weather Research and Forecasting (WRF) Model (WRF-ARW). A mesoscale convective system and a tropical storm (Cindy) that occurred on 16 June 2017 in a strong shear environment and on 21 June 2017 in a weak shear environment, respectively, are selected as case studies. The DAWN wind profiles are assimilated with the NCEP Gridpoint Statistical Interpolation analysis system using a three-dimensional variational (3DVar) and a hybrid three-dimensional ensemble-variational (3DEnVar) data assimilation systems to provide the initial conditions for a short-range forecast. Results show that the assimilation of DAWN wind profiles has significant positive impacts on convective simulations with the two assimilation approaches. The assimilation of DAWN wind profiles creates notable adjustments in the analysis of the divergence field for WRF simulations with a good agreement of wind forecasts with radiosonde observations. The quantitative precipitation forecasting is also improved. In general, the 3DEnVar data assimilation method is deemed more promising for DAWN data assimilation. There are cases with Tropical Storm Cindy in which DAWN data have slight to neutral impact on rainfall forecasts with 3DVAR, implying complicated interactions between errors of retrieved wind data and background error covariance in the lower and upper troposphere.

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