Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Jennifer A. Franck ◽  
Janet Blume ◽  
Joseph J. Crisco ◽  
Christian Franck
Keyword(s):  
Rotational Velocity ◽  
Equations Of Motion ◽  
Accurate Solution ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Accelerometer Data ◽  
Accurate Analysis ◽  
Centripetal Acceleration ◽  
The Impact ◽  
Acceleration Term

Sports-related concussions are of significant concern in many impact sports, and their detection relies on accurate measurements of the head kinematics during impact. Among the most prevalent recording technologies are videography, and more recently, the use of single-axis accelerometers mounted in a helmet, such as the HIT system. Successful extraction of the linear and angular impact accelerations depends on an accurate analysis methodology governed by the equations of motion. Current algorithms are able to estimate the magnitude of acceleration and hit location, but make assumptions about the hit orientation and are often limited in the position and/or orientation of the accelerometers. The newly formulated algorithm presented in this manuscript accurately extracts the full linear and rotational acceleration vectors from a broad arrangement of six single-axis accelerometers directly from the governing set of kinematic equations. The new formulation linearizes the nonlinear centripetal acceleration term with a finite-difference approximation and provides a fast and accurate solution for all six components of acceleration over long time periods (>250 ms). The approximation of the nonlinear centripetal acceleration term provides an accurate computation of the rotational velocity as a function of time and allows for reconstruction of a multiple-impact signal. Furthermore, the algorithm determines the impact location and orientation and can distinguish between glancing, high rotational velocity impacts, or direct impacts through the center of mass. Results are shown for ten simulated impact locations on a headform geometry computed with three different accelerometer configurations in varying degrees of signal noise. Since the algorithm does not require simplifications of the actual impacted geometry, the impact vector, or a specific arrangement of accelerometer orientations, it can be easily applied to many impact investigations in which accurate kinematics need to be extracted from single-axis accelerometer data.

A parameter-uniform finite difference scheme for singularly perturbed parabolic problem with two small parameters

2021 ◽  
Author(s):  
Tesfaye Aga Bullo ◽  
Guy Aymard Degla ◽  
Gemechis File Duressa
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Variable Parameter ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Finite Difference Approximation ◽  
Parabolic Problems ◽  
Difference Approximation ◽  
Uniform Mesh

A parameter-uniform finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with two parameters. The solution involves boundary layers at both the left and right ends of the solution domain. A numerical algorithm is formulated based on uniform mesh finite difference approximation for time variable and appropriate piecewise uniform mesh for the spatial variable. Parameter-uniform error bounds are established for both theoretical and experimental results and observed that the scheme is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods existing in the literature.   

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

Computational Study On Skin Tissue Freezing Using Three Phase Lag Bioheat Model

2021 ◽  
Author(s):  
Rohit Verma ◽  
Sushil Kumar
Keyword(s):  
Phase Change ◽  
Computational Study ◽  
Time Derivative ◽  
Finite Difference Approximation ◽  
Skin Tissue ◽  
Difference Approximation ◽  
Freezing Process ◽  
Phase Lag ◽  
Three Phase ◽  
The Impact

Abstract This paper considers the three-phase lag (TPL) bioheat model, to study the phase change phenomena in skin tissue during cryosurgery. The considered TPL model is based on the model of thermoelasticity, i.e., the combination of the rate of thermal conductivity and new phase lag $\left( {{\tau _v}} \right)$ due to thermal displacement. We establish an effective heat capacity based numerical algorithm to solve the non-linear governing equation for biological tissue freezing. We use radial basis functions (RBFs) and finite difference approximation for space and time derivative, respectively. We study the impact of three non-classical models, single-phase change (SPL), dual-phase lag (DPL), and triple-phase lag (TPL) on the freezing process. The effects of phase lags involved in the models on freezing are also the part of this study.

scholarly journals Investigation of thermal behavior and fluid motion in DC magnetohydrodynamic pumps

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 551-562 ◽  
Author(s):  
Mehdi Kiyasatfar ◽  
Nader Pourmahmoud ◽  
Maqsood Golzan ◽  
Iraj Mirzaee
Keyword(s):  
Thermal Behavior ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Finite Difference Approximation ◽  
Entropy Generation Rate ◽  
Difference Approximation ◽  
Magnetic Flux Density ◽  
Working Medium

Motivated by increasingly being used MHD micropumps for pumping biological and chemical specimens, this study presents a simplified MHD flow model based upon steady state, incompressible and fully developed laminar flow theory in rectangular channel to offer the characteristics of MHD pumps for prediction of pumping performance in MHD flow. The nonlinear governing equations of motion and energy including viscous and Joule dissipation are solved numerically for velocity and temperature distributions. To aim this goal a finite difference approximation based code is developed and utilized. In addition, the effects of magnetic flux density, applied electric current and channel size on flow velocity field as well as thermal behavior are investigated in various working medium with different physical properties. Also the entropy generation rate is discussed. The simulation results are in good agreement with experimental data from literature.

scholarly journals Quartic Non-Polynomial Spline Method for Singularly Perturbed Differential-difference Equation with Two Parameters

2021 ◽  
pp. 9-15
Author(s):  
Gemadi Roba Kusi ◽  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa
Keyword(s):  
Difference Equation ◽  
Polynomial Spline ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Spline Method ◽  
Numerical Experimentation ◽  
Differential Difference Equation ◽  
Two Parameters

Quartic non-polynomial spline method is presented to solve the singularly perturbed differential-difference equation containing two parameters. The considered equation is transformed into an asymptotical equivalent differential equation, and the derivatives are replaced finite difference approximation using the quartic non-polynomial spline method. The convergence analysis of the method has been established. Numerical experimentation is carried out on model examples, and the results are presented both in tables and graphs. Furthermore, the present method gives a more accurate solution than some existing methods reported in the literature.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals Nonlocal and Size-Dependent Dielectric Function for Plasmonic Nanoparticles

2019 ◽  
Vol 9 (15) ◽  
pp. 3083
Author(s):  
Kai-Jian Huang ◽  
Shui-Jie Qin ◽  
Zheng-Ping Zhang ◽  
Zhao Ding ◽  
Zhong-Chen Bai
Keyword(s):  
Metallic Nanoparticles ◽  
High Efficiency ◽  
Finite Size ◽  
Plasmonic Nanostructures ◽  
Accurate Analysis ◽  
Finite Size Effects ◽  
Size Dependent ◽  
Quantum Size ◽  
The Impact ◽  
Electron Energy Loss

We develop a theoretical approach to investigate the impact that nonlocal and finite-size effects have on the dielectric response of plasmonic nanostructures. Through simulations, comprehensive comparisons of the electron energy loss spectroscopy (EELS) and the optical performance are discussed for a gold spherical dimer system in terms of different dielectric models. Our study offers a paradigm of high efficiency compatible dielectric theoretical framework for accounting the metallic nanoparticles behavior combining local, nonlocal and size-dependent effects in broader energy and size ranges. The results of accurate analysis and simulation for these effects unveil the weight and the evolution of both surface and bulk plasmons vibrational mechanisms, which are important for further understanding the electrodynamics properties of structures at the nanoscale. Particularly, our method can be extended to other plasmonic nanostructures where quantum-size or strongly interacting effects are likely to play an important role.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

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