scholarly journals Mathematical Modelling of Biomechanical Interactions between Backpack and Bearer during Load Carriage

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Lei Ren ◽  
David Howard ◽  
Richard K. Jones
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Measurement Data ◽  
Load Carriage ◽  
Human Gait ◽  
Test Rig ◽  
Interaction Forces ◽  
Suspension Model

This paper proposes a three-dimensional mathematical model of the biomechanical interactions between backpack and bearer during load carriage. The model considers both the coupled pack motions, which follow the torso, and also the longitudinal compliance and damping in the backpack suspension. The pack interaction forces and moments, acting on the bearer, are determined from kinematic relationships, equations of motion, and a dynamic pack suspension model. The parameters of the pack suspension model were identified from test data obtained using a load carriage test rig. Output from the load carriage mathematical model has been compared with measurement data during human gait and conclusions drawn with regard to the validity of the proposed approach.

scholarly journals A Mathematical Model for Forced Vibration of Pre-Stressed Piezoelectric Plate-Strip Resting On Rigid Foundation

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 419-431
Author(s):  
Ahmet Daşdemir
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Initial Stress ◽  
Piezoelectric Plate ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Foundation ◽  
Time Harmonic ◽  
Governing System ◽  
Plate Strip

A mathematical model to investigate the dynamic response of a piezoelectric plate-strip with initial stress under the action of a time-harmonic force resting on a rigid foundation is presented within the scope of the three-dimensional linearized theory of electro-elasticity waves in initially stressed bodies (TLTEEWISB). The governing system of equations of motion is solved by employing the Finite Element Method (FEM). The numerical results illustrating the dependencies of different problem parameters are investigated. In particular, the influence of a change in the value of the initial stress parameter on the dynamic response of the plate-strip is discussed.

A Three-Dimensional Transient Thermal Model for Machining

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Coskun Islam ◽  
Ismail Lazoglu ◽  
Yusuf Altintas
Keyword(s):  
Mathematical Model ◽  
Thermal Model ◽  
Three Dimensional ◽  
Measurement Data ◽  
Time Discretization ◽  
Temperature Fields ◽  
Implicit Time ◽  
Machining Processes ◽  
Transient Thermal ◽  
Interrupted Turning

This article presents an enhanced mathematical model for transient thermal analysis in machining processes. The proposed mathematical model is able to simulate transient tool, workpiece, and chip temperature fields as a function of time for interrupted processes with time varying chip loads such as milling and continuous machining processes such as turning and drilling. A finite difference technique with implicit time discretization is used for the solution of partial differential equations to simulate the temperature fields on the tool, workpiece, and chip. The model validations are performed with the experimental temperature measurement data available in the literature for the interrupted turning of Ti6Al6V–2Sn, Al2024, gray cast iron and for the milling of Ti6Al4V. The simulation results and experimental measurements agree well. With the newly introduced modeling approach, it is demonstrated that time-dependent dynamic variations of the temperature fields are predicted with maximum 12% difference in the validated cases by the proposed transient thermal model.

Mathematical model of an inadvertent stall

2018 ◽  
Vol 123 ◽  
pp. 111-120
Author(s):  
Patrycja Pacak
Keyword(s):  
Mathematical Model ◽  
Safety Concern ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Loss Of Control ◽  
Flight Phase ◽  
Rigid Plane ◽  
Basic Equations ◽  
Aircraft Accident ◽  
The Mathematical Model

This paper contains the mathematical model of an inadvertent stall as the incipient phase of a spin. Some further simplifications were included. Representation of a rigid plane was modeled as the three-dimensional movement of center of gravity. The equations of motion were presented, as well as the basic equations for the LLT method. The aerodynamic stall as the specific flight phase and the Loss of Control in Flight cause of aircraft accident sets the global safety concern that needs further actions. The created mathematical model shall be used for creating simulation algorithms for an inadvertent stall.

Design, Validation and Application of a Radial Cascade for Centrifugal Compressors

2008 ◽  
Author(s):  
Alexander Simpson ◽  
Christian Aalburg ◽  
Michael Schmitz ◽  
Robbert Pannekeet ◽  
Florian Larisch ◽  
...  
Keyword(s):  
Design Space ◽  
Three Dimensional ◽  
Measurement Data ◽  
Test Results ◽  
Pressure Loading ◽  
Test Rig ◽  
Three Dimensional Flow ◽  
Blow Down ◽  
Operation Conditions ◽  
Flow Pressure

A novel sector test rig has been used to evaluate a new airfoil concept for multistage radial compressors. The test rig is supported by a blow-down facility where the operation conditions are adjusted by controlling mass flow, pressure and temperature. At inlet to the sector test rig itself a set of adjustable inlet guide vanes provide the test vanes with the correct inlet three-dimensional flow-field. The rig is equipped with instrumentation to allow a detailed description of the inlet and outlet conditions, as well as the blade pressure loading. This rig, using rapid prototyped vanes, allows design candidates to be screened quickly and is ideal for conducting an experimental investigation of a design space using a Design-of-Experiments approach. In this paper the rationale for the sector approach is described, the design of the test rig with 3D-CFD methods is outlined and a detailed validation of the rig is presented. For the vane in question detailed investigations of different operation points close to stall are reported, blade pressures and inlet and exit flow profiles are given. Where applicable, measurement data from the sector rig was compared to 3D-CFD calculations of the full annulus multistage configuration, to 3D-CFD calculations of the sector rig itself and to the test results from a 1.5-stage rotating test rig. The measurement data are compared to the CFD predictions and served as a calibration basis for the design tools.

Experimental Validation of a Walking Model for Planar Bipeds With Curved Feet

2011 ◽  
Author(s):  
Anne E. Martin ◽  
James P. Schmiedeler
Keyword(s):  
Mathematical Model ◽  
Humanoid Robot ◽  
Experimental Validation ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Bipedal Walking ◽  
Human Gait ◽  
Bipedal Robots ◽  
Simplifying Assumptions ◽  
The Mathematical Model

Bipeds with curved feet typically require less energy for walking than do point- or flat-footed bipeds, and they tend to mimic human gait more closely. Thus, understanding the effects of curved feet on bipedal walking gaits has the potential to improve both humanoid robot efficiency and human rehabilitation. This paper derives the equations of motion for planar bipeds with curved feet under the assumption, among others, of instantaneous transfer of support between the legs. The paper then verifies the mathematical model by comparing the results of simulation to previous experimental results for two very different bipedal robots — McGeer’s two-link, passive dynamic walker traversing a decline and the five-link, actuated biped ERNIE walking on a treadmill with a supporting boom. In both cases, the results from simulation match the experimental results very well despite the simplifying assumptions, indicating that the mathematical model captures the dominate dynamics of bipedal robots with curved feet.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

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