Search results for "Euler"
showing 10 items of 159 documents
Forces and flow structures evolution on a car body in a sudden crosswind
2014
A vehicle driver is commonly exposed to strong side air flows, for example when passing through a wind gust. The aerodynamic efforts generated in these situations may induce undesired lateral deviations, which can lead to dramatic effects, if the driver is surprised. In order to simulate a sudden yaw angle change on a moving vehicle, a double wind tunnel facility, adapted from the one of Ryan, Dominy, 2000. Wake Surveys Behind a Passenger Car Subjected to a Transient Cross-wind Gust. SAE Technical Paper No. 2000-01-0874 is developed. Two Windsor car body models, differing from their rear geometry, are analysed. The transient evolution of the side force and yaw moment aerodynamic coefficient…
Expected principal stress directions under multiaxial random loading. Part II: Numerical simulation and experimental assessment through the weight fu…
1999
In Part I of the present work, the theoretical aspects of a proposed procedure to determine the expected principal stress directions under multiaxial random loading have been discussed. This procedure consists of averaging the instantaneous values of the three Euler angles through weight functions. In Part II here, a numerical simulation is presented to illustrate the above theoretical method. As an example, the algorithm proposed is applied to some experimental biaxial in- and out-of-phase stress states to assess the correlation between the expected principal stress directions and the position of the experimental fatigue fracture plane for such tests.
On Detection of Yaw and Roll Angle Information for Vehicle Oblique Crash using Hough Transform
2014
When performing vehicle crash tests, it is common to capture high frame rate video (HFR) to observe the vehicle motion during the impact. Such videos contain a lot of information, especially when it comes to geometric data. The yaw and roll angles from the HFR video is detected by using the Hough Transform and Matlab's Image processing Toolbox. The measured Yaw angle from the HFR video are compared with real life test data captured with a gyroscopic device inside the vehicle during the oblique vehicle impact.
Reduction of parameters in failure criteria for multiaxial Random Fatigue
1990
In the paper some equivalent methods of determining the expected fatigue fracture plane position have been presented. These methods make use of elements of a full linear rotation group. Replacing nine direction cosines, mutually related, by three Euler angles we obtain a reduced number of parameters used for the description of the excepted fatigue fracture plane position. New mathematical forms of the fatigue criteria with a reduced number of independent parameters have been presented well.
Critical Fracture Plane Under Multiaxial Random Loading by Means of Euler Angles Averaging
1999
ABSTRACT Several authors have experimentally observed that the position of the fatigue fracture plane strongly depends on the directions of the principal stresses or strains. The expected principal stress directions under multiaxial random loading are obtained herein by averaging the instantaneous values of the three Euler angles through some suitable weight functions, in order to take into account the main factors influencing the fatigue fracture behaviour. Then the correlation between such theoretical principal directions and the experimental fracture plane is examined for some biaxial random fatigue tests.
On the statistics of pairs of logarithms of integers
2022
We study the statistics of pairs of logarithms of positive integers at various scalings, either with trivial weights or with weights given by the Euler function, proving the existence of pair correlation functions. We prove that at the linear scaling, which is not the usual scaling by the inverse of the average gap, the pair correlations exhibit a level repulsion similar to radial distribution functions of fluids. We prove total loss of mass phenomena at superlinear scalings, and constant nonzero asymptotic behavior at sublinear scalings. The case of Euler weights has applications to the pair correlation of the lengths of common perpendicular geodesic arcs from the maximal Margulis cusp nei…
An application of the arithmetic euler function to the construction of nonclassical states of a quantum harmonic oscillator
2001
Abstract All quantum superpositions of two equal intensity coherent states exhibiting infinitely many zeros in their Fock distributions are explicitly constructed and studied. Our approach is based on results from number theory and, in particular, on the properties of arithmetic Euler function. The nonclassical nature of these states is briefly pointed out. Some interesting properties are brought to light.
Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral
2014
A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…
MAST solution of advection problems in irrotational flow fields
2007
Abstract A new numerical–analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the so…