Investigation of Damping of Vibrations in a System With Two‐Disc Inseparable Clutch

This paper presents the results of tests on free and forced harmonic torsional vibrations in a system with a two‐disc inseparable clutch, with structural friction taken into account. Nonlinear histeresis loop describing the frictional‐elastic properties of the system was introduced into the model. The mathematical model of the vibrating system containing two disks inseparable clutch was built. During free vibrations of the system, its damping characteristics were tested by a digital simulation method. The vibration damping decrement as a function of amplitude torsional displacement was determined. When vibrations were harmonically forced, the amplitude ‐ frequency characteristics of the system were determined numerically. The system was used as a nonlinear torsional vibration damper in a linear system with a harmonic force. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tuned preconditioners for inexact two‐sided inverse and Rayleigh quotient iteration

Convergence results are provided for inexact two‐sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized non‐Hermitian eigenproblem and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two‐sided methods is considered, and the successful tuning strategy for preconditioners is extended to two‐sided methods, creating a novel way of preconditioning two‐sided algorithms. Furthermore, it is shown that inexact two‐sided Rayleigh quotient iteration and the inexact two‐sided Jacobi‐Davidson method (without subspace expansion) applied to the generalized preconditioned eigenvalue problem are equivalent when a certain number of steps of a Petrov–Galerkin–Krylov method is used and when this specific tuning strategy is applied. Copyright © 2014 John Wiley & Sons, Ltd.     

Prevention of Stick‐Slip Vibrations by Passive Normal Force Control

The classical stick‐slip oscillator is extended by an additional degree of freedom which couples the slipping motion to the normal force. Using this, the effective friction force can be altered without changing the friction‐velocity characteristic. The paper deals with the optimization problem of finding parameters of the additional system that prevent stick‐slip motion or minimize the amplitude of the residual limit cycle. Another goal is to increase the decay rate of vibration. Results were achieved by numerical integration based on analytical investigations.     

Damping Functions correct over‐dissipation of the Smagorinsky Model

This paper studies the time‐averaged energy dissipation rate ?ε _{S M D} (u )? for the combination of the Smagorinsky model and damping function. The Smagorinsky model is well known to over‐damp. One common correction is to include damping functions that reduce the effects of model viscosity near walls. Mathematical analysis is given here that allows evaluation of ?ε _{S M D} (u )? for any damping function. Moreover, the analysis motivates a modified van Driest damping. It is proven that the combination of the Smagorinsky with this modified damping function does not over‐dissipate and is also consistent with Kolmogorov phenomenology. Copyright © 2017 John Wiley & Sons, Ltd.     

Vibrations of the Beam with Variable Cross‐Section Caused by Moving Stochastic Load

We present the problem of vibrations of a beam with variable geometry which are caused by stochastic moving load. The approach is based on concepts of the tolerance averaged model [4]. In this way we formulate the averaged equations of the structured beam which describe the length‐scale effect. Using the averaged equations we obtain the probabilistic characteristics of the beam with periodically variable geometry.     

Maximal Induced Matchings in Triangle‐Free Graphs

An induced matching in a graph is a set of edges whose endpoints induce a 1‐regular subgraph. It is known that every n‐vertex graph has at most  maximal induced matchings, and this bound is the best possible. We prove that every n‐vertex triangle‐free graph has at most  maximal induced matchings; this bound is attained by every disjoint union of copies of the complete bipartite graph K_{3, 3}. Our result implies that all maximal induced matchings in an n‐vertex triangle‐free graph can be listed in time , yielding the fastest known algorithm for finding a maximum induced matching in a triangle‐free graph.     

Measuring Concentrations with Laser‐Induced Thermal Acoustics

Laser‐induced thermal acoustics is used to measure non‐intrusively the concentration of a resonantly excited seed species (iodine vapor) diluted within a non‐resonantly excited species (nitrogen) by comparing the contributions from thermalization and electrostriction to the density perturbations of a density grating, which is inscribed in the fluid by two pulsed intersecting laser beams. The ratio of the characteristic density perturbation caused by thermalization to the perturbations from electrostriction is proportional to the concentration of the resonant species. The ratio is found by a least‐squares fit of a closed‐form analytical model to the data. When the importances of thermalization and electrostriction are comparable, the uncertainty for the concentration is 5%, but higher when one mechanism's contributions outweigh the other's greatly.     

4‐Coloring P6‐Free Graphs with No Induced 5‐Cycles

We show that the 4‐coloring problem can be solved in polynomial time for graphs with no induced 5‐cycle C₅ and no induced 6‐vertex path P₆     

Graphs with No Induced Five‐Vertex Path or Antipath

We prove that a graph G contains no induced ‐vertex path and no induced complement of a ‐vertex path if and only if G is obtained from 5‐cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class‐preserving operation introduced here.     

Spatial Velocity and Temperature Measurements in Non‐Isothermal Liquid Flows

A surface tension driven flow in the liquid vicinity of an air bubble on a heated wall is studied experimentally. The liquid flow caused by the temperature gradient along the surface of the bubble is termed thermocapillary convection. The surface tension force and the buoyancy force oppose one another. The measurement technique is the 3D particle tracking velocity and thermometry, 3D PTV/T, using thermochromic liquid crystals and digital image processing. The paper describes the method in some detail and presents quantitative results for different Marangoni numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simplicial Vertices in Graphs with no Induced Four‐Edge Path or Four‐Edge Antipath,and the H6‐Conjecture

Let be the class of all graphs with no induced four‐edge path or four‐edge antipath. Hayward and Nastos 6 conjectured that every prime graph in not isomorphic to the cycle of length five is either a split graph or contains a certain useful arrangement of simplicial and antisimplicial vertices. In this article, we give a counterexample to their conjecture, and prove a slightly weaker version. Additionally, applying a result of the first author and Seymour 1 we give a short proof of Fouquet's result 3 on the structure of the subclass of bull‐free graphs contained in .     

Capillary driven Oscillations of a Free Liquid Interface under Non‐Isothermal Conditions

In this study the reorientation behavior of a free liquid interface in a partly filled right circular cylinder upon a step reduction in gravity is investigated experimentally. The experiments focus on the investigation of non‐isothermal boundary conditions on the liquid reorientation. The situation is similar to a spacecraft which enters a ballistic flight after the end of thrust. Heat flux between the liquid propellant and the tank wall occurs and influences the behavior of the liquid reorientation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Triangle‐Free Graphs That Do Not Contain a Subdivision of the Complete Graph on Four Vertices as an Induced Subgraph

We prove a decomposition theorem for the class of triangle‐free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph. We prove that every graph of girth at least five in this class is 3‐colorable.