PAMM
It is well known that one of the most time consuming problem in non‐destructive evaluation (NDE) is the near‐field modeling. In our approach the near field radiated by an ultrasonic transducer (UT) to the first Fresnel zone is approximated in the frequency domain by a closed form asymptotic solution based on the 3‐D generalized orthogonality conditions of Lamb waves and on the stationary phase method...
In nondestructive testing, the use of ultrasonic elastic waves has proven as one of the most successful techniques to detect structural damage such as cracks or delaminations. Especially, Structural Health Monitoring (SHM) is characterized by permanently installed actuators and sensors. As the capability of most approaches strongly depends on adequate choice of parameters like excitation signals and...
Volume 10 (2010) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the 81st Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik, held 22 — 26 March 2010 at the Universität Karlsruhe (TH), Germany.The contributions are grouped according to the minisymposia and sessions of the conference.
Overview of the SectionsMinisymposia MathematicsMa2...
Unterschiede zwischen Haft‐ und Gleitreibkräften führen zu dynamischen Anregungen. Insbesondere Losbrechkräfte von Dichtungen in Stoßdämpfern, Kupplungen, Lenk‐ und Bremssystemen verursachen Probleme wie Schwingungen und Geräusche. Ziel dieser Arbeit ist die Modellierung, Simulation und experimentelle Untersuchung der Systemdynamik mit einem Schwerpunkt auf der Kontaktbeschreibung. Dabei spielt die...
Debonding in adhesive joints is modelled and analyzed with the concept of interfacial mechanics. Material equations are presented for the inelastic behaviour of ductile‐modified epoxy resins. A two surface function for the onset of yielding is advantageously expressed in terms of the stress vector on the interface. The theory may be extended to material softening due to damage and to rate dependency...
Bremsenquietschen ist ein hochfrequentes störendes Geräusch, welches auf reibungsinduzierte selbsterregte Schwingungen des Bremssystems zurückzuführen ist. Dabei verliert die nicht quietschende Konfiguration ihre Stabilität, das Bremssystem beginnt mit wachsenden Amplituden zu schwingen und erreicht schließlich einen Grenzzykel. Bei der mechanisch‐mathematischen Modellbildung zur Vorhersage des Bremsenquietschens...
Based on analytical considerations about how near‐wall turbulence needs to be modified in order to reduce the momentum loss towards solid walls and to yield lower energy losses, a mechanism of turbulent drag reduction is proposed. This mechanism suggests that drag reducing flow control at high Reynolds numbers should be designed to minimize the turbulent dissipation rate. A previously published approach...
The emphasis of this work lies in the development of a numerical method which is capable of representing the complex physical phenomena arising in the case of crack branching in brittle materials. In particular, the formation of crack micro‐branches needs to be accounted for when it comes to the prediction of the propagation pattern of crack macro‐branches which will ultimately lead to the failure...
The macroscopic mechanical behavior of multi‐phasic materials depends on the formation and evolution of their microstructure by means of phase transformation. In case of martensitic transformations, the resulting phase boundaries are sharp interfaces. We carry out a geometrically motivated discussion of the regularization of such sharp interfaces by use of an order parameter/phase‐field and exploit...
We consider four‐dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2‐regularisation, a widely used method for solving ill‐posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1‐norm regularisation, recovers sharp edges better than L2‐norm regularisation. We apply this idea...
In 2004, a gyro with cardanic suspension was recovered in the physical collection of a school in Tübingen, Germany. Up to now, this instrument seems to be the only original corresponding explicitly with the first systematic explanation of such an apparatus. This description dates back to 1817 and was written by the inventor J.G.F. Bohnenberger (1765‐1831), who called the device simply Machine. At...
In this paper a two‐dimensional discrete element method with rigid, polygonal particles is used to model material failure of granular as well as quasi‐brittle materials. Different models for soft contact as well as cohesion between the particles are presented. The capabilities of the method are demonstrated simulating simplistic granular model materials as well as complex concrete specimens with an...
The eigenvalues of the self‐adjoint Schrödinger operators on a bounded domain with Dirichlet and Neumann boundary conditions are characterized by the singularities of an associated Dirichlet‐to‐Neumann map and its inverse, respectively. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by diffusive crack modeling, based on the introduction of a crack phase field as outlined in [1, 2]. Following these formulations, we outline a thermodynamically consistent framework for phase field models of crack...
We discuss the numerical solution of positive Differential‐Algebraic‐Equations (DAEs). For Ordinary Differential Equations (ODEs) where the system matrix is a ‐M‐Matrix, Runge‐Kutta‐ or Multistep‐Method are positive if the stepsize is chosen within the absolutely monotonicity radius of the considered method. We extend this concept to matrix pairs and present conditions for positivity preserving discretizations...
Collaborating multi‐agent systems can handle complex tasks with several or changing mission objectives. We developed a potential field method that allows various information layers to influence the control over a group of vehicles. The gradient of the potential field is the driving force for local action, whereas the global waypoint is determined by the minimum of the agent's potential field. The...
In this paper, we propose a projection technique for model order reduction of discrete‐time bilinear control systems based on the concept of so‐called multimoments. We will make use of an explicit solution formula of the system and consider its Z‐transform which allows us to characterize the system output by generalized transfer functions. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Iterative learning control is used to find input signals which match a previously generated output trajectory by repetitively correcting the inputs through the tracking errors. Using causal learning operators this only works up to a relative degree of one. We overcome this restriction with an anti‐causal approach following [1] and show a practical implementation in the state‐space with some examples...
The paper proposes a method for simultaneous measurements of the material conductivity and its surface roughness for non‐ferromagnetic materials. The method takes advantage of the effect exercised by eddy currents onto impedance of a contact coil. The essence of the method is to eliminate the influence of the surface unevenness onto measurements of conductivity by the calculation of a correcting factor...
A tracking control problem for systems in state representation possessing a Lie symmetry group G is considered. By designing an invariant feedback control law based on invariant tracking errors the symmetry group G can be preserved under feedback. An extension of this approach to the popular integrator backstepping design method is presented. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)