The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

Charles A. Weibel - One of the best experts on this subject based on the ideXlab platform.

Keith Conrad - One of the best experts on this subject based on the ideXlab platform.

  • the mobius function and the Residue Theorem
    Journal of Number Theory, 2005
    Co-Authors: Brian Conrad, Keith Conrad
    Abstract:

    Abstract A classical conjecture of Bouniakowsky says that a non-constant irreducible polynomial in Z [ T ] has infinitely many prime values unless there is a local obstruction. Replacing Z [ T ] with κ [ u ] [ T ] , where κ is a finite field, the obvious analogue of Bouniakowsky's conjecture is false. All known counterexamples can be explained by a new obstruction, and this obstruction can be used to fix the conjecture. The situation is more subtle in characteristic 2 than in odd characteristic. Here, we illustrate the general theory for characteristic 2 in some examples.

Christian Haesemeyer - One of the best experts on this subject based on the ideXlab platform.

Wim Desmet - One of the best experts on this subject based on the ideXlab platform.

  • optimal dynamic vibration absorber design for minimizing the band averaged input power using the Residue Theorem
    Journal of Sound and Vibration, 2015
    Co-Authors: R D Amico, Bert Pluymers, Claus Claeys, Wim Desmet
    Abstract:

    Abstract This paper deals with an efficient strategy to improve the vibro-acoustic behavior of a structure over frequency bands. Genetic Algorithms are used to identify the optimal resonance frequency and location of Dynamic Vibration Absorbers (DVAs) which minimize the band-averaged input power into a plate, leading to an indirect reduction of the radiated acoustic power and global vibration. Instead of classic numerical quadrature schemes, the Residue Theorem is used to evaluate the band-averaged input power. This results into a considerable reduction of computational effort, as it requires only few function evaluations at complex frequencies, regardless of the analyzed bandwidth. The structural response is simulated by using the Wave Based Method (WBM). Besides an increased convergence rate as compared to classical element-based techniques, the WBM is also free in determining the optimal position of the DVAs, not restricting it to nodal grid locations. Moreover, when point connections are taken into account, only a small part of the WB matrices needs to be recomputed at each iteration, resulting in a strong reduction of the computation time. Numerical examples illustrate the benefits and the efficiency of the proposed optimization strategy.

  • design sensitivity analysis and optimization of frequency averaged input power using the Residue Theorem
    Computers & Structures, 2014
    Co-Authors: Roberto Damico, Bert Pluymers, Wim Desmet
    Abstract:

    The Residue Theorem is employed in the design optimization of a vibrating structure.The adjoint variable method is used for the design sensitivity computation.Numerical examples demonstrate the computational efficiency of the optimization scheme.High enhancement of the optimization process for the reduction of the radiated sound power. The Residue Theorem is employed in the design optimization of the frequency averaged power injected into a linear second-order system. The dynamic behavior of a vibrating structure is obtained with the finite element method and the frequency averaged input power into the structure is adopted as an objective function. The design sensitivity with respect to each structural element is computed by the adjoint variable method with consideration for the Residue Theorem. The proposed method highly enhances the computational efficiency of the optimization and the design of the optimization leads to substantial reduction of the radiated sound power from the structure.

  • a refined use of the Residue Theorem for the evaluation of band averaged input power into linear second order dynamic systems
    Journal of Sound and Vibration, 2014
    Co-Authors: Roberto Damico, Daan Huybrechs, Wim Desmet
    Abstract:

    Abstract In a recent work, a strategy was proposed which exploits the Residue Theorem as an efficient tool for evaluating the frequency averaged input power into vibrating systems. In this paper, such a technique is generalised and further insight and improvements are presented. Evaluating band-averages requires the solution of a weighted integral over a real frequency variable. In this paper, the integration path is moved to the complex plane, where the input mobility shows a smoother behaviour. Consequently, a smaller number of quadrature points are needed to perform an accurate integration, which leads to a significant reduction of computational time. In addition, the connection between the use of quadrature rules in the complex plane and weighting functions on real frequencies is considered. Two application examples prove the accuracy of the present strategy for different quadrature rules. Adaptive integration schemes are also investigated.

Brian Conrad - One of the best experts on this subject based on the ideXlab platform.

  • the mobius function and the Residue Theorem
    Journal of Number Theory, 2005
    Co-Authors: Brian Conrad, Keith Conrad
    Abstract:

    Abstract A classical conjecture of Bouniakowsky says that a non-constant irreducible polynomial in Z [ T ] has infinitely many prime values unless there is a local obstruction. Replacing Z [ T ] with κ [ u ] [ T ] , where κ is a finite field, the obvious analogue of Bouniakowsky's conjecture is false. All known counterexamples can be explained by a new obstruction, and this obstruction can be used to fix the conjecture. The situation is more subtle in characteristic 2 than in odd characteristic. Here, we illustrate the general theory for characteristic 2 in some examples.