Optimization strategy for actuator and sensor placement in active structural acoustic control

In active structural acoustic control the goal is to reduce the sound radiation of a structure by means of changing the vibrational behaviour of that structure. The performance of such an active control system is to a large extent determined by the locations of the actuators and sensors. In this work an approach is presented for the optimization of the actuator and sensor locations. The approach combines a numerical modelling technique, for predicting the control performance, and genetic optimization, to find the optimal actuator and sensor locations. The approach is tested for a setup consisting of clamped rectangular plate with a piezoelectric actuator and either structural or acoustic sensors. The results show that a control system with optimal actuator and sensor configuration outperforms an arbitrary chosen configuration in terms of reduction in radiated sound power

Natural Density Distribution of Hermite Normal Forms of Integer Matrices

The Hermite Normal Form (HNF) is a canonical representation of matrices over any principal ideal domain. Over the integers, the distribution of the HNFs of randomly looking matrices is far from uniform. The aim of this article is to present an explicit computation of this distribution together with some applications. More precisely, for integer matrices whose entries are upper bounded in absolute value by a large bound, we compute the asymptotic number of such matrices whose HNF has a prescribed diagonal structure. We apply these results to the analysis of some procedures and algorithms whose dynamics depend on the HNF of randomly looking integer matrices

Nearfield Acoustic Holography using sparsity and compressive sampling principles

Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions, new regularization schemes can be developed, based on the sparsity of the normal velocity of the plate in a well-designed basis, i.e. the possibility to approximate it as a weighted sum of few elementary basis functions. In particular, these new techniques can handle discontinuities of the velocity field at the boundaries, which can be problematic with standard techniques. This comes at the cost of a higher computational complexity to solve the associated optimization problem, though it remains easily tractable with out-of-the-box software. Furthermore, this sparsity framework allows us to take advantage of the concept of Compressive Sampling: under some conditions on the sampling process (here, the design of a random array, which can be numerically and experimentally validated), it is possible to reconstruct the sparse signals with significantly less measurements (i.e., microphones) than classically required. After introducing the different concepts, this paper presents numerical and experimental results of NAH with two plate geometries, and compares the advantages and limitations of these sparsity-based techniques over standard Tikhonov regularization.Comment: Journal of the Acoustical Society of America (2012

The automatic solution of partial differential equations using a global spectral method

A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential operators and the one-dimensional ultraspherical spectral method. If a partial differential operator is of splitting rank $2$, such as the operator associated with Poisson or Helmholtz, the corresponding PDE is solved via a generalized Sylvester matrix equation, and a bivariate polynomial approximation of the solution of degree $(n_x,n_y)$ is computed in $\mathcal{O}((n_x n_y)^{3/2})$ operations. Partial differential operators of splitting rank $\geq 3$ are solved via a linear system involving a block-banded matrix in $\mathcal{O}(\min(n_x^{3} n_y,n_x n_y^{3}))$ operations. Numerical examples demonstrate the applicability of our 2D spectral method to a broad class of PDEs, which includes elliptic and dispersive time-evolution equations. The resulting PDE solver is written in MATLAB and is publicly available as part of CHEBFUN. It can resolve solutions requiring over a million degrees of freedom in under $60$ seconds. An experimental implementation in the Julia language can currently perform the same solve in $10$ seconds.Comment: 22 page

Structural Analysis and Matrix Interpetive System /SAMIS/ program Technical report, Feb. - Aug. 1966

Development of characteristic equations and error analysis for computer programs contained in structural analysis and matrix interpretive syste