Effective use of the Fourier series boundary element method ͑FBEM͒ for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general.

The subject of this paper is the development and assessment of a new nonlinear parametric identification method for dynamic systems using periodic equilibrium states or outputs. The method consists of a modified Bayesian point estimation technique which can be used in combination with a time discretization method or a shooting method to obtain the periodic equilibrium states. It is assumed that the specific excited and measured periodic solution can be computed directly from a static initial guess. An important feature of this estimator is the possibility to estimate the best parameters based on all experiments of the complete experimental set-up. The choice of using periodic states appears to be computationally efficient compared to using transient states. The new method is applied to multiple sets of nonlinear shaker-test measurements of a uniaxially loaded F-16 nose landing gear damper, for which a standard 1 dof mechanical model and a more comprehensive 2 dof thermo-mechanical model are postulated. Finally, the predictive power of the method is assessed by comparison of predictions for a transient drop-test load case of the 'best' 2 dof model with corresponding parameters and real drop-test measurements.

Abstract. The subject of this paper is the development of a nonlinear parametric identification method using chaotic data. In former research, the main problem in using chaotic data in parameter estimation appeared to be the numerical computation of the chaotic trajectories. This computational problem is due to the highly unstable character of the chaotic orbits. The method proposed in this paper is based on assumed physical models and has two important components. Firstly, the chaotic time series is characterized by a 'skeleton' of unstable periodic orbits. Secondly, these unstable periodic orbits are used as the input information for a nonlinear parametric identification method using periodic data. As a consequence, problems concerning the numerical computation of chaotic trajectories are avoided. The identifiability of the system is optimized by using the structure of the phase space instead of a single physical trajectory in the estimation process. Furthermore, before starting the estimation process, a huge data reduction has been accomplished by extracting the unstable periodic orbits from the long chaotic time series. The method is validated by application to a parametrically excited pendulum, which is an experimental nonlinear dynamical system in which transient chaos occurs.

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