On the forced response of multi-layered systems using the modified wave finite element method

International audienceIn this paper, the forced response of multi-layered elastic waveguides is addressed. The formalism uses global wave modes as a projection basis. These global modes are numerically constructed from the local wave modes of the layers within the framework of the modified wave finite element (MWFE) method. The method uses a dynamic substructuring scheme which allows the dynamics of each layer cross-section to be projected onto a reduced local wave mode basis with appropriate dimension. The MWFE method is used to predict the forced response of multi-layered systems. The convergence of the model with regard to the size of the wave mode basis is discussed. Numerical simulations and comparisons with standard techniques show the pertinence of the model

A wave finite element-based formulation for computing the forced response of structures involving rectangular flat shells

International audienceThe harmonic forced response of structures involving several noncoplanar rectangular flat shells is investigated by using the Wave Finite Element method. Such flat shells are connected along parallel edges where external excitation sources as well as mechanical impedances are likely to occur. Also, they can be connected to one or several coupling elements whose shapes and dynamics can be complex. The dynamic behavior of the connected shells is described by means of numerical wave modes traveling towards and away from the coupling interfaces. Also, the coupling elements are modeled by using the conventional finite element (FE) method. A FE mesh tying procedure between shells having incompatible meshes is considered, which uses Lagrange multipliers for expressing the coupling conditions in wave-based form. A global wave-based matrix formulation is proposed for computing the amplitudes of the wave modes traveling along the shells. The resulting displacement solutions are obtained by using a wave mode expansion procedure. The accuracy of the wave-based matrix formulation is highlighted in comparison with the conventional FE method through three test cases of variable complexities. The relevance of the method for saving large CPU times is emphasized. Its efficiency is also highlighted in comparison with the component mode synthesis technique

A recursive approach for the finite element computation of waveguides

The finite element computation of structures such as waveguides can lead to heavy computations when the length of the structure is large compared to the wavelength. Such waveguides can in fact be seen as one-dimensional periodic structures. In this paper a simple recursive method is presented to compute the global dynamic stiffness matrix of finite periodic structures. This allows to get frequency response functions with a small amount of computations. Examples are presented to show that the computing time is of order $\log_2 N$ where $N$ is the number of periods of the waveguide

A wave-based reduction technique for the dynamic behavior of periodic structures

International audienceThe wave finite element (WFE) method is investigated to describe the dynamic behavior of periodic structures like those composed of arbitrary-shaped substructures along a certain straight direction. A generalized eigenproblem based on the so-called S + S −1 transformation is proposed for accurately computing the wave modes which travel in right and left directions along those periodic structures. Besides, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two extra substructures. In doing so, a few wave modes are only required for modeling the central periodic structure. A comprehensive validation of the technique is performed on a 2D periodic structure. Also, its efficiency in terms of CPU time savings is highlighted regarding a 3D periodic structure that exhibits substructures with large-sized FE models

New advances in the forced response computation of periodic structures using the wave finite element (WFE) method

International audienceThe wave finite element (WFE) method is investigated to describe the harmonic forced response of onedimensional periodic structures like those composed of complex substructures and encountered in engineering applications. The dynamic behavior of these periodic structures is analyzed over wide frequency bands where complex spatial dynamics, inside the substructures, are likely to occur.Within theWFE framework, the dynamic behavior of periodic structures is described in terms of numerical wave modes. Their computation follows from the consideration of the finite element model of a substructure that involves a large number of internal degrees of freedom. Some rules of thumb of the WFE method are highlighted and discussed to circumvent numerical issues like ill-conditioning and instabilities. It is shown for instance that an exact analytic relation needs to be considered to enforce the coherence between positive-going and negative-going wave modes. Besides, a strategy is proposed to interpolate the frequency response functions of periodic structures at a reduced number of discrete frequencies. This strategy is proposed to tackle the problem of large CPU times involved when the wave modes are to be computed many times. An error indicator is formulated which provides a good estimation of the level of accuracy of the interpolated solutions at intermediate points. Adaptive refinement is carried out to ensure that this error indicator remains below a certain tolerance threshold. Numerical experiments highlight the relevance of the proposed approaches

Wave Finite Element based Strategies for Computing the Acoustic Radiation of Stiffened or Non-Stiffened Rectangular Plates subject to Arbitrary Boundary Conditions

20 pagesInternational audienceThe wave finite element method (WFE) is investigated for the computation of the acoustic radiation of stiffened or non-stiffened rectangular plates under arbitrary boundary conditions. The method aims at computing the forced response of periodic waveguides (e.g. rectangular plates that are homogeneous or that contain a periodic distribution of stiffeners) using numerical wave modes. A WFE-based strategy is proposed which uses the method of elementary radiators for expressing the radiation efficiencies of stiffened or non-stiffened baffled rectangular plates immersed in a light acoustic fluid. In addition, a model reduction strategy consisting in using reduced wave bases for computing these radiation efficiencies with small CPU times is proposed. Numerical experiments highlight the relevance of the strategies

A wave-based model reduction technique for the description of the dynamic behavior of periodic structures involving arbitrary-shaped substructures and large-sized finite element models

International audienceThe wave finite element (WFE) method is investigated to describe the dynamic behavior of periodic structures like those composed of arbitrary-shaped substruc-tures along a certain straight direction. Emphasis is placed on the analysis of non-academic substructures that are described by means of large-sized finite element (FE) models. A generalized eigenproblem based on the so-called S + S −1 transformation is proposed for accurately computing the wave modes which travel in right and left directions along those periodic structures. Besides, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two extra substructures. In doing so, a few wave modes are only required for modeling the central periodic structure. An error indicator is also proposed to determine in an a priori process the number of those wave modes that need to be considered. Their computation hence follows by considering the Lanczos method, which can be achieved in a very fast way. Numerical experiments are carried out to highlight the relevance of the proposed reduction technique. A comprehensive validation of the technique is performed on a 2D periodic structure. Also, its efficiency in terms of CPU time savings is highlighted regarding a 3D periodic structure that exhibits substructures with large-sized FE models

Interpolatory model reduction for component mode synthesis analysis of structures involving substructures with frequency-dependent parameters

International audienceAn interpolatory model order reduction (MOR) strategy is proposed to compute the harmonic forced response of structures built up of substructures with frequency-dependent parameters. In this framework, the Craig-Bampton (CB) method is used for modeling each substructure by means of static modes and a reduced number of fixed-interface modes which are interpolated between several master frequencies. Emphasis is on the analysis of several substructures which can vibrate at different scales and, as such, do not need to be modeled with the same sets of interpolation points, depending on whether their modal density is low or high. For this purpose, an error indicator is developed to determine, through greedy algorithm procedure, the optimal number of interpolation points needed for each substructure. Additional investigations concern the selection of the fixed-interface modes which need to be retained for each substructure. Numerical experiments are carried out to highlight the relevance of the proposed approach, in terms of computational saving and accuracy

A subspace fitting method based on finite elements for fast identification of damages in vibrating mechanical systems

International audienceIn this paper, a method based on subspace fitting is proposed for identification of faults in mechanical systems. The method uses the modal information from an observability matrix, provided by a stochastic subspace identification. It is used for updating a Finite Element Model through the Variable Projection algorithm. Experimental example aims to demonstrate the ability and the efficiency of the method for diagnosis of structural faults in a mechanical system

A Subspace Fitting Method based on Finite Elements for Identification and Localization of Damage in Mechanical Systems

International audienceIn this work, a subspace fitting method based on finite elements for identification of modal parameters of a mechanical system is proposed. The technique uses prior knowledge resulting from a coarse finite element model (FEM) of the structure. The proposed technique is applied to identify the parameters of several mechanical systems under deterministic and stochastic excitations. Numerical experiments highlight the relevance of the technique compared to the conventional identification techniques. Identification, localization and estimation of severity of damages are carried out