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The aim of this paper is to describe the development of a reduced order model for modal analysis in a design context. The design process of most industrial systems is based on the re-utilization of certain components. Here, we propose a reduction method involving component eigenmodes to recover the modal behaviour of an assembled structure. The contribution of this work is that it uses component eigenmodes to build an interface reduction basis. Lastly, the reduction methodology proposed is compared to the Craig and Bampton method by applying it to two case studies of which one is an industrial model of an open rotor blade. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method to measure the vibrations of a 3D mechanical structure. It requires only a video sequence taken by a single camera and a Finite Element model of the structure. First, the intrinsic and extrinsic parameters of the camera are identified. Then, a collection of numerical deflection shapes and normal modes are projected in the image frame of the camera. This is done thanks to a linearization of the perspective projection model. Comparing the motion of targets seen by the camera and the motion of Finite Element model at the same location gives the time evolution of modes amplitude. Finally the motion of the model is reconstructed in 2D in the image frame and in 3D in the world frame. By following this procedure, vibration amplitude can be magnified applying a scale factor on a modal basis covering a large frequency bandwidth. • New method for 3D vibrations reconstruction with only one camera. • 3D vibrations are identified by projection on the image frame of FE eigenmodes. • Projection is done thanks to a linearization of the perspective projection. • Vibration can be magnified thanks to the scale factor of the eigenmodes. • Extension to several cameras is possible without any overlapping field of view. [ABSTRACT FROM AUTHOR]

Abstract: The operating deflection shape of a pad during squeal noise is measured on a real brake system with three-axis accelerometers. A time-frequency analysis is performed that highlights the dependency of squeal on the hydraulic pressure of the system and shows that squeal occurs simultaneously with harmonic components. The operating deflection shape of this pad before and during squeal is then visualized using interpolation, showing the predominance of bending motion. Finally, the pad motions observed are compared to the real modal basis of a detailed Finite Element model. [Copyright &y& Elsevier]

Abstract: This paper focuses on the generalized Maxwell model (GMM) identification. The formulation of the transfer function of the GMM is defined, as well as its asymptotes. To compare identification methods of the parameters of the GMM, a test transfer function and two quality indicators are defined. Then, three graphical methods are described, the enclosing curve method, the CRONE method and an original one. But the results of graphical methods are not good enough. Thus, two optimization recursive processes are described to improve the results of graphical methods. The first one is based on an unconstrained non-linear optimization algorithm and the second one is original and allows constraining identified parameters. This new process uses the asymptotes of the modulus and the phase of the transfer function of the GMM. The result of the graphical method optimized with the new process is very accurate and fast. [Copyright &y& Elsevier]

The behaviour of dynamical systems is modified by the use of viscoelastic materials. In order to lead realistic complex eigenvalues analysis on dynamical systems, one need to model the behaviour of viscoelastic materials. The experiments show that the stiffness and the damping of such materials are frequency dependent. A large number of models often used are not able to describe this dependence; this is why the generalised Maxwell's model has been chosen. This paper describes a method based on modulus and angle curves to identify the parameters of this model. Between all the different formulations of generalized Maxwell, the pole-zero formulation is the most suited to lead the identification. However, some formulas allow to find the parameters of others formulations like the Prony one. The identification method presented here is based on the asymptotic curves of generalised Maxwell's model. This identification is led in two step, first parameters are initialised and second they are optimised. This method is confronted to others ones. If several viscoelastic materials have to be modelled in the same dynamical system, the size of the finite element model grows as quick as the number of poles. A way to reduce this size consists in constraining the poles to be equal for all materials. The method presented in this paper allows to perform the identification by taking this new constraint into account. [ABSTRACT FROM AUTHOR]

This paper describes a method for the identification and the tracking of poles of a weakly nonlinear structure from its free responses. This method is based on a model of multichannel damped sines whose parameters evolve over time. Their variations are approximated in discrete time by a nonlinear state space model. States are estimated by an iterative process which couples a two-pass Bayesian smoother with an Expectation-Maximization (EM) algorithm. The method is applied on numerical and experimental cases. As a result, accurate frequency and damping estimates are obtained as a function of amplitude. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to investigate non linear dynamic behavior of viscoelastic components. The dynamic characteristics of viscoelastic components depend on frequency, amplitude, preload, and temperature. A Non Linear Generalized Maxwell Model (NLGMM), with only 4 independent parameters, is proposed. The NLGMM is based on the separation between the linear viscoelasticity and the non linear stiffness. This assumption is validated on a large range of experimental measures. The NLGMM can be used for different kinds of excitations in non linear dynamics: periodic, transient or random excitations. The non linear stiffness is represented by a simple polynomial function. Comparisons between measures and computed values have been carried on several viscoelastic samples. The NLGMM shows a good accordance with experimental results. [Copyright &y& Elsevier]

In the context of brake system simulation, the highlight of phenomenon like squeal needs specific methods. We will focus on stability analysis by complex modal analysis. The use of damping system called shims for squeal noise reduction implies that simulations take into account the damping of materials. To do this, we use parametric viscoelastic models and particularly the generalised Maxwell model. Work consisted in tools choice and validation (viscoelastic models, finite elements formulations, ...) and in simulation method implementation. It was divided in several steps. In a first step, we have selected, among several mathematical models able to describe viscoelasticity, the best for damping modelisation in brake systems. We studied the complex modulus model, the Kelvin-Voigt model and the generalised Maxwell model. In a second step, we sought a formulation of the finite element problem adapted to the modal analysis. We then used a state space model formulation. A capital hypothesis on the equality of the pole of the generalised Maxwell model permits to reduce the size of the model and in the same time to simplify its formulation. Finally, the developed methods have been applied to simulate a pad and a full brake system. The influence of the number of modes used in model reduction and the order of the Maxwell model has been quantified in parametric studies. In the pad case, we performed a complex modal analysis with friction material considered as viscoelastic. The objective was to update the pad frequencies and damping according to FRF measures. In the brake case, we performed a complex modal analysis with the two friction materials and one shim considered as viscoelastic. This model has also been used to exhibit the link between the strain energy distribution in the brake and the damping level obtained by complex modal analysis. To conclude, we developed a simulation method using Abaqus® and Matlab® for the complex modal analysis with viscoelasticity effects and Python to make data exchange between Abaqus® and Matlab® possible. This method permits to perform stability analysis with several viscoelastic materials, on large models, without degradation of computation time. [ABSTRACT FROM AUTHOR]