José Maria Campos dos Santos

Damage Detection in an Energy Flow Model Including Parameter Uncertainty

Structural energy dissipation pattern is modified by the presence of discontinuities like a crack. Crack nucleation and growth reduces the structural stiffness which makes this effect useful as a damage indicator. Computational models have become the main tool for understanding the behavior of complex structures when experimental evaluation can be difficult to perform. However, many of this classical numerical analysis assumes a deterministic model and almost nothing is understood about the effect of uncertainty in the parameters, external forces and boundary conditions. This work presents a study about the energy flow patterns caused by localized damage in structures like rod, including uncertainties in a geometric parameter. The problem is solved in two steps. First, the structure is modeled by the Spectral Element Method (SEM). The mean and variance of displacement responses are obtained by using the Polynomial Chaos (PC) expansion. In PC the stochastic solutions are expanded as orthogonal polynomials of the input random parameters. Second, by using the displacements obtained in the step before, the mean and variance of energies are calculated by applying the expectation into the equations of energy density and energy flow. However, this approach produces unusual equations for expected values and covariances. Like, the expected value for a product of three random correlated variables, whose solution includes the covariance between one variable and a product of two others variables. A formulation is developed and proposed to solve this problem. Monte Carlo Simulation (MCS) is used to validate the results obtained by these solutions. Numerical examples are analyzed for some different cases, which present good approximation as compared with MCS results.

Modelling Uncertainty in Mechanical Joint Parameters using Component Modal and Fuzzy Approaches

Built-up structures consist of substructures connected through mechanical joints such as spot welds, rivets, bolts, etc., whose physical properties (stiffness, damping, thickness, etc.) can vary significantly from one structure to another. Uncertainties in these parameters generate uncertainties in the dynamic behaviour of the structure and there is an interest in predicting the variability of the response given the variability of the joint parameters. In this paper, modelling and identification of a system consisting of two substructures connected by mechanical joints modelled by stiffness parameters is evaluated. Each substructure is modelled by a classical finite element method formulation and a modal solution obtained. The resulting modal solutions for the substructures are assembled in a Craig-Bampton component mode synthesis approach, which includes the joint parameters. The stiffness properties of the joints are described by fuzzy-valued parameters. Fuzzy-parameterized models are obtained using advanced fuzzy arithmetic based on the transformation method. Simulation results for this fuzzy model are obtained for different scenarios. Experimental results for a structure comprising two aluminum beams connected by steel wires are presented and compared with the simulated ones.

Flexural Wave Band Gaps in a 1D Phononic Crystal Beam

The forced response of flexural waves propagating in a 1D phononic crystal (PC) beam and its band structure are investigated theoretically and experimentally. PC beam unit cell is composed by steel and polyethylene. The study is performed by using six methods, finite element (FE), spectral element (SE), wave finite element (WFE), wave spectral element (WSE), conventional plane wave expansion (CPWE) and improved plane wave expansion (IPWE). Simulated examples of a 1D PC beam considering unit cells of different sizes are analyzed. Forced response results are presented in the form of displacement, transmittance and receptance, and the elastic band structure is investigated using its real and imaginary (attenuation) parts. Numerical and analytical results of all approaches are in a good agreement, except by WFE and FE numerical results in high frequencies. The effect of the amounts of polyethylene on the attenuation constant is studied. Depending on the application, choosing polyethylene quantity correctly is not simple, because it is related to the unit cell size and in which frequency the band gap is opened up. An experiment with a 1D PC beam is proposed and numerical and analytical results can localize the band gap position and width close to the experimental results. A small Bragg-type band gap with low attenuation is observed between 405 and 720 Hz. The 1D PC beam with unit cells of steel and polyethylene presents potential application for vibration control.

Passive Control of Noise Propagation in Tube Systems Using Bragg Scattering

Noise control in acoustic tube systems is a classical problem. The use of periodic geometries and resonators is also classic in acoustic filter design. The phononic approach to the problem is much more recent. Looking at this classic problem with a novel approach may lead to innovative solutions. This work investigates the band gaps created in acoustic pipe systems using axisymmetric finite element models, wave finite element models and experiments. Periodic geometry variations are investigated. The Floquet-Bloch theorem is used on a transfer matrix of the periodic cell rearranged from a dynamic stiffness matrix to obtain the dispersion diagrams that reveal the band gaps caused by Bragg scattering. Numerical predictions of the forced response obtained with the full finite element axisymmetric model of a duct system with five cells are compared with a wave finite element model and with experimental results.

Active Noise Control in a Y-Shaped Duct: Simulation and Experimental Results

There are different approaches to active noise control (ANC). The time domain Filtered-X LMS adaptive control scheme is currently used in most applications. The purpose of this paper is to describe an experiment consisting of a Y-shaped duct with two loudspeakers attached to the two branches of the Y duct. One of the loudspeakers acts as the perturbation source and the other acts as the control source. Tonal noise control is investigated, and control implementation issues such as number of filter weights, value of step-size parameter, and sampling frequency are discussed. The reference signal is taken from the signal sent to the perturbation loudspeaker and the error signal is taken from a microphone that can be placed anywhere along the stem of the Y-shaped duct. Simulations and experimental results are presented. The setup is simple and may be easily implemented for leaching purposes.