Early damage detection on structures plays a very important role for ensuring safety and reliability. This paper provides an efficient method based on wavelet transforms in order to detect and localize damage on structures subjected to moving loads such as beams and bridges. A numerical model based on the experimental test-rig utilized in this study is developed by using a finite element commercial software. Different types of damage on the bridge of the numerical model are simulated and transient analyses are performed by incorporating a load which moves constantly along the beam nodes. Continuous wavelet transform diagrams using the vertical acceleration responses show that damage can be identified and localized even with significant percentages of noise. Nevertheless, the method is improved by filtering the signals, removing the border effects, and calculating the total wavelet energy of the beam from the coefficients along the selected range of scales. Thus, the accumulation of wavelet energy could indicate the presence of damage. Finally, laboratory experiments are conducted to validate this work and a good agreement between numerical and experimental results is obtained.

We consider the linearized elasticity system in a multidomain of ${\bf R}^3$ . This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius $r^{\varepsilon}$ . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and $r^{\varepsilon}$ tend to zero simultaneously, with $r^{\varepsilon}\gg\varepsilon^2$ , we identify the limit problem. This limit problem involves six junction conditions.

Between the accelerator and fusion chamber, the heavy ion beams are subject to a dramatic but vital series of manipulations, some of which are carried out simultaneously and involve large space charge forces. The beams' quality must be maintained at a level sufficient for the fusion application; this general requirement significantly impacts beam line design, especially in the considerations of momentum dispersion. Immediately prior to final focus onto a fusion target, heavy ion driver beams are compressed in length by typically an order of magnitude. This process is simultaneous with bending through large angles to achieve the required target illumination configuration. The large increase in beam current is accommodated by a combination of decreased lattice period, increased beam radius, and increased strength of the beamline quadrupoles. However, the large head-to-tail momentum tilt (up to 5%) needed to compress the pulse results in a very significant dispersion of the pulse centroid from the design axis. General design features are discussed. A principal design goal is to minimize the magnitude of the dispersion while maintaining approximate first order achromaticity through the complete compression/bend system. Configurations of bends and quadrupoles, which achieve this goal while simultaneously maintaining a locally matched beam-envelope, are analyzed.

We consider a dynamical one-dimensional nonlinear von Kármán model for beamsdepending on a parameter ε > 0 and studyits asymptotic behavior for t large, as ε → 0. Introducing appropriate dampingmechanisms we show that the energy of solutionsof the corresponding damped models decayexponentially uniformly with respect to theparameter ε. In order for this to be true thedamping mechanism has to have the appropriatescale with respect to ε. In the limit as ε → 0 we obtain damped Berger–Timoshenko beam modelsfor which the energy tends to zero exponentiallyas well. This is done both in the case ofinternal and boundary damping. We address the sameproblem for plates with internal damping.