Drop impacts are difficult to characterize due to their transient, non-stationary nature. We discuss the force generated during such impacts, a key quantity for animals, plants, roofs or soil erosion. Although a millimetric drop has a modest weight, it can generate collision forces on the order of thousand times this weight. We measure and discuss this amplification, considering natural parameters such as drop radius and density, impact speed and response time of the substrate. We finally imagine two kinds of devices allowing us to deduce the size of the raindrop from impact forces.

No abstract

Man-made slender structures are known to be sensitive to high levels of vibration, due to their flexibility, which often cause irreversible damage. In nature, trees repeatedly endure large amplitudes of motion, mostly caused by strong climatic events, yet with minor or no damage in most cases. A new damping mechanism inspired by the architecture of trees is here identified and characterized in the simplest tree-like structure, a Y-shape branched structure. Through analytical and numerical analyses of a simple two-degree-of-freedom model, branching is shown to be the key ingredient in this protective mechanism that we call damping-by-branching. It originates in the geometrical nonlinearities so that it is specifically efficient to damp out large amplitudes of motion. A more realistic model, using flexible beam approximation, shows that the mechanism is robust. Finally, two bioinspired architectures are analyzed, showing significant levels of damping achieved via branching with typically 30% of the energy being dissipated in one oscillation. This concept of damping-bybranching is of simple practical use in the design of slender flexible structures.

Research highlights: - Nonlinearity characterization of a structure independently from its exciting device. - Experimental modal identification, including damping, in the mid-frequency range. - Boundary conditions, low-and high-frequency regimes clarified in the piano soundboard. - Good match between experimental observations and FEM results at low frequencies. - FEM of a non-regularly ribbed soundboard reveals high-frequency localization in piano.International audienceThe piano soundboard transforms the string vibration into sound and therefore, its vibrations are of primary importance for the sound characteristics of the instrument. An original vibro-acoustical method is presented to isolate the soundboard nonlinearity from that of the exciting device (here: a loudspeaker) and to measure it. The nonlinear part of the soundboard response to an external excitation is quantitatively estimated for the first time, at ≈ -40 dB below the linear part at the ff nuance. Given this essentially linear response, a modal identification is performed up to 3 kHz by means of a novel high resolution modal analysis technique (Ege et al., High-resolution modal analysis, JSV, 325(4-5), 2009). Modal dampings (which, so far, were unknown for the piano in this frequency range) are determined in the midfrequency domain where FFT-based methods fail to evaluate them with an acceptable precision. They turn out to be close to those imposed by wood. A finite-element modelling of the soundboard is also presented. The low-order modal shapes and the comparison between the corresponding experimental and numerical modal frequencies suggest that the boundary conditions can be considered as blocked, except at very low frequencies. The frequency-dependency of the modal density and the observation of modal shapes reveal two well-separated regimes. Below ≈ 1 kHz, the soundboard vibrates more or less like a homogeneous plate. Above that limit, the structural waves are confined by ribs, as already noticed by several authors, and localised in restricted areas (one or a few inter-rib spaces), presumably due to a slightly irregular spacing of the ribs across the soundboard