Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method

Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.     

Hyperplane Sections of Grassmannians and the Number of MDS Linear Codes

We obtain some effective lower and upper bounds for the number of (n,k)-MDS linear codes over _q. As a consequence, one obtains an asymptotic formula for this number. These results also apply for the number of inequivalent representations over _q of the uniform matroid or, alternately, the number of _q-rational points of certain open strata of Grassmannians. The techniques used in the determination of bounds for the number of MDS codes are applied to deduce several geometric properties of certain sections of Grassmannians by coordinate hyperplanes.     

Pairing of α-Fused BODIPY: Towards Panchromatic n-Type Semiconducting Materials

A chemical strategy to efficiently perform the dimerization of α-fused boron-dipyrromethene (BODIPY) is reported. The straightforward synthesis of one of these dimers is described and its properties have been investigated through UV/Vis spectroscopy, cyclic voltammetry, differential scanning calorimetry, and charge-carrier mobility measurements by using organic field-effect transistors and space–charge-limited current diodes. The results allow a chemical strategy to decrease the tendency of α-fused BODIPY to crystallize, to increase its light-harvesting properties, and to promote isotropic charge carriers transport. Moreover, the disclosed approach is also a way to maintain the deep LUMO level of α-fused BODIPY; thus making this class of materials highly desirable for optoelectronic applications.     

A General One-Pot Methodology for the Preparation of Mono- and Bimetallic Nanoparticles Supported on Carbon Nanotubes: Application in the Semi-hydrogenation of Alkynes and Acetylene

A facile and straightforward methodology for the preparation of monometallic (copper and palladium) and bimetallic nanocatalysts (NiCu and PdCu) stabilized by a N-heterocyclic carbene ligand is reported. Both colloidal and supported nanoparticles (NPs) on carbon nanotubes (CNTs) were prepared in a one-pot synthesis with outstanding control on their size, morphology and composition. These catalysts were evaluated in the selective hydrogenation of alkynes and alkynols. PdCu/CNTs revealed an efficient catalytic system providing high selectivity in the hydrogenation of terminal and internal alkynes. Moreover, this catalyst was tested in the semi-hydrogenation of acetylene in industrially relevant acetylene/ethylene-rich model gas feeds and showed excellent stability even after 40 h of reaction.     

Impact of the Structural Changes on the Fracture Behavior of Naturally Weathered Low-Density Polyethylene (LDPE) Films

Weathering of LDPE films was performed in a sub-Saharan facility in Laghouat, Algeria. Ageing led to a rapid change of the physicochemical properties resulting from the alteration of the material's microstructure. XRD revealed the progressive increase of the crystallinity ratio and the thickness of the crystalline lamellae as well. SEM revealed the presence of white particles, which look like crystalline phase emerging from the surface of the film. The oxidation and crystallinity varied according to a concentration gradient across the thickness. The impact of the microstructural changes on the mechanical properties was highlighted based on the essential work of fracture (EWF) method. There was a progressive decrease of the total energy of fracture and a lowering of the net stress (σ_net) and the (β_wp) term. Nevertheless, this loss of the mechanical properties was characterized by a rapid transition from a ductile mode of failure to a very brittle mode.     

Unraveling the Composition of Rembrandt's Impasto through the Identification of Unusual Plumbonacrite by Multimodal X‐ray Diffraction Analysis

Rembrandt (1606–1669) is renowned for his impasto technique, involving his use of lead white paint with outstanding rheological properties. This paint was obtained by combining lead white pigment (a mixture of cerussite PbCO₃ and hydrocerussite Pb₃(CO₃)₂(OH)₂) with an organic binding medium, but the exact formulation used by Rembrandt remains a mystery. A powerful combination of high‐angle and high‐lateral resolution x‐ray diffraction was used to investigate several microscopic paint samples from four Rembrandt masterpieces. A rare lead compound, plumbonacrite (Pb₅(CO₃)₃O(OH)₂), was detected in areas of impasto. This can be considered a fingerprint of Rembrandt's recipe and is evidence of the use of an alkaline binding medium, which sheds a new light on Rembrandt's pictorial technique.     

A note on the derivation of rigid-plastic models

This note is devoted to a rigorous derivation of rigid-plasticity as the limit of elasto-plasticity when the elasticity tends to infinity.