Model updating of the non-linear vibrating structures through Volterra series and proper orthogonal decomposition

Classical procedures for model updating in non-linear mechanical systems based on vibration data can fail because the common linear metrics are not sensitive for non-linear behavior caused by gaps, backlash, bolts, joints, materials, etc. Several strategies were proposed in the literature in order to allow a correct representative model of non-linear structures. The present paper evaluates the performance of two approaches based on different objective functions. The first one is a time domain methodology based on the proper orthogonal decomposition constructed from the output time histories. The second approach uses objective functions with multiples convolutions described by the first and second order discrete-time Volterra kernels. In order to discuss the results, a benchmark of a clamped-clamped beam with an pre-applied static load is simulated and updated using proper orthogonal decomposition and Volterra Series. The comparisons and discussions of the results show the practical applicability and drawbacks of both approaches.

Screening of Conditions for the Preparation of Poly( -Caprolactone) Nanocapsules Containing the Local Anesthetic Articaine

The local anesthetic articaine (ATC) is widely used in dentistry; however, its side effects can include paresthesia and nerve injury. Polymeric nanocapsules (PN) can be used as carriers for drugs, and help to reduce undesirable symptoms. The objective of this study was to evaluate the influence of different factors on the average size, polydispersion, and encapsulation efficiency of PN containing ATC. Poly(ε-caprolactone) (PCL) nanocapsules containing ATC were prepared by the oil-in-water emulsion/solvent evaporation method. The final ATC concentration was 2%. The preparation conditions were optimized using a central composite blocked cube-star design to investigate the influence of two variables at five levels, with 22 factorial points (–1 and +1), two replicates of the central point, 2×2 axial points (–1.414 and +1.414), and an orthogonal distribution, resulting in 10 experiments. The factors varied were the PVA concentration and the sonication time. The nanocapsules showed a satisfactory size range, a polydispersivity index less than 0.2, and high encapsulation efficiency. The values of the factors had no significant influence on either average size or polydispersion, although the encapsulation efficiency was significantly influenced by the sonication time. Improved formulations were identified using the central composite design, which revealed that the main consideration in selecting a suitable formulation was the encapsulation efficiency. Two of the formulations showed both high encapsulation efficiency and colloidal characteristics appropriate for the route of administration.

Para-orthogonal polynomials from constant Verblunsky coefficients

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