Free and forced propagation of Bloch waves in viscoelastic beam lattices

Beam lattice materials can be characterized by a periodic microstructure realizing a geometrically regular pattern of elementary cells. Within this framework, governing the free and forced wave propagation by means of spectral design techniques and/or energy dissipation mechanisms is a major issue of theoretical interest with applications in aerospace, chemical, naval, biomedical engineering. The first part of the Thesis addresses the free propagation of Bloch waves in non-dissipative microstructured cellular materials. Focus is on the alternative formulations suited to describe the wave propagation in the bidimensional infinite material domain, according to the classic canons of linear solid or structural mechanics. Adopting the centrosymmetric tetrachiral cell as prototypical periodic topology, the frequency dispersion spectrum is obtained by applying the Floquet-Bloch theory. The dispersion spectrum resulting from a synthetic Lagrangian beam lattice formulation is compared with its counterpart derived from different continuous models (high-fidelity first-order heterogeneous and equivalent homogenized micropolar continua). Asymptotic perturbation-based approximations and numerical spectral solutions are compared and cross-validated. Adopting the low-frequency band gaps of the dispersion spectrum as functional targets, parametric analyses are carried out to highlight the descriptive limits of the synthetic models and to explore the enlarged parameter space described by high-fidelity models. The microstructural design or tuning of the mechanical properties of the cellular microstructure is employed to successfully verify the wave filtering functionality of the tetrachiral material. Alternatively, band gaps in the material spectrum can be opened at target center frequencies by using metamaterials with inertial resonators. Based on these motivations, in the second part of the Thesis, a general dynamic formulation is presented for determining the dispersion properties of viscoelastic metamaterials, equipped with local dissipative resonators. The linear mechanism of local resonance is realized by tuning periodic auxiliary masses, viscoelastically coupled with the beam lattice microstructure. As peculiar aspect, the viscoelastic coupling is derived by a mechanical formulation based on the Boltzmann superposition integral, whose kernel is approximated by a Prony series. Consequently, the free propagation of damped Bloch waves is governed by a linear homogeneous system of integro-differential equations of motion. Therefore, differential equations of motion with frequency-dependent coefficients are obtained by applying the bilateral Laplace transform. The corresponding complex-valued branches characterizing the dispersion spectrum are determined and parametrically analyzed. Particularly, the spectra corresponding to Taylor series approximations of the equation coefficients are investigated. The standard dynamic equations with linear viscous damping are recovered at the first order approximation. Increasing approximation orders determine non-negligible spectral effects, including the occurrence of pure damping spectral branches. Finally, the forced response to harmonic single frequency external forces in the frequency and the time domains is investigated. The response in the time domain is obtained by applying the inverse bilateral Laplace transform. The metamaterial responses to non-resonant, resonant and quasi-resonant external forces are compared and discussed from a qualitative and quantitative viewpoint

Analytical and computational methods for modeling mechanical filters against Bloch wave propagation

The free propagation of elastic waves through periodic microstructured materials can be studied by the analytical formulation of beam lattice models for the elementary cell, in combination with the Floquet-Bloch theory. Within this framework, the present paper deals with periodic tetrachiral materials characterized by a monoatomic cell. Alternative analytical formulations can be developed by continualization-homogenization techniques in micropolar equivalent continua, characterized by overall elastic and inertial tensors. Valid approaches for the solution of the wave propagation problems are offered by perturbation methods, numerical continuation techniques, and \u2013 finally \u2013 computational analyses, suited to account for some mechanical updates or improvements that can hardly be included in synthetic formulations. Based on these considerations, the dispersion curves achievable by different formulations are compared and discussed. The major interest is focused on the spectral effects determined by changes in the geometry, inertia, elasticity of the microstructural elements and, finally, by variations in the cellular symmetry. Some attention is paid to the parameter combinations, which might open band gaps in the low-frequency range, useful to filter undesired dynamic signals for vibration shielding purposes

INTERLEUKIN 6 PLASMA LEVELS PREDICT WITH HIGH SENSITIVITY AND SPECIFICITY CORONARY STENOSIS DETECTED BY CORONARY ANGIOGRAPHY

In recent years new biomarkers able to measure the coronary atherosclerotic burden have been investigated. The aim of the present study was: i) to measure plasma levels of four biomarkers: C reactive protein (CRP), soluble intercellular adhesion molecule-1 (sICAM-1), interleukin 6 (IL-6), 8-isosprostane (8-ISO), in a series of patients undergoing coronary angiography; ii) to assess the power of the biomarkers to predict critical coronary stenosis detected by angiography. The study population consisted of a group of 438 subjects undergoing coronary angiography; 160 patients with 0, 1, 2, or 3 critical vessels were selected, and biomarkers plasma levels were measured in plasma samples obtained before the procedure. The most predictive biomarker was then assayed in 120 patients with critical stenosis and 120 unmatched patients without stenosis. CRP, sICAM-1, IL-6 and 8-ISO plasma levels increased with the number of diseased vessels. All biomarkers were good predictors of critical stenosis (receiver-operator-curve [ROC] areas; CRP = 0.880, IL-6 = 0.936, sICAM-1 = 0.907, 8-ISO = 0.873). IL-6 was confirmed in an expanded sample of 240 subjects to be the best predictor with a ROC area = 0.959. With a threshold of 3.6 ng/l, a 100% sensitivity (120/120) and a 90% specificity (108/120) was observed. In conclusion, IL-6, sICAM-1, CRP and 8-ISO are predictive of CAD. IL-6 predicts critical coronary stenosis with the highest sensitivity and specificity