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Abstract:

Bone quantitative ultrasound (QUS) relies on the dispersion of guided waves propagating in the cortical shell of long bones. Analytical fluid–solid–fluid trilayer models obtain the dispersion relation from a characteristic determinant whose roots must be located numerically, a procedure that becomes delicate near mode osculations and for anisotropic cortical bone. Here the fluid–solid–fluid waveguide is reformulated as a linear generalized eigenvalue problem using a Chebyshev spectral-collocation method. Each layer is discretized on a Chebyshev–Gauss–Lobatto grid, and the interface and free-surface conditions are imposed directly by row replacement. For a prescribed wavenumber, the eigenvalue is W = ω², so every finite discrete eigenmode follows from a single generalized eigensolve without determinant root searching; the physical guided branches are then selected by explicit admissibility and participation criteria. The method is validated against an independently implemented analytical global-matrix solver for a water/aluminum/water trilayer: the fundamental extensional (S₀) and flexural (A₀) phase velocities agree within numerical tolerance (better than 10⁻⁵ %), and a convergence study with eigen-residual norms confirms spectral accuracy at about fourteen collocation nodes per layer. The same framework is then extended to a transversely isotropic cortical-bone layer and, with one additional volume-fraction field, to a linear elastic material with voids. Transverse isotropy raises the low-frequency extensional plateau by about 8.2 %, whereas increasing void coupling lowers it by up to 15 %. A Hellmann–Feynman sensitivity analysis shows that this plateau constrains only one stiffness combination, so these figures are forward-model discrepancies rather than uniquely recoverable inverse biases.

Keywords:

guided waves; cortical bone; quantitative ultrasound; spectral collocation; transverse isotropy; elastic materials with voids,

References:

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Abstract:

With the rapid increase of the societal requirements and the complexity of the industrial systems there is a great need to achieve high reliability without losing profitability. Small system failures might lead to huge loss of operational activities, downtimes and low productivity. In this paper, the authors propose a stochastic reliability model to analyze the availability and profitability of an industrial system under environmental factors and fluctuating demand. The proposed model assumes that it is a single unit system where there are no failures that can be tolerated. It is also equipped with an inspection mechanism to identify the kind of failure occurring in the system. The failures are called minor and major failures.Minor failures are caused by lubrication or greasing problems which can be repaired and major failures are caused by electrical short circuiting, water ingestion in the time of adverse weather and overloading as well as prolonged continuous operation . In case of major failures the system is either repaired or replaced depending upon the extent of damage. The two operating cases are studied where the demand is higher than or equal to the production and the demand is lower than the production. The regenerative point technique and Semi-Markov processes are used to evaluate key performance measures and profit thoroughly with respect to the effects of different parameters of the system.Data has been collected from a steel manufacturing plant, Rajpura, Punjab, India.The outcomes are very informative for the visited plant and provide suggestions for best management of inspection, maintenance, and operational strategies.

Keywords:

Reliability,Inspection,Variation in demand,Regenerative point technique,Semi-Markov process,Innovation.,

References:

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