This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations converge to the strong solution of the viscous or inviscid incompressible magnetohydrodynamic equations as long as the latter exists both for the well-prepared initial data and general initial data. Furthermore, the convergence rates are also obtained in the case of the well-prepared initial data.

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The three-dimensional compressible magnetohydrodynamic equation in the whole space are studied in this paper. The global classical solution is established when the initial data are small perturbations of some given constant state. Moreover, the optimal decay rate of the solution is also obtained.

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With the objective of improving the temperature stability of the quantitative comparison of Lamb wave signals captured in different states, a damage diagnostic imaging algorithm integrated with Shannon-entropy-based interrogation was proposed. It was evaluated experimentally by identifying surface damage in a stiffener-reinforced CF/EP quasi-isotropic woven laminate. The variations in Shannon entropy of the reference (without damage) and present (with damage) signals from individual sensing paths were calibrated as damage signatures and utilized to estimate the probability of the presence of damage in the monitoring area enclosed by an active sensor network. The effects of temperature change on calibration of the damage signatures and estimation of the probability values for the presence of damage were investigated using a set of desynchronized signals. The results demonstrate that the Shannon-entropy-based damage diagnostic imaging algorithm with improved robustness in the presence of temperature change has the capability of providing accurate identification of damage in actual environments.