This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a high-order compact PRADI like method. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms.
In order to jointly identify the damage locations of superstructure and substructure of the piles-supported frame structures, a damage identification method based on vibration is proposed. Firstly, the high-efficiency modes which are sensitive to the damage of the piles-supported frame structures are determined. Then, the element modal strain energy difference functions of the corresponding high-efficiency modes are calculated before and after the damage, and finally the damage locations are identified by the average values of the absolute values of the wavelet transform coefficients of the element modal strain energy difference functions of high-efficiency modes. The effectiveness of the method is studied by numerical simulation. Numerical results show that the method can identify the damage location of the single damage or multiple damage of the piles-supported frame structures. Although the adjacent effect exists, the damage areas can be effectively located. At the same time, the method can effectively identify the damage locations of the hidden pile foundation.
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