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Numerical simulation of ultrasonic wave propagation provides an efficienttool for crack identification in structures, while it requires a highresolution and expensive time calculation cost in both time integration andspatial discretization. Wavelet finite element model provides a highorderfinite element model and gives a higher accuracy on spatial discretization,B-Spline wavelet interval (BSWI) has been proved to be one of the most commonlyused wavelet finite element model with the advantage of getting the sameaccuracy but with fewer element so that the calculation cost is much lower thantraditional finite element method and other high-order element methods. PreciseIntegration Method provides a higher resolution in time integration and hasbeen proved to be a stable time integration method with a much lower cut-offerror for same and even smaller time step. In this paper, a wavelet finiteelement model combined with precise integration method is presented for thenumerical simulation of ultrasonic wave propagation and crack identification in1D structures. Firstly, the wavelet finite element based on BSWI is constructedfor rod and beam structures. Then Precise Integrated Method is introduced withapplication for the wave propagation in 1D structures. Finally, numericalexamples of ultrasonic wave propagation in rod and beam structures areconducted for verification. Moreover, crack identification in both rod and beamstructures are studied based on the new model.

Wave analysis in one dimensional structures with a wavelet finite element model and precise integration method