  Numerical simulation of ultrasonic wave propagation provides an efficient
tool for crack identification in structures, while it requires a high
resolution and expensive time calculation cost in both time integration and
spatial discretization. Wavelet finite element model provides a highorder
finite element model and gives a higher accuracy on spatial discretization,
B-Spline wavelet interval (BSWI) has been proved to be one of the most commonly
used wavelet finite element model with the advantage of getting the same
accuracy but with fewer element so that the calculation cost is much lower than
traditional finite element method and other high-order element methods. Precise
Integration Method provides a higher resolution in time integration and has
been proved to be a stable time integration method with a much lower cut-off
error for same and even smaller time step. In this paper, a wavelet finite
element model combined with precise integration method is presented for the
numerical simulation of ultrasonic wave propagation and crack identification in
1D structures. Firstly, the wavelet finite element based on BSWI is constructed
for rod and beam structures. Then Precise Integrated Method is introduced with
application for the wave propagation in 1D structures. Finally, numerical
examples of ultrasonic wave propagation in rod and beam structures are
conducted for verification. Moreover, crack identification in both rod and beam
structures are studied based on the new model.
