  Beam structure is one of the most widely used structures in mechanical
engineering and civil engineering. Ultrasonic guided wave based crack
identification is one of the most important and accepted approaches applied to
detect unseen small flaws in structures. Numerical simulations of ultrasonic
guided wave propagation have caught more and more attention due to the fast
development of hardware and software in the last few years. From all the
numerical simulation methods, wavelet based finite element method has been
proved to be one of the most efficient methods due to its better spatial
resolution, which means it needs fewer elements to get the same accuracy and it
can improve the calculation cost significantly. However, it needs a very small
time interval. Laplace transform can easily convert the time domain into a
frequency domain and then revert it back to a time domain. Laplace transform
has thus the advantage of finding better results with a very large time
interval. which can save a lot of time cost. This paper will present an
innovative method combining Laplace transform and the B-spline wavelet on
interval (BSWI) finite element method. This novel method allows to get results
with the same accuracy and with a significantly lower time cost, which would
not only decrease the total number of elements in the structure but also
increase the time integration interval. The numerical Laplace transform and
BSWI finite element will be introduced. Moreover, this innovative method is
applied to simulate the ultrasonic wave propagation in a beam structure in
different materials. Numerical examples for crack identification in beam
structures have been studied for verification.
