Study on the convergence of plane wave expansion method in calculation the band structure of one-dimensional typical phononic crystal

We study the convergence of plane wave expansion method (PWEM) while calculating the band structure of one-dimensional typical phononic crystals by taking the example of Euler-Bernoulli beam. The both algebraic formats of the conventional and improved PWEM (CPWEM and IPWEM) were derived from the dynamic differential equation. The convergence of the PWEM was analyzed through the low and high eigen-frequencies of highly symmetric points. The numerical experiment shows that the IPWEM has better convergence, which is very efficient to calculate the band structure of one-dimensional typical phononic crystal systems of large elastic mismatch in searching for large band gaps.