Symplectic method for calculation of band gap of one-dimensional phononic crystals

The unit cell of one-dimensional phononic crystal was reduced to a spring-mass structure with limited number of degrees of freedom. The lattice vibrations were investigated in agreement with the dual variables system, and the dispersion relation was obtained by the symplectic mathematical method. Furthermore, the eigenfrequency was given by using the Wittrick-Williams algorithm, thus the band gap was obtained. Comparing the results calculated by the present method with those by the traditional lumped-mass method, it is obvious that there is a good agreement. However, the former is capable of improving the calculation accuracy and computational efficiency, and more importantly, is of better convergence.