Because the dimensions of the mass and stiffness matrices will become very large if the structure is meshed with a number of small elements, we introduce the symplectic solution method to overcome the above difficulties of solving the eigenvalue problem.  Excellent agreement is obtained between the results obtained by the symplectic solution method and numerical simulations. 
the symplectic solution method
Excellent agreement is obtained between the results obtained by the symplectic solution method and numerical simulations.  The measured transmission coefficients in lattices with different geometrical parameters and slenderness ratios are in good agreement with the numerical simulations. 
numerical simulations