Ultrafast Wave Finite Element Method for the computation of dispersion properties in periodic viscoelastic waveguides

Abstract In this work a procedure to compute the dispersion curves for one dimensional viscoelastic waveguides exploiting the finite element based global mass matrix and complex stiffness matrix is proposed. The global matrices of a finite length portion of the waveguide, the unit cell, are post-processed by enforcing Bloch-type boundary conditions along the wave propagation direction and next used to formulate a complex k(ω) quadratic eigenvalue problem. The roots of the eigenvalue problem at different frequency values ω yield in addition to the wavenumber (phase velocity) information also the attenuation dispersion curves for the waveguide. No finite element coding is needed since the global mass and stiffness matrix can be obtained from commercial FE software. To improve the computational efficiency a modal reduction scheme based on the Component Mode Synthesis method has been applied to reduce the dimension of the eigenvalue problem. As a result the computational time is enormously reduced without loss of accuracy in the complex roots calculation.