Dynamic characteristics of infinite-length and finite-length rods with high-wave-number periodic parameters:

The dynamic characteristics of the infinite-length and finite-length rods with periodic distribution parameters are studied. The differential equation of longitudinal motion of the period-parametric rod is given. The algebraic matrix equation for the wave motion characteristics of the infinite-length periodic rod is derived based on the Bloch theorem and Fourier series. The characteristic frequencies are determined by the matrix eigenvalues which depend on the characteristic wave number and parametric wave number. Then the algebraic matrix equation for the dynamic characteristics of the finite-length periodic rod is derived based on the Galerkin method. The natural frequencies are determined by the matrix eigenvalues which depend on only the parametric wave number. An improving approach algorithm for solving the eigenvalue problem of high degree-of-freedom systems is developed based on the Rayleigh quotient. Finally, the circular cross-section rod with period-varying diameter is considered and numerical r...