The band-gap properties of non-uniform periodic beams are analyzed using numerical and experimental methods. The flexural wave equations are established based on the Euler–Bernoulli and Timoshenko beam theories. The beams with periodically variable cross sections are investigated. The transfer matrix method is used to explore the dynamic behaviors of the periodic beams, that is, the natural frequencies of the finite periodic beams with different cross-section ratios between the adjacent sub-cells and the band-gaps of the infinite periodic beams based on the Bloch theory. The validity and accuracy of the band-gaps acquired by the present method are verified by comparing the results with those obtained from the finite element method and the vibration experiments. The effects of the different lengths of adjacent sub-cells on the band-gap properties are then investigated. The research results and conclusions should be useful in the study of vibration control applications.

A new kind of elastic metamaterial plate is designed to control the vibration and elastic wave propagation based on the band-gap mechanism. For the proposed elastic metamaterial plate, local resonant rods are periodically distributed between the two cover plates of the metamaterial plate structure. The dynamic stiffness matrix and the frequency response function of the structure under the time-harmonic excitation are obtained by the finite element and spectral element hybrid method (FE-SEHM). The experiment and simulation validations have been carried out. The effects of the material and structural parameters on the band-gap characteristics are analyzed. It is shown that the band-gaps can be computed more accurately and efficiently based on the FE-SEHM to avoid confusion between the pass-bands and band-gaps. Three band-gaps of the elastic metamaterial plate appear near the odd-order natural frequencies of the local resonant rods. Increasing the damping and mass of the local resonant rods results in the enlargement of the band-gap width, this enhances the capacity of the vibration reduction and sound isolation more effectively.